المراجعة النهائية ومراجعة ليلة الامتحان فى الميكانيكا

1. ‫اﻻﺳﺘﺎﺗﯿﻜﺎ‬ ‫ﻋﻠﻰ‬ ‫ﺷﺎﻣﻠﺔ‬ ‫ﻣﺮاﺟﻌﺔ‬
‫ﺷﺎﻣﻠﺔ‬ ‫ﻣﺮاﺟﻌﺔ‬

2. ‫اﻻﺳﺘﺎﺗﯿﻜﺎ‬ ‫ﻋﻠﻰ‬ ‫ﺷﺎﻣﻠﺔ‬ ‫ﻣﺮاﺟﻌﺔ‬
: ‫اﻷول‬ ‫اﻟﺴﺆال‬
)١‫ﻣﻘﺪارھﻤﺎ‬ ‫(ﻗﻮﺗﺎن‬٤‫ﺑﯿﻨﮭﻤﺎ‬ ‫واﻟﺰاوﯾﺔ‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺆﺛﺮان‬ ‫ﻧﯿﻮﺗﻦ‬ ‫ق‬ ،١٣٥ْ‫اﺗﺠﺎه‬ ‫ﻛﺎن‬ ‫إذا‬‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬
‫ﺑﺰاوﯾﺔ‬ ‫ﯾﻤﯿﻞ‬٤٥ْ‫ق‬ ‫أوﺟﺪ‬ ‫ق‬ ‫اﻟﻘﻮة‬ ‫ﻋﻠﻰ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٢‫ق‬ ‫اﻟﻘﻮﺗﺎن‬ (١=٥‫س‬–٤‫ق‬ ، ‫ص‬٢‫س‬ =–٤‫ﺧﻂ‬ ‫أن‬ ‫أﺛﺒﺖ‬ ‫اﻷﺻﻞ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺗﺆﺛﺮان‬ ‫ص‬‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬ ‫ﻋﻤﻞ‬
) = ‫أ‬ ‫ﺑﺎﻟﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬-٣،٤) = ‫ب‬ ‫ﻟﻠﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻤﺤﺼﻠﺔ‬ ‫ﻋﺰم‬ ‫ﻣﺘﺠﮫ‬ ‫أوﺟﺪ‬ ‫ﺛﻢ‬ (٢،-٥(
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٣‫ق‬ ، ‫ق‬ ‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻗﻮﺗﺎن‬ (]٣/ ‫ﺢ‬‫ﺧ‬‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺆﺛﺮان‬ ‫ﻧﯿﻮﺗﻦ‬٠‫ﯾﺴﺎوى‬ ‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬ ‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬٢‫ق‬
‫اﻟﻘﻮﺗﯿﻦ‬ ‫ھﺎﺗﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﻗﯿﺎس‬ ‫ﻓﺄوﺟﺪ‬ ‫ﻧﯿﻮﺗﻦ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
.....................................................................................................................................................................................................................
)٤‫اﻟﻘ‬ ‫ﺗﺆﺛﺮ‬ () = ‫أ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺛﺎﺑﺘﯿﻦ‬ ‫ن‬ ، ‫م‬ ‫ﺣﯿﺚ‬ ‫ص‬ ‫ن‬ + ‫س‬ ‫م‬ = ‫ق‬ ‫ﻮة‬٤،٢‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻋﺰﻣﮭﻤﺎ‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ (
) = ‫و‬ ‫اﻷﺻﻞ‬ ‫ﻟﻨﻘﻄﺔ‬٠،٠‫ﯾﺴﺎوى‬ (-١٥) = ‫ب‬ ‫ﻟﻠﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫وﻋﺰﻣﮭﻤﺎ‬ ، ‫ع‬٠،٥‫ﯾﺴﺎوى‬ (١٥‫ﻓﺄوﺟﺪ‬ ‫ع‬
‫ن‬ ، ‫م‬ ‫ﻗﯿﻤﺘﻰ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

3. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٢
)٥‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻗﻮﺗﺎن‬ (٨‫اﻟﺰا‬ ‫وﻗﯿﺎس‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺆﺛﺮان‬ ‫ﻧﯿﻮﺗﻦ‬ ‫ق‬ ،‫ﺑﯿﻨﮭﻤﺎ‬ ‫وﯾﺔ‬١٢٠ْ‫ﻛﺎﻧﺖ‬ ‫ﻓﺈذا‬
‫اﻟﻘﻮﺗﯿﻦ‬ ‫ھﺎﺗﯿﻦ‬ ‫وﻣﺤﺼﻠﺘﺔ‬ ‫ق‬ ‫ﻗﯿﻤﺔ‬ ‫ﻓﺄوﺟﺪ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻘﻮة‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدﯾﺔ‬ ‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٦(‫ق‬ ‫اﻟﻘﻮى‬ ‫ﺗﺆﺛﺮ‬١+‫س‬ =٦‫ق‬ ، ‫ص‬٢=٣+ ‫س‬٥‫ق‬ ، ‫ص‬٣) = ‫أ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫+ص‬ ‫س‬ =٢،٣(٠‫أوﺟﺪ‬
) = ‫ب‬ ‫ﻟﻠﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻘﻮى‬ ‫ھﺬه‬ ‫ﻣﺤﺼﻠﺔ‬ ‫ﻋﺰم‬ ‫ﻣﺘﺠﮫ‬-١،٢‫اﻟﻌﻤﻮد‬ ‫طﻮل‬ ‫أوﺟﺪ‬ ‫ﺛﻢ‬ (‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺮﺳﻮم‬
‫اﻟﻤﺤﺼﻠﺔ‬ ‫ﻋﻤﻞ‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٧‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻗﻮﺗﺎن‬ (١٦‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺰاوﯾﺔ‬ ‫وﻗﯿﺎس‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺆﺛﺮان‬ ‫ﻧﯿﻮﺗﻦ‬ ‫ق‬ ،١٢٠ْ‫ﻛﺎﻧﺖ‬ ‫ﻓﺈذا‬
‫اﻟﻘﻮة‬ ‫ﻋﻠﻰ‬ ‫ﺗﻤﯿﻞ‬ ‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬١٦‫ﻧﯿﻮﺗﻦ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬٣٠ْ‫اﻟﻘﻮﺗﯿﻦ‬ ‫ﻣﺤﺼﻠﺔ‬ ‫وﻣﻘﺪار‬ ‫ق‬ ‫ﻗﯿﻤﺔ‬ ‫أوﺟﺪ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٨‫اﻟﻤﺴﺘﻮﯾ‬ ‫اﻟﻘﻮى‬ ‫ﺗﺆﺛﺮ‬ (‫ﻣﻘﺎدﯾﺮھﺎ‬ ‫اﻟﺘﻰ‬ ‫ﺔ‬٢،٤،٦،٨]٣/ ‫ﺢ‬‫ﺧ‬‫ﺑﯿﻦ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﻗﯿﺎس‬ ‫وﻛﺎن‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﻧﯿﻮﺗﻦ‬
‫واﻟﺜﺎﻧﯿﺔ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻘﻮة‬٦٠ْ‫واﻟﺜﺎﻟﺜﺔ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫وﺑﯿﻦ‬ ،٦٠ْ‫واﻟﺮاﺑﻌﺔ‬ ‫اﻟﺜﺎﻟﺜﺔ‬ ‫وﺑﯿﻦ‬٩٠ْ‫اﻟﻤﺤﺼﻠﺔ‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬
‫اﻷوﻟﻰ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻊ‬ ‫اﻟﻤﺤﺼﻠﺔ‬ ‫ﺗﺼﻨﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺰاوﯾﺔ‬ ‫وﻗﯿﺎس‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

4. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٣
)٩(‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻗﻮﺗﺎن‬ ‫أﺛﺮت‬٢، ‫ق‬]۲‫ﺢ‬‫ﺧ‬/٤‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺰاوﯾﺔ‬ ‫وﻗﯿﺎس‬ ‫ﻛﺠﻢ‬ ‫ث‬١٣٥ْ‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬
‫ﻣ‬‫ﯾﺴﺎوى‬ ‫ﺤﺼﻠﺘﮭﻤﺎ‬٢‫ق‬ ‫ﻗﯿﻤﺔ‬ ‫ﻓﺄوﺟﺪ‬ ‫ﻛﺠﻢ‬ ‫ث‬ ‫ق‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)١٠‫س‬ = ‫ق‬ ‫اﻟﻘﻮة‬ ‫ﺗﺆﺛﺮ‬ (–) = ‫أ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ص‬٠،٣) ‫ھﻰ‬ ‫د‬ ، ‫ﺟـ‬ ، ‫ب‬ ‫اﻟﻨﻘﻂ‬ ‫وﻛﺎﻧﺖ‬ (٣،٠) ، (٤،٣، (
)-٢،١‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ (٠‫د‬ ‫ﺟـ‬ ‫وﯾﻨﺼﻒ‬ ‫ﺟـ‬ ‫ﺑﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬ ‫ق‬ ‫ﻋﻤﻞ‬ ‫ﺧﻂ‬ ‫أن‬ ‫أﺛﺒﺖ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)١١(‫س‬ ‫م‬ = ‫ق‬ ‫اﻟﻘﻮة‬–٣= ‫أ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺗﺆﺛﺮ‬ ‫ص‬)٢،-٣‫ﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻘﻮة‬ ‫ھﺬه‬ ‫ﻋﺰم‬ ‫اﻧﻌﺪم‬ ‫إذا‬ (
) = ‫و‬ ‫اﻷﺻﻞ‬٠،٠‫م‬ ‫اﻟﺜﺎﺑﺖ‬ ‫ﻗﯿﻤﺔ‬ ‫ﻓﺄوﺟﺪ‬ (
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)١٢‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻗﻮﺗﺎن‬ (١٢،١٥‫ﯾﺴﺎوى‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺰاوﯾﺔ‬ ‫وظﻞ‬ ‫ﻣﺎدﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺆﺛﺮان‬ ‫ﻧﯿﻮﺗﻦ‬-‫؛‬#٤‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬
‫اﻷوﻟﻰ‬ ‫اﻟﻘﻮة‬ ‫ﻋﻠﻰ‬ ‫ﻣﯿﻠﮭﺎ‬ ‫زاوﯾﺔ‬ ‫وﻗﯿﺎس‬ ‫ﻣﺤﺼﻠﺘﮭﻤﺎ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
....................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

5. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٤
: ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺴﺆال‬
)١‫وزﻧﮫ‬ ‫ﺟﺴﻢ‬ ‫(وﺿﻊ‬٩٠‫ﻗﯿﺎﺳﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻷﻓﻘﻰ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ‫أﻣﻠﺲ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫ﺟﻢ‬ ‫ث‬٣٠ْ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﻔﻆ‬ ‫إذا‬
‫ﺑﻮاﺳﻄﺔ‬ ‫ﺗﻮازن‬ ‫ﺣﺎﻟﺔ‬‫ﻓﻌﻞ‬ ‫ورد‬ ‫اﻟﻘﻮة‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬ ، ‫أﻋﻠﻰ‬ ‫إﻟﻰ‬ ‫ﻟﻠﻤﺴﺘﻮى‬ ‫ﻣﯿﻞ‬ ‫أﻛﺒﺮ‬ ‫ﺧﻂ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﺗﻌﻤﻞ‬ ‫ﻗﻮة‬
‫اﻟﺠﺴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮى‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٢‫طﻮﻟﮫ‬ ‫ﻗﻀﯿﺐ‬ ‫ب‬ ‫أ‬ (٥٠‫ووزﻧﮫ‬ ‫ﺳﻢ‬٢٠‫ﻣﻔﺼﻞ‬ ‫ﺣﻮل‬ ‫رأﺳﻰ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻰ‬ ‫ﯾﺘﺤﺮك‬ ، ‫ﻣﻨﺘﺼﻔﮫ‬ ‫ﻓﻰ‬ ‫ﯾﺆﺛﺮ‬ ‫ﻧﯿﻮﺗﻦ‬
‫أ‬ ‫طﺮﻓﮫ‬ ‫ﻋﻨﺪ‬ ‫ﺛﺎﺑﺖ‬٠‫اﻟﻘ‬ ‫ﻋﻠﻰ‬ ‫أﺛﺮ‬‫ﻋﺰﻣﮫ‬ ‫ﻣﻌﯿﺎر‬ ‫رأﺳﻰ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻰ‬ ‫ازدواج‬ ‫ﻀﯿﺐ‬٢٥٠‫ﻧﯿﻮﺗﻦ‬٠‫ﻓﻌﻞ‬ ‫رد‬ ‫أوﺟﺪ‬ ‫ﺳﻢ‬
‫ﻣﯿﻞ‬ ‫وزاوﯾﺔ‬ ‫اﻟﻤﻔﺼﻞ‬‫اﻟﺘﻮازن‬ ‫وﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﻀﯿﺐ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٣(‫طﻮﻟﮫ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻗﻀﯿﺐ‬ ‫ب‬ ‫أ‬٦٠‫ووزﻧﮫ‬ ، ‫ﺳﻢ‬٣٠‫ﺑﻮاﺳﻄﺔ‬ ‫أﻓﻘﻰ‬ ‫وﺿﻊ‬ ‫ﻓﻰ‬ ‫ﻣﻌﻠﻖ‬ ( ‫ﻣﻨﺘﺼﻔﮫ‬ ‫ﻓﻰ‬ ‫ﯾﺆﺛﺮ‬ ) ‫ﻧﯿﻮﺗﻦ‬
‫ﺛﻘﻠﯿ‬ ‫اﻟﻘﻀﯿﺐ‬ ‫وﯾﺤﻤﻞ‬ ‫طﺮﻓﯿﮫ‬ ‫ﻣﻦ‬ ‫رأﺳﯿﯿﻦ‬ ‫ﺧﻔﯿﻔﯿﻦ‬ ‫ﺧﯿﻄﯿﻦ‬‫ﻣﻘﺪارھﻤﺎ‬ ‫ﻦ‬١٠‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫ﻧﯿﻮﺗﻦ‬١٠،‫أ‬ ‫اﻟﻄﺮف‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬
٢٠‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫ﻧﯿﻮﺗﻦ‬٢٠‫ب‬ ‫اﻟﻄﺮف‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬٠‫اﻟﺨﯿﻄﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫اﻟﺸﺪ‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٤‫طﻮﻟﮫ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻗﻀﯿﺐ‬ ‫ب‬ ‫أ‬ (١٠٥‫ووزﻧﮫ‬ ‫ﺳﻢ‬١٢‫ﻣﻨﺘﺼﻔﮫ‬ ‫ﻋﻨﺪ‬ ‫ﯾﺆﺛﺮ‬ ‫ﻧﯿﻮﺗﻦ‬٠‫ﻋﻠﻰ‬ ً‫ﺎ‬‫أﻓﻘﯿ‬ ‫اﻟﻀﯿﺐ‬ ‫ارﺗﻜﺰ‬ ‫ﻓﺈذا‬
= ‫ﺟـ‬ ‫أ‬ ‫ﺑﺤﯿﺚ‬ ‫د‬ ، ‫ﺟـ‬ ‫ﻋﻨﺪ‬ ‫ﺣﺎﻣﻠﯿﻦ‬٢٥‫ﻣﻘﺪارھﻤﺎ‬ ‫ﺛﻘﻼن‬ ‫ب‬ ، ‫أ‬ ‫طﺮﻓﯿﮫ‬ ‫ﻣﻦ‬ ‫،وﻋﻠﻖ‬ ‫ﺳﻢ‬٤٨،٢٤‫ﻋﻠﻰ‬ ‫ﻧﯿﻮﺗﻦ‬
‫د‬ ‫ﻋﻨﺪ‬ ‫اﻟﻀﻐﻂ‬ ‫ﻣﻘﺪار‬ ‫ﺿﻌﻒ‬ ‫ﺟـ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻀﻐﻂ‬ ‫ﻣﻘﺪار‬ ‫ﻟﯿﻜﻮن‬ ‫د‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻮﺿﻊ‬ ‫ﻋﯿﻦ‬ ، ‫اﻟﺘﺮﺗﯿﺐ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

6. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٥
)٥‫طﻮﻟﮫ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻗﻀﯿﺐ‬ ‫ب‬ ‫(أ‬٢‫ووزﻧﮫ‬ ‫ل‬٨‫ﺑﻤﻔﺼﻞ‬ ‫أ‬ ‫طﺮﻓﮫ‬ ‫وﯾﺘﺼﻞ‬ ‫ﻣﻨﺘﺼﻔﮫ‬ ‫ﻓﻰ‬ ‫ﯾﺆﺛﺮ‬ ‫ﻛﺠﻢ‬ ‫ﺛﻘﻞ‬‫ﺣﺎﺋﻂ‬ ‫ﻓﻰ‬ ‫ﻣﺜﺒﺖ‬
‫اﻟﺤﺎﺋﻂ‬ ‫ﻋﻠﻰ‬ ‫ﺟـ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺜﺒﺘﺔ‬ ‫ﻟﻠﺨﯿﻂ‬ ‫اﻷﺧﺮى‬ ‫واﻟﻨﮭﺎﯾﺔ‬ ‫ﺧﻔﯿﻒ‬ ‫ﺧﯿﻂ‬ ‫ﻧﮭﺎﯾﺘﻰ‬ ‫إﺣﺪى‬ ‫ﻓﻰ‬ ‫ﻣﺮﺑﻮط‬ ‫ب‬ ‫وطﺮﻓﮫ‬ ‫رأﺳﻰ‬
‫أ‬ ‫أﻋﻠﻰ‬ ً‫ﺎ‬‫رأﺳﯿ‬ ‫وﺗﻘﻊ‬٠‫ﻛﺎن‬ ‫ﻓﺈذا‬‫ﻣﺴﺘﻮى‬ ‫ﻓﻰ‬ ‫اﻟﻘﻀﯿﺐ‬ ‫واﺗﺰن‬ ‫ﺟـ‬ ‫ب‬ = ‫ﺟـ‬ ‫أ‬ = ‫ب‬ ‫أ‬‫اﻟﺤﺎﺋﻂ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدى‬ ‫رأﺳﻰ‬
‫أ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﻔﺼﻞ‬ ‫ﻓﻌﻞ‬ ‫ورد‬ ‫اﻟﺨﯿﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺸﺪ‬ ‫ﻣﻘﺪار‬ ‫ﻓﺄوﺟﺪ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٦‫طﻮﻟﮭﺎ‬ ‫ﻣﺴﻄﺮة‬ ‫ب‬ ‫أ‬ (٥٠‫ووزﻧﮭﺎ‬ ‫ﺳﻢ‬‫؛‬!٢‫ﺑﻮاﺳﻄﺔ‬ ‫أﻓﻘﻰ‬ ‫وﺿﻊ‬ ‫ﻓﻰ‬ ‫ﻋﻠﻘﺖ‬ ، ‫ﻣﻨﺘﺼﻔﮭﺎ‬ ‫ﻓﻰ‬ ‫ﯾﺆﺛﺮ‬ ‫ﻛﺠﻢ‬ ‫ﺛﻘﻞ‬
‫ﻣﻨﮭﺎ‬ ‫ﻛﻞ‬ ‫ﻣﻘﺪار‬ ‫أﺛﻘﺎل‬ ‫ﺛﻼﺛﺔ‬ ‫اﻟﻤﺴﻄﺮة‬ ‫ﻓﻰ‬ ‫وﻋﻠﻘﺖ‬ ‫طﺮﻓﯿﮭﺎ‬ ‫ﻋﻨﺪ‬ ‫رأﺳﯿﯿﻦ‬ ‫ﺧﯿﻄﯿﻦ‬١٠٠‫أﺑﻌﺎد‬ ‫ﻋﻠﻰ‬ ‫ﺟﺮام‬ ‫ﺛﻘﻞ‬
١٠، ‫ﺳﻢ‬٢٠، ‫ﺳﻢ‬٣٠‫أ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬٠‫اﻟﺨﯿﻄﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫اﻟﺸﺪ‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٧(‫وزﻧﮫ‬ ‫ﺟﺴﻢ‬ ‫وﺿﻊ‬٦‫ﺑﻮاﺳﻄﺔ‬ ‫ﺗﻮازﻧﮫ‬ ‫وﺣﻔﻆ‬ ‫ھـ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻷﻓﻘﻰ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ‫أﻣﻠﺲ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫ﻧﯿﻮﺗﻦ‬
‫ﻣﻘﺪارھﺎ‬ ‫ﻗﻮة‬٢]٣/ ‫ﺢ‬‫ﺧ‬‫ﻧﯿﻮﺗﻦ‬.‫ﻋﻠﻰ‬ ‫وﺗﻤﯿﻞ‬‫ﻷﻋﻠﻰ‬ ‫ھـ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬ ‫ﻟﻠﻤﺴﺘﻮى‬ ‫ﻣﯿﻞ‬ ‫أﻛﺒﺮ‬ ‫ﺧﻂ‬٠‫ورد‬ ‫ھـ‬ ‫ﻗﯿﻤﺔ‬ ‫أوﺟﺪ‬
‫اﻟﺠﺴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻌﻞ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤـــــــ‬‫ـــﻞ‬
www.mathtop4.alafdal.net

7. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٦
)٨‫وزﻧﮫ‬ ‫ﺟﺴﻢ‬ ‫وﺿﻊ‬ (٦‫ﻗﯿﺎﺳﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻷﻓﻘﻰ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ‫أﻣﻠﺲ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫ﻛﺠﻢ‬ ‫ث‬٣٠ْ◌‫ﺗﻮازن‬ ‫وﺣﻔﻆ‬
‫أﻓﻘﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺑﻮاﺳﻄﺔ‬ ‫اﻟﺠﺴﻢ‬٠‫اﻟﺠﺴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻌﻞ‬ ‫ورد‬ ‫اﻟﻘﻮة‬ ‫ھﺬه‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٩(‫طﻮﻟﮫ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻗﻀﯿﺐ‬ ‫ب‬ ‫أ‬١.٥‫ووزﻧﮫ‬ ً‫ا‬‫ﻣﺘﺮ‬١٤٠‫أﻓﻘﻰ‬ ‫وﺿﻊ‬ ‫ﻓﻰ‬ ‫وﯾﺮﺗﻜﺰ‬ ‫ﻣﻨﺘﺼﻔﮫ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﯾﺆﺛﺮ‬ ‫ﻧﯿﻮﺗﻦ‬
‫أ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﺎﻣﻞ‬ ‫ﻓﻌﻞ‬ ‫رد‬ ‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ ‫اﻟﻘﻀﯿﺐ‬ ‫ﻣﻦ‬ ‫ﺟـ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫واﻟﺜﺎﻧﻰ‬ ‫أ‬ ‫اﻟﻄﺮف‬ ‫ﻋﻨﺪ‬ ‫أﺣﺪھﻤﺎ‬ ‫ﺣﺎﻣﻠﯿﻦ‬ ‫ﻋﻠﻰ‬
: ‫أوﺟﺪ‬ ‫ﺟـ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﺎﻣﻞ‬ ‫ﻓﻌﻞ‬ ‫رد‬ ‫ﻣﻘﺪار‬ ‫ﺛﻠﺜﻰ‬ ‫ﯾﺴﺎوى‬
‫ﻣ‬ ‫ﻛﻞ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻔﻌﻞ‬ ‫رد‬ ‫ﻣﻘﺪار‬ :ً‫ﻻ‬‫أو‬‫ب‬ ‫ﺗﺎطﺮف‬ ‫ﻋﻦ‬ ‫ﺟـ‬ ‫ﺑﻌﺪ‬ : ً‫ﺎ‬‫ﺛﺎﻧﯿ‬ ‫اﻟﺤﺎﻣﻠﯿﻦ‬ ‫ﻦ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
: ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺴﺆال‬
)١(‫ﻣﻘﺎدﯾﺮھﺎ‬ ‫ﻗﻮى‬ ‫أﺛﺮت‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﺳﺪاﺳﻰ‬ ‫ﺷﻜﻞ‬ ‫و‬ ‫ھـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫أ‬٨٠،٦٠، ‫ق‬ ،٤٠‫ث‬٠‫ﺟـ‬ ‫ب‬ ، ‫ب‬ ‫أ‬ ‫ﻓﻰ‬ ‫ﺟﻢ‬
‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ ‫د‬ ‫ھـ‬ ، ‫د‬ ‫ﺟـ‬ ،٠‫ق‬ ‫ﻓﺄوﺟﺪ‬ ‫أ‬ ‫اﻟﺮأس‬ ‫ﺣﻮل‬ ‫اﻟﻘﻮى‬ ‫ھﺬه‬ ‫ﻟﻌﺰوم‬ ‫اﻟﺠﺒﺮى‬ ‫اﻟﻤﺠﻤﻮع‬ ‫اﻧﻌﺪم‬ ‫ﻓﺈذا‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
...................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

8. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٧
)٢(= ‫ب‬ ‫أ‬ ‫ﻓﯿﮫ‬ ‫أﺿﻼع‬ ‫ﻣﺘﻮازى‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫أ‬٦= ‫ﺟـ‬ ‫ب‬ ، ‫ﺳﻢ‬٨= ( ‫أ‬ ) ‫ق‬ ، ‫ﺳﻢ‬٦٠ْ‫ﻣﻘﺎدﯾﺮھﺎ‬ ‫ﻗﻮى‬ ‫أﺛﺮت‬٨،
١٠،٨،١٠‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ ‫د‬ ‫أ‬ ، ‫د‬ ‫ﺟـ‬ ، ‫ب‬ ‫ﺟـ‬ ، ‫ب‬ ‫أ‬ ‫ﻓﻰ‬ ‫ﻧﯿﻮﺗﻦ‬ ،٠‫اﻟﺬى‬ ‫اﻷزدواج‬ ‫ﻋﺰم‬ ‫ﻣﻌﯿﺎر‬ ‫أوﺟﺪ‬
‫اﻟﻘﻮى‬ ‫ھﺬه‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﻜﺎﻓﻰء‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٣(‫ﻣﻨﺘﻈﻢ‬ ‫ﺳﺪاﺳﻰ‬ ‫و‬ ‫ھـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫أ‬٠‫ﻣﻘﺎدﯾﺮھﺎ‬ ‫ﻗﻮى‬ ‫أﺛﺮت‬٦،٢]٣/ ‫ﺢ‬‫ﺧ‬،٦،٢]٣/ ‫ﺢ‬‫ﺧ‬‫أ‬ ، ‫ﺟـ‬ ‫أ‬ ، ‫ب‬ ‫أ‬ ‫ﻓﻰ‬ ‫ﻧﯿﻮﺗﻦ‬
‫واﺗﺠ‬ ‫ﻣﻘﺪار‬ ‫أوﺟﺪ‬ ‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ ‫ھـ‬ ‫أ‬ ، ‫د‬‫اﻟﻘﻮى‬ ‫ھﺬه‬ ‫ﻣﺤﺼﻠﺔ‬ ‫ﺎه‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٤(‫ﻣﻠﺴﺎء‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻛﺮة‬‫وزﻧﮭﺎ‬٦٠٠‫ﻗﻄﺮھﺎ‬ ‫ﻧﺼﻒ‬ ‫وطﻮل‬ ‫ﻛﺠﻢ‬ ‫ﺛﻘﻞ‬٣٠‫ﺳﻄﺤﮭﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻣﻌﻠﻘﺔ‬ ‫ﺳﻢ‬
‫طﻮﻟﮫ‬ ‫ﺧﻔﯿﻒ‬ ‫ﺧﯿﻂ‬ ‫ﺑﻮاﺳﻄﺔ‬٢‫ﻓﺈذا‬ ‫أﻣﻠﺲ‬ ‫رأﺳﻰ‬ ‫ﺣﺎﺋﻂ‬ ‫ﻓﻰ‬ ‫ﻣﺜﺒﺖ‬ ‫ﻣﺴﻤﺎر‬ ‫ﻓﻰ‬ ‫اﻵﺧﺮ‬ ‫طﺮﻓﮫ‬ ‫ﻣﺮﺑﻮط‬ ‫ﺳﻢ‬
‫اﻟﺤﺎﺋﻂ‬ ‫ﻓﻌﻞ‬ ‫ورد‬ ‫اﻟﺨﯿﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺸﺪ‬ ‫ﻣﻘﺪار‬ ‫ﻓﺄوﺟﺪ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ﺳﻄﺤﮭﺎ‬ ‫ﯾﻼﻣﺲ‬ ‫ﺑﺤﯿﺚ‬ ‫اﻟﻜﺮة‬ ‫اﺗﺰﻧﺖ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
..................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

9. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٨
)٥(‫ﺿﻠﻌﮫ‬ ‫طﻮل‬ ‫ﻣﺮﺑﻊ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫أ‬٣‫ﻣﻘﺎدﯾﺮھﺎ‬ ‫ﻗﻮى‬ ‫أﺛﺮت‬ ، ‫ﺳﻢ‬١٠،١٥،١٠،١٥، ‫ب‬ ‫ﺟـ‬ ، ‫ب‬ ‫أ‬ ‫ﻓﻰ‬ ‫ﻧﯿﻮﺗﻦ‬
‫ﻣﻨﮭﻤﺎ‬ ‫ﻛﻞ‬ ‫ﻣﻘﺪار‬ ‫ﻗﻮﺗﺎن‬ ‫أﺛﺮت‬ ‫ﻛﻤﺎ‬ ، ‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ ‫د‬ ‫أ‬ ، ‫د‬ ‫ﺟـ‬٥]۲/ ‫ﺢ‬‫ﺧ‬‫ﻓﻰ‬ ‫ﺟـ‬ ، ‫أ‬ ‫اﻟﻨﻘﻄﺘﯿﻦ‬ ‫ﻋﻨﺪ‬ ‫ﻧﯿﻮﺗﻦ‬
‫اﻟﺘﺮﺗﯿﺐ‬ ‫ﻋﻠﻰ‬ ‫ب‬ ‫د‬ ، ‫د‬ ‫ب‬ ‫اﻻﺗﺠﺎھﯿﻦ‬٠: ‫أوﺟﺪ‬
)‫أ‬(‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﯾﻜﺎﻓﻰء‬ ‫اﻟﺬى‬ ‫اﻹزدواج‬ ‫ﻋﺰم‬ ‫ﻣﻌﯿﺎر‬
)‫ب‬(‫اﺗﺰان‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫وﺗﺠﻌﻼن‬ ‫ﺟـ‬ ‫أ‬ ‫وﺗﻮازﯾﺎن‬ ‫د‬ ، ‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺗﻌﻤﻼن‬ ‫ﻗﻮﺗﯿﻦ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
)٦(‫ﺿﻠﻌﮫ‬ ‫طﻮل‬ ‫ﻣﺮﺑﻊ‬ ‫ھﯿﺌﺔ‬ ‫ﻋﻠﻰ‬ ‫رﻗﯿﻘﺔ‬ ‫ﺻﻔﯿﺤﺔ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫أ‬٥٠‫ووزﻧﮭﺎ‬ ‫ﺳﻢ‬٣٠٠‫ﻣﺮﻛﺰ‬ ‫ﻋﻨﺪ‬ ‫ﯾﺆﺛﺮ‬ ‫ﺟﺮام‬ ‫ث‬
‫اﻟﻤﺮﺑﻊ‬٠ً‫ﺎ‬‫رأﺳﯿ‬ ‫ﻣﺴﺘﻮاھﺎ‬ ‫ﺑﺤﯿﺚ‬ ‫أﻓﻘﻰ‬ ‫ﻣﺴﻤﺎر‬ ‫ﻓﻰ‬ ‫أ‬ ‫اﻟﺮأس‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﻘﺮب‬ ‫ﺻﻐﯿﺮ‬ ‫ﺛﻘﺐ‬ ‫ﻣﻦ‬ ‫اﻟﺼﻔﯿﺤﺔ‬ ‫ﻋﻠﻘﺖ‬
٠‫ﻟﻌﺰﻣﺔ‬ ‫اﻟﺠﺒﺮى‬ ‫اﻟﻘﯿﺎس‬ ‫إزدواج‬ ‫ﻣﺴﺘﻮاھﺎ‬ ‫ﻓﻰ‬ ‫اﻟﺼﻔﯿﺤﺔ‬ ‫ﻋﻠﻰ‬ ‫أﺛﺮ‬٧٥٠٠‫أ‬ ‫اﻟﻘﻄﺮ‬ ‫ﻣﯿﻞ‬ ‫أوﺟﺪ‬ ‫ﺳﻢ‬ ‫ﺟﻢ‬ ‫ث‬
‫ﺟـ‬‫اﻟﺘﻮازن‬ ‫وﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫ﻋﻠﻰ‬
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
......................................................................................................................................................................................................................
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

10. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ٩
‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫ﻛﺎﻧﺖ‬ ‫وﻋﻨﺪﻣﺎ‬ ‫اﻟﻤﯿﻨﺎء‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﺑﺎﺧﺮة‬ ‫ﺗﺘﺤﺮك‬٦٠‫ﻣﺮ‬ ‫ﻛﻢ‬‫اﻟﻤﻀﺎد‬ ‫اﻻﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﺗﻄﯿﺮ‬ ‫طﺎﺋﺮة‬ ‫ﻓﻮﻗﮭﺎ‬ ‫ت‬
‫ﺑﺴﺮﻋﺔ‬٨٠٠‫وﻛ‬ ‫اﻟﻄﺎﺋﺮة‬ ‫ﻟﻘﺎﺋﺪ‬ ‫اﻟﺒﺎﺧﺮة‬ ‫ﻓﺒﺪت‬ ‫ﻛﻢ/ﺳﺎﻋﺔ‬‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺤﺮك‬ ‫ﺄﻧﮭﺎ‬٨٩٠‫ﻛﻢ/ﺳﺎﻋﺔ‬٠‫اﻟﺬى‬ ‫اﻟﺰﻣﻦ‬ ‫اﺣﺴﺐ‬
‫اﻟﻤﯿﻨﺎء‬ ‫إﻟﻰ‬ ‫اﻟﺒﺎﺧﺮة‬ ‫ﺗﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫ﯾﻤﻀﻰ‬
‫ع‬ ، ‫اﻟﻄﺎﺋﺮة‬ ‫ﺣﺮﻛﺔ‬ ‫ﻋﻜﺲ‬ ‫وﺣﺪة‬ ‫ى‬ ‫أن‬ ‫ﺑﻔﺮض‬‫ب‬‫ع‬ ، ‫اﻟﻄﺎﺋﺮة‬ ‫ﺳﺮﻋﺔ‬‫أ‬‫اﻟﺒﺎﺧﺮة‬ ‫ﺳﺮﻋﺔ‬
‫ﺇ‬‫ع‬‫ب‬ ‫أ‬‫ع‬ =‫أ‬–‫ع‬‫ب‬،‫ﺇ‬٨٩٠‫ع‬ = ‫ى‬‫أ‬+٨٠٠‫ى‬‫ﺇ‬‫ع‬‫أ‬=٩٠‫ى‬
‫ﺇ‬‫ﺳﺎﻋﺔ‬ ‫ــــــــــ‬ = ‫ــــــــ‬ = ‫ـــــــــــــــــــــ‬ = ‫ﻟﻠﻤﯿﻨﺎء‬ ‫اﻟﺒﺎﺧﺮة‬ ‫وﺻﻮل‬ ‫زﻣﻦ‬
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫ﯾ‬ ‫واﺣﺪ‬ ‫طﺮﯾﻖ‬ ‫ﻓﻰ‬ ‫ﯾﺘﺤﺮﻛﺎن‬ ‫ﺟﺴﻤﺎن‬‫ﺘ‬‫اﻵﺧﺮ‬ ‫ﻧﺤﻮ‬ ‫ﻣﻨﮭﻤﺎ‬ ‫ﻛﻞ‬ ‫ﺠﮫ‬٠‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻓﺈذا‬١٠٠‫وﺳﺮﻋﺔ‬ ‫م‬
‫أﺣﺪھﻤﺎ‬٨‫ﺑﻌﺪ‬ ‫اﻟﺠﺴﻤﺎن‬ ‫وﺗﻘﺎﺑﻞ‬ ‫م/ق‬٥‫اﻵﺧﺮ‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻔﻌﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻓﺄوﺟﺪ‬ ‫دﻗﺎﺋﻖ‬
‫ع‬ ‫ﻧﻔﺮض‬‫أ‬=٨‫ع‬ ،‫ب‬‫؟‬ =
‫ﰈ‬‫ـــــــــــــــــ‬ = ‫اﻟﺠﺴﻤﯿﻦ‬ ‫ﻟﻘﺎء‬ ‫زﻣﻦ‬‫ﺇ‬٥‫ـــــــــ‬ =‫ﺇ‬‫||ع‬‫ب‬=||٢٠‫ق‬ /‫م‬
‫ﰈ‬‫ع‬ ||‫ب‬‫ع‬ = ||‫أ‬‫ع‬ +‫ب‬‫ﺇ‬٢٠=٨‫ع‬ +‫ب‬‫ﺇ‬‫ع‬‫ب‬=١٢‫ق‬ /‫م‬
‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫ن‬ ) = ‫ر‬ = ‫ى‬ ‫ﻛﺎن‬ ‫إذا‬٢
-٣+ ‫ن‬٥‫وﻛﺬﻟﻚ‬ ‫ف‬ ‫اﻹزاﺣﺔ‬ ‫ﻣﺘﺠﮫ‬ ‫ﻋﯿﻦ‬ ‫ى‬ (‫واﻛﻨﺐ‬ ‫زﻣﻨﯿﺔ‬ ‫ﻟﺤﻈﺔ‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫ﺳﺮﻋﺘﮫ‬ ‫ﻗﯿﻤﺔ‬
‫ﺗﻘﺼﯿﺮﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫وﻣﺘﻰ‬ ، ‫ﻣﺘﺴﺎرﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻣﺘﻰ‬
‫ﰈ‬‫ر‬‫ن‬ ) =٢
-٣+ ‫ن‬٥‫ى‬ (‫ﺇ‬‫ر‬ = ‫ف‬–‫ر‬٠‫ن‬ ) =٢
-٣+ ‫ن‬٥‫(ى‬–)٥‫ن‬ ) = ‫ى‬ (٢
-٣‫ى‬ ( ‫ن‬
‫ﺇ‬) = ‫ـــــــ‬ = ‫ع‬٢‫ن‬–٣) = ‫ــــــــ‬ = ‫ﺟـ‬ ، ‫ى‬ (٢‫ى‬ (
< ‫ﺟـ‬ ‫ع‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻣﺘﺴﺎرﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬٠> ‫ﺟـ‬ ‫ع‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺗﻘﺼﯿﺮﯾﺔ‬ ‫اﻟﺤﺮﻛﺔ‬٠
‫ﺇ‬٢)٢‫ن‬-٣< (٠‫ﺇ‬٢)٢‫ن‬-٣>(٠
‫ﺇ‬< ‫ن‬‫؛‬#٢،‫ﺇ‬>‫ن‬‫؛‬#٢
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــ‬‫ـــــــــــــــــــــــــــ‬
‫اﻷول‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺒﺎﺧﺮة‬ ‫ﺳﺮﻋﺔ‬٩٠٣
‫واﻟﻤﯿﻨﺎء‬ ‫اﻟﺒﺎﺧﺮة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬٦٠٢
‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﻤﺴﺎﻓﺔ‬
‫||ع‬‫ب‬||
١٠٠
‫||ع‬‫ب‬||
‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫ف‬ ‫د‬
‫ن‬ ‫د‬
‫ع‬ ‫د‬
‫ن‬ ‫د‬
www.mathtop4.alafdal.net

11. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١٠
) = ‫ف‬ : ‫ھﻮ‬ ‫ﻟﺤﻈﺔ‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫إزاﺣﺘﮫ‬ ‫ﻗﯿﻤﺔ‬ ‫ﯾﻜﻮن‬ ‫ﺑﺤﯿﺚ‬ ‫ﺟﺴﻢ‬ ‫ﯾﺘﺤﺮك‬‫؛‬!٣‫ن‬٢
-٢‫ن‬٢
+٣‫اﻟﺘﻰ‬ ‫اﻟﻔﺘﺮات‬ ‫أوﺟﺪ‬ ‫ى‬ ( ‫ن‬
‫ﺗﻘﺼﯿﺮﯾﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬ ‫اﻟﺘﻰ‬ ‫واﻟﻔﺘﺮات‬ ‫ﻣﺘﺴﺎرﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬
‫ﰈ‬) = ‫ف‬‫؛‬!٣‫ن‬٣
-٢‫ن‬٢
+٣‫ى‬ ( ‫ن‬‫ﺇ‬‫ن‬ ) = ‫ع‬٢
-٤+ ‫ن‬٣‫ى‬ (‫ﺇ‬) = ‫ﺟـ‬٢‫ن‬-٤‫ى‬ (
‫ﺇ‬< ‫ﺟـ‬ ‫ع‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻣﺘﺴﺎرﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬٠> ‫ﺟـ‬ ‫ع‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺗﻘﺼﯿﺮﯾﺔ‬ ‫اﻟﺤﺮﻛﺔ‬٠
‫اﻟﻔﺘﺮة‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎرﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬‫اﻟﻔﺘﺮة‬ ‫ﻓﻰ‬ ‫ﻧﻘﺼﯿﺮﯾﺔ‬ ‫اﻟﺤﺮﻛﺔ‬
[٣،∞]‫ﺢ‬‫ﺣ‬[]١،٣[ ]٠،١]‫ﺢ‬‫ﺣ‬[٢،٣]
‫ــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــ‬
‫ﻛﺘﻠﺘﮭﺎ‬ ‫ﻛﺮة‬٢٠‫ارﺗﻔﺎع‬ ‫ﻣﻦ‬ ‫ﺳﻘﻄﺖ‬ ‫ﺟﺮام‬٠.٤‫ر‬ ‫ﻷﻋﻠﻰ‬ ‫وارﺗﺪت‬ ‫ﺑﺎﻷرض‬ ‫ﻓﺎﺻﻄﺪﻣﺖ‬ ‫اﻷرض‬ ‫ﺳﻄﺢ‬ ‫ﻋﻦ‬ ‫ﻣﺘﺮ‬ً‫ﺎ‬‫أﺳﯿ‬
‫ﯾﺴﺎوى‬ ‫اﻟﺘﺼﺎدم‬ ‫ﻧﺘﯿﺠﺔ‬ ‫اﻟﻜﺮة‬ ‫ﺣﺮﻛﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬٨٤٠٠‫ﺟﺮام‬٠‫ارﺗﻔﺎع‬ ‫أﻗﺼﻰ‬ ‫ﻓﺄوﺟﺪ‬ ‫/ث‬ ‫ﺳﻢ‬
‫اﻟﺘﺼﺎدم‬ ‫ﺑﻌﺪ‬ ‫إﻟﯿﮫ‬ ‫ﺗﺼﻞ‬
: ‫ﻟﻸرض‬ ‫اﻟﻜﺮة‬ ‫وﺻﻮل‬ ‫ﺳﺮﻋﺔ‬
‫ع‬٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫د‬=‫ع‬٠‫ى‬‫ع‬٠=٠
‫ع‬٢
=٠+٢×٩٨٠×٤٠=‫د‬٩٨٠=‫د‬٩٨٠
‫ﺇ‬= ‫ع‬٢٨٠‫ث‬ /‫ﺳﻢ‬=‫ف‬ ‫ف=؟‬٤٠‫ﺳﻢ‬
‫ﰈ‬: ‫ﻷﻋﻠﻰ‬ ‫ارﺗﺪت‬ ‫اﻟﻜﺮة‬
= ‫ع‬-٢٨٠‫/ث‬ ‫ﺳﻢ‬‫ع‬/
‫ع=؟‬ ‫=؟‬
‫ﺇ‬‫ع‬ ) ‫ك‬ = ‫اﻟﺤﺮﻛﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺘﻐﯿﺮ‬/
-( ‫ع‬
٨٤٠٠=٢٠+‫ع‬ )٢٨٠(
‫ﺇ‬= ‫ع‬١٤٠‫ﻟﻼرﺗﺪاد‬ ‫اﻻﺑﺘﺪاﺋﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫وھﻰ‬ ‫/ث‬ ‫ﺳﻢ‬
‫ارﺗﺪاد‬ ‫ﺑﻌﺪ‬
‫ع‬٢
‫ع‬ =٠
٢
-٢‫ف‬ ‫د‬
٠) =١٤٠(٢
–٢×٩٨٠×‫ف‬
‫ﺇ‬= ‫ف‬١٠‫ﺳﻢ‬
‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬
‫ﻛﺘﻠﺘﮫ‬ ‫ﻗﻄﺎر‬٥٠‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫طﻦ‬٤٠‫ﺑﺴﺮﻋﺔ‬ ‫ﻓﺎرﺗﺪ‬ ‫ﺛﺎﺑﺖ‬ ‫ﺗﺼﺎدم‬ ‫ﺑﺤﺎﺟﺰ‬ ‫اﺻﻄﺪم‬ ‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬١٥‫ﻛﻢ/ﺳﺎﻋﺔ‬
‫اﻟﺘﺼﺎدم‬ ‫ﻧﺘﯿﺠﺔ‬ ‫اﻟﻘﻄﺎر‬ ‫ﺣﺮﻛﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬
‫ع‬٠=٤٠
‫ﰈ‬‫ى‬ ‫اﻟﺘﺼﺎدم‬ ‫ﺑﻌﺪ‬ ‫ارﺗﺪ‬ ‫اﻟﻘﻄﺎر‬
‫ﺇ‬‫ع‬ ) ‫ك‬ = ‫ﺣﺮﻛﺘﮫ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺘﻐﯿﺮ‬/
-( ‫ع‬‫ع‬/
=٥
=٥٠)١٥+٤٠= (٥٠×٥٥=٢٧٥‫طﻦ‬٠‫ﻛﻢ/ﺳﺎﻋﺔ‬
‫اﻟﺮاﺑﻊ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺨﺎﻣﺲ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺴﺎدس‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

12. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١١
‫ارﺗﻔﺎع‬ ‫ﻣﻦ‬ ‫ﺣﺠﺮ‬ ‫ﺳﻘﻂ‬٢٠‫ﻓﻘﺪ‬ ‫رﻣﻠﯿﺔ‬ ‫أرض‬ ‫ﻋﻠﻰ‬ ً‫ا‬‫ﻣﺘﺮ‬‫؛‬%٧‫ﻣﺴﺎﻓﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫وﻏﺎص‬ ‫ﺳﺮﻋﺘﮫ‬٢: ‫أوﺟﺪ‬ ‫ﺳﻜﻦ‬ ‫ﺛﻢ‬ ‫ﻣﺘﺮ‬
)١() ‫اﻷرض‬ ‫ﻟﺴﻄﺢ‬ ‫اﻟﺠﺴﻢ‬ ‫وﺻﻮل‬ ‫ﺳﺮﻋﺔ‬٢‫اﻷرض‬ ‫ﺑﺎطﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻋﺠﻠﺔ‬ (
)١(‫اﻷرض‬ ‫ﻟﺴﻄﺢ‬ ‫اﻟﺠﺴﻢ‬ ‫وﺻﻮل‬ ‫ﺳﺮﻋﺔ‬
‫ع‬٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫د‬‫ع‬٠=٠
=٠+٢×٩.٨×٢٠=‫د‬٩.٨
‫ﺇ‬‫ع‬=١٤]۲/ ‫ﺢ‬‫ﺧ‬‫ث‬ / ‫م‬= ‫ف‬٢٠
‫ﯾﻔﻘﺪ‬ ‫ﺛﻢ‬‫؛‬%٧‫ﺳﺮﻋﺘﮫ‬‫؟‬ =‫ع‬
‫ﺇ‬= ‫ﻟﻠﻐﻮص‬ ‫ع‬١٤]۲/ ‫ﺢ‬‫ﺧ‬×‫؛‬@٧=٤]۲/ ‫ﺢ‬‫ﺧ‬‫ث‬ / ‫م‬
)٢(:‫اﻷرض‬ ‫ﺑﺎطﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬
‫ع‬٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫ﺟـ‬‫ع‬٠=٤]۲/ ‫ﺢ‬‫ﺧ‬
٠=٣٢+٢‫ﺟـ‬×٢=‫ف‬٢
‫ﺇ‬= ‫ﺟـ‬-٨‫ث‬ / ‫م‬٢
‫ع‬=٠
‫ـــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫ﺑﺴﺮﻋﺔ‬ ‫ﻷﻋﻠﻰ‬ ً‫ﺎ‬‫رأﺳﯿ‬ ‫ﺟﺴﻢ‬ ‫ﻗﺬف‬٣٩.٢‫ﺳ‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ث‬ /‫م‬‫وﺑﻌﺪ‬ ‫اﻷرض‬ ‫ﻄﺢ‬٧‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﺳﻘﻂ‬ ‫ﺛﻮان‬
‫اﻟﻤﺒﻨﻰ‬ ‫ارﺗﻔﺎع‬ ‫أوﺟﺪ‬ ‫اﻟﻤﺒﻨﻰ‬
‫ارﺗﻔﺎع‬ ‫ﻷﻗﺼﻰ‬ ‫اﻟﻮﺻﻮل‬ ‫زﻣﻦ‬=‫ع‬٠
‫ع‬ = ‫ع‬٠–‫ن‬ ‫د‬=‫ن‬٤
=٣٩.٢–٩.٨‫ن‬‫ع‬٠=٣٩.٢
‫ﺇ‬= ‫ن‬٤
‫ﺇ‬‫اﻟﻤﺒﻨﻰ‬ ‫ارﺗﻔﺎع‬ ‫ھﻰ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﺧﻼل‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬:‫ع‬ = ‫ف‬٠‫ن‬-‫؛‬!٢‫ن‬ ‫د‬٢
=٣٩.٢-‫؛‬!٢×٩.٨×١=٣٤.٣ً‫ا‬‫ﻣﺘﺮ‬
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــــ‬
‫ﻛﺘﻠﺘﮫ‬ ‫ﺟﺴﻢ‬ ‫ﺗﺮك‬٥٠‫طﻮﻟﮫ‬ ‫ﻣﺎﺋﻞ‬ ‫أﻣﻠﺲ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻗﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺟﺮام‬١٠‫وارﺗﻔﺎﻋﮫ‬ ‫م‬٥‫م‬٠‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫طﺎﻗﺔ‬ ‫أوﺟﺪ‬
‫اﻟﻤﺴﺘﻮى‬ ‫ﻟﻘﺎﻋﺪة‬ ‫ﯾﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬
‫ﰈ‬‫ﺟـ‬ ‫ك‬ = ‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ ‫ك‬١٠‫م‬
= ‫ھـ‬ ‫ﺟﺎ‬‫؛‬!٢‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ = ‫ﺟـ‬ ،٥‫دﺟﺎھـ‬ ‫ك‬ ‫م‬‫طﺎﻗﺔ‬ ‫وﺗﻜﻮن‬=‫ﺣﺮﻛﺘﮫ‬‫؛‬!٢×٥٠×٩٨٠٠
=٩.٨×‫؛‬!٢=٤.٩‫ھـ‬
=٢٤٥٠٠٠‫أرج‬
‫ﺇ‬‫اﻟﻤﺴﺘﻮى‬ ‫ﻟﻘﺎﻋﺪة‬ ‫اﻟﺠﺴﻢ‬ ‫وﺻﻮل‬ ‫ﺳﺮﻋﺔ‬
‫ع‬٢
‫ع‬ =٠
٢
+٢= ‫ف‬ ‫ﺟـ‬٠+٢×٤.٩×١٠=٩٨
‫اﻟﺴﺎﺑﻊ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺜﺎﻣﻦ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺘﺎﺳﻊ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

13. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١٢
‫ارﺗﻔﺎع‬ ‫ﻣﻦ‬ ‫ﺟﺴﻢ‬ ‫ﺳﻘﻂ‬٤٠‫وﻓﻰ‬ ‫اﻷرض‬ ‫ﺳﻄﺢ‬ ‫ﻓﻮق‬ ً‫ا‬‫ﻣﺘﺮ‬‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﻷﻋﻠﻰ‬ ً‫ﺎ‬‫رأﺳﯿ‬ ‫آﺧﺮ‬ ‫ﺟﺴﻢ‬ ‫ﻗﺬف‬ ‫اﻟﻠﺤﻈﺔ‬ ‫ﻧﻔﺲ‬
‫ﺑﺴﺮﻋﺔ‬ ‫اﻷرض‬٢٠‫ن‬ ‫زﻣﻦ‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﺴﻤﺎن‬ ‫ﺗﻘﺎﺑﻞ‬ ‫ﻓﺈذا‬ ‫/ث‬ ‫ﻣﺘﺮا‬٠‫ﻗﻄﻌﮭﺎ‬ ‫ﻗﺪ‬ ‫ﯾﻜﻮن‬ ‫اﻟﺘﻰ‬ ‫واﻟﻤﺴﺎﻓﺔ‬ ‫ن‬ ‫ﻗﯿﻤﺔ‬ ‫ﻓﺄوﺟﺪ‬
‫ﺟﺴﻢ‬ ‫ﻛﻞ‬
)١(: ‫ﻣﺴﺎﻓﺔ‬ ‫ﯾﻘﻄﻊ‬ ‫اﻟﮭﺎﺑﻂ‬ ‫اﻟﺒﺠﺴﻢ‬
‫ف‬١‫ع‬ =٠+ ‫ن‬‫؛‬!٢‫ن‬ ‫د‬٢
‫ع‬٠=٠
=٠+٤.٩‫ن‬٢
)٢(‫ﻣﺴﺎﻓﺔ‬ ‫ﯾﻘﻄﻊ‬ ‫اﻟﺼﺎﻋﺪ‬ ‫اﻟﺠﺴﻢ‬٤٠‫م‬
‫ف‬٢‫ع‬ =٠‫ن‬-‫؛‬!٢‫ن‬ ‫د‬٢
=٢٠‫ن‬–٤.٩‫ن‬٢
‫ع‬٠=٠
)٣(‫ﻓﺈن‬ ‫اﻟﺠﺴﻤﺎن‬ ‫ﯾﺘﻘﺎﺑﻞ‬ ‫وﻋﻨﺪﻣﺎ‬
‫ف‬١‫+ف‬٢=٤٠
‫ﺇ‬٤.٩‫ن‬٢
+٢٠‫ن‬–٤.٩‫ن‬٢
=٤٠
‫ﺇ‬= ‫ن‬٢‫ث‬
‫ف‬ ‫وﺗﻜﻮن‬١=٤.٩×٤=١٩.٦‫م‬
‫ف‬٢=٢٠×٢-٤.٩×٤=٢٠.٤‫م‬
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــ‬‫ـ‬
‫ﻛﺘﻠﺘﮭﺎ‬ ‫ﺷﺎﺣﻨﺔ‬٥٠‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ ، ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﻊ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﺄﺛﯿﺮ‬ ‫ﺗﺤﺖ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫ﺗﺘﺤﺮك‬ ‫طﻦ‬
‫طﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬٢٠‫ث‬٠‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻛﺠﻢ‬٥٠‫إذا‬ ‫اﻟﺸﺎﺣﻨﺔ‬ ‫ﻟﻤﺤﺮك‬ ‫ﻗﻮة‬ ‫أﻗﺼﻰ‬ : ‫أوﺟﺪ‬ ‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬
‫ﻟﮭﺎ‬ ‫ﺳﺮﻋﺔ‬ ‫أﻗﺼﻰ‬ ‫ﻛﺎﻧﺖ‬١٠٠‫ﻛﻢ‬
‫ﰈ‬‫م‬α‫ع‬٢
‫ﺇ‬‫ــــــــــــ‬ = ‫ـــــ‬
‫ﺇ‬‫ـــــــ‬ = ‫ـــــ‬‫ﺇ‬‫م‬٢=‫ـــــــــــــــــــ‬ = ‫ﺳﺮﻋﺔ‬ ‫أﻗﺼﻰ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬٤٠٠٠‫ث‬٠‫ﻛﺠﻢ‬
= ‫م‬ = ‫ق‬ ‫ﺳﺮﻋﺔ‬ ‫أﻗﺼﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻋﻨﺪ‬٤٠٠٠‫ث‬٠‫ﻛﺠﻢ‬
‫م‬١=٢٠×٥٠‫ث‬٠‫ﻛﺠﻢ‬
‫ع‬١=٥٠‫ﺳﺎﻋﺔ‬ / ‫ﻛﻢ‬‫ق‬ ‫م‬
‫ع‬٢=١٠٠‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬
‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫اﻟﻌﺎﺷﺮ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫اﻟﺴ‬‫ﻋﺸﺮ‬ ‫اﻟﺤﺎدى‬ ‫ﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫م‬١‫ع‬٢
١
‫م‬٢‫ع‬٢
٢
١٠٠٠)٥٠(٢
‫م‬٢)١٠٠(٢
١٠٠٠×١٠٠٠
٢٥٠٠
www.mathtop4.alafdal.net

14. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١٣
‫ﻛﺘﻠﺘﮫ‬ ‫ﺟﺴﻢ‬٢‫ﻗﺪرھﺎ‬ ‫ﻗﻮة‬ ‫ﻋﻠﯿﮫ‬ ‫أﺛﺮت‬ ‫ﻛﺠﻢ‬٢‫ث‬٠‫ﻟﻤﺪة‬ ‫ﻛﺠﻢ‬٤‫ﺗﺄﺛﯿﺮھﺎ‬ ‫أوﻗﻒ‬ ‫ﺛﻢ‬ ‫ﺛﻮان‬٠‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫أوﺟﺪ‬
‫ﺧﻼل‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬‫؛‬!٤‫اﻟﻤﻘﺎوﻣﺎت‬ ‫إھﻤﺎل‬ ‫ﻣﻊ‬ ‫ﺣﺮﻛﺘﮫ‬ ‫ﺑﺪاﯾﺔ‬ ‫ﻣﻦ‬ ‫دﻗﯿﻘﺔ‬
‫ﻧ‬ ‫ﻗﺎﻧﻮن‬ ‫ﻣﻦ‬‫اﻟﻌﺠﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫ﯿﻮﺗﻦ‬
‫ﰈ‬‫ﺟـ‬ ‫ك‬ = ‫ق‬‫ﺇ‬٢×٩.٨=٢‫ﺟـ‬‫ﺇ‬= ‫ﺟـ‬٩.٨‫ث‬ /‫م‬٢
‫ﺧﻼل‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫وﺗﻜﻮن‬٤‫ﺛﻮان‬
‫ع‬ = ‫ف‬٠+ ‫ن‬‫؛‬!٢‫ن‬ ‫ﺟـ‬٢
=٠+‫؛‬!٢×٩.٨) ×٤(٢
=٧٨.٤‫م‬
‫ﺑﻌﺪ‬ ‫اﻟﻨﮭﺎﯾﺔ‬ ‫وﺳﺮﻋﺔ‬٤‫ﺛﻮان‬
‫ع‬ = ‫ع‬٠‫ن‬ ‫ﺟـ‬ +
=٠+٤×٩.٨=٣٩.٢/‫م‬‫ث‬
‫وﺗﻌﺘﺒﺮ‬٣٩.٢‫وﯾﻘﻄﻊ‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫وإھﻤﺎل‬ ‫اﻟﻘﻮة‬ ‫إﯾﻘﺎف‬ ‫وﻋﻨﺪ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫م/ث‬
‫ﻓﻰ‬١١‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﺒﺎﻗﯿﺔ‬ ‫ﺛﺎﻧﯿﺔ‬
‫ع‬ = ‫ف‬×= ‫ن‬٣٩.٢×١١=٤٣١.٢ً‫ا‬‫ﻣﺘﺮ‬
‫ﺇ‬= ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬٧٨.٤+٤٣١.٢=٥٠٩.٦ً‫ا‬‫ﻣﺘﺮ‬
‫ــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫ظﻠﮭﺎ‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻷﻓﻘﻰ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺟﺴﻢ‬ ‫ﯾﮭﺒﻂ‬‫؛‬#٤‫ﻷﻋﻠﻰ‬ ‫ﯾﺼﻌﺪھﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫أوﺟﺪ‬
‫ﻗﺪرھﺎ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻗﺬف‬ ‫ﻟﻮ‬ ‫اﻟﻤﺴﺘﻮى‬٨.٤‫م‬‫اﻟﺤﺎﻟﺘﯿﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﺛﺒﻮت‬ ‫ﻣﻊ‬ ‫/ث‬
)١(‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﮭﺒﻮط‬ ‫ﻋﻨﺪ‬
).......... ‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ ‫ك‬ = ‫م‬١(
)٢(‫ﺑﻌﺠﻠﺔ‬ ‫ﻷﻋﻠﻰ‬ ‫اﻟﺼﻌﻮد‬ ‫ﻋﻨﺪ‬
‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ ‫ك‬-) ........... ‫ﺟـ‬ ‫ك‬ = ‫م‬٢(
) ‫ﻣﻦ‬ ‫ﺑﺎﻟﺘﻌﻮﯾﺾ‬١) ‫ﻓﻰ‬ (٢(
‫ﺇ‬-‫ك‬‫ھـ‬ ‫ﺟﺎ‬ ‫د‬-‫ﺟـ‬ ‫ك‬ = ‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ ‫ك‬
‫ﺇ‬‫ﺟـ‬=-٢×٩.٨×‫؛‬#٥=-١١.٧٦‫م/ث‬٢
‫ﺇ‬‫ﺗﻘﺼﯿﺮﯾﺔ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻷﻋﻠﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻋﻨﺪ‬
‫ع‬ ،٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫ﺟـ‬
‫ﺇ‬٠) =٨.٤(٢
–٢×١١.٧٦‫ف‬‫ﺇ‬= ‫ف‬٣‫ﻣﺘﺮ‬
‫ﻋﺸﺮ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫ﻋﺸﺮ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

15. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١٤
‫ﻛﺘﻠﺘﮭﺎ‬ ‫ﻗﺎطﺮة‬٦٠‫آﻟﺘﮭﺎ‬ ‫وﻗﻮة‬ ً‫ﺎ‬‫طﻨ‬٥٦‫ث‬٠‫ﻣﻨﮭﺎ‬ ‫ﻛﻞ‬ ‫ﻛﺘﻠﺔ‬ ‫اﻟﻌﺮﺑﺎت‬ ‫ﻣﻦ‬ ً‫ا‬‫ﻋﺪد‬ ‫ﺗﺠﺮ‬ ‫طﻦ‬١٠‫ﺑﮭﺎ‬ ‫ﺻﺎﻋﺪة‬ ‫طﻦ‬
‫ﺑﺰا‬ ‫اﻷﻓﻘﻰ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ً‫ا‬‫ﻣﻨﺤﺪر‬‫ﺟﯿﺒﮭﺎ‬ ‫وﯾﺔ‬‫؛‬!٠‫؛‬٢‫ﻗﺪرھﺎ‬ ‫ﺑﻌﺠﻠﺔ‬٣.٣٣٢‫ث‬ /‫م‬٢
‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻗﻮة‬ ‫ﻛﺎﻧﺖ‬ ‫ﻓﺈذا‬١٠‫ث‬٠
‫اﻟﻜﺘﻠﺔ‬ ‫ﻣﻦ‬ ‫طﻦ‬ ‫ﻟﻜﻞ‬ ‫ﻛﺠﻢ‬٠‫اﻟﻌﺮﺑﺎت‬ ‫ﻋﺪد‬ ‫أوﺟﺪ‬
‫ك‬ = ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﺗﻜﻮن‬ ‫وﺑﺬﻟﻚ‬ ‫ك‬ ً‫ﺎ‬‫ﻣﻌ‬ ‫واﻟﻌﺮﺑﺎت‬ ‫اﻟﻘﺎطﺮة‬ ‫ﻛﺘﻠﺔ‬ ‫ﻧﻔﺮض‬×١٠×٩.٨‫ﻧﯿﻮﺗﻦ‬
‫ق‬ ‫ھﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬–‫م‬–‫ﺟـ‬ ‫ك‬ = ‫ھـ‬ ‫ﺟﺎ‬ ‫د‬ ‫ك‬
٥٦×١٠٣
×٩.٨–١٠×‫ك‬×٩.٨–‫ك‬×١٠٣
×٩.٨×‫؛‬!٠‫؛‬٢‫ك‬ =×١٠٣
×٣.٣٣٢
‫ﺇ‬= ‫ك‬١٤٠‫طﻦ‬
‫ﺇ‬= ‫وﺣﺪھﺎ‬ ‫اﻟﻌﺮﺑﺎت‬ ‫ﻛﺘﻠﺔ‬١٤٠–٦٠=٨٠= ‫اﻟﻌﺮﺑﺎت‬ ‫ﻋﺪد‬ ، ً‫ﺎ‬‫طﻨ‬‫؛‬)٠‫؛‬*١=٨‫ﻋﺮﺑﺎت‬
‫ــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــ‬
‫ﻛﺘﻠﺘﮫ‬ ‫ﺟﺴﻢ‬٩.٤‫ارﺗﻔﺎع‬ ‫ﻣﻦ‬ ‫ﺳﻘﻂ‬ ‫ﻛﺠﻢ‬١.٦‫ﻣﺴﺎﻓﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﻓﻐﺎص‬ ‫رﺧﻮة‬ ‫أرض‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺮ‬٨‫اﺣﺴﺐ‬ ‫ﺳﻢ‬
‫ﺟﺮام‬ ‫اﻟﻜﯿﻠﻮ‬ ‫ﺑﺜﻘﻞ‬ ‫اﻷرض‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻣﻘﺪار‬
‫أ‬‫اﻷرض‬ ‫إﻟﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫وﺻﻮل‬ ‫ﺳﺮﻋﺔ‬ : ً‫ﻻ‬‫و‬
‫ع‬٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫د‬
=٠+٢×٩.٨×١.٦
‫ﺇ‬= ‫ع‬]۲‫ﺢ‬‫ﺧ‬/×//٨/./٩//×//٦/./١‫ذﻟﻚ‬ ‫ﻏﯿﺮ‬ ‫ﯾﺬﻛﺮ‬ ‫ﻣﺎﻟﻢ‬ ‫اﻷرض‬ ‫ﺑﺎطﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫وھﻰ‬ ‫ث‬ /‫م‬
‫اﻷرض‬ ‫ﺑﺎطﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻋﺠﻠﺔ‬ ‫ﻟﺤﺴﺎب‬
‫ع‬٢
‫ع‬ =٠
٢
+٢‫ف‬ ‫ﺟـ‬
٠=٢×٩.٨×١.٦+٢‫ﺟـ‬×٠.٠٨
‫ﺇ‬= ‫ﺟـ‬-١٩٦‫ث‬ / ‫م‬
‫اﻷرض‬ ‫ﺑﺎطﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬
-‫ﺟـ‬ ‫ك‬ = ‫د‬ ‫ك‬ + ‫م‬
‫د‬ ‫ك‬–‫ﺟـ‬ ‫ك‬ = ‫م‬‫ﺇ‬
‫ﺇ‬‫د‬ ‫ك‬ = ‫م‬–‫ﺟـ‬ ‫ك‬‫ﺇ‬‫د‬ ) ‫ك‬ = ‫م‬–( ‫ﺟـ‬‫ﺇ‬= ‫م‬٤.٩)٩.٨+١٩٦= (١٠٢.٩‫ﻛﺠﻢ‬ ‫ث‬
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــــــــــ‬
‫ﻋﺸﺮ‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
‫ﻋﺸﺮ‬ ‫اﻟﺨﺎﻣﺲ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
www.mathtop4.alafdal.net

16. ‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫ﻓﻰ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻣﻨﺘﺪى‬ ١٥
‫ﺑﺪاﺧﻠﺔ‬ ‫ﻣﺼﻌﺪ‬‫وزﻧﮫ‬ ‫رﺟﻞ‬٨٠‫ﻛﺠﻢ‬ ‫ث‬٠‫ﻓﯿﮫ‬ ‫ﺑﻤﺎ‬ ‫اﻟﻤﺼﻌﺪ‬ ‫وزن‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ ‫اﻟﻤﺼﻌﺪ‬ ‫داﺧﻞ‬ ‫ﺿﻐﻂ‬ ‫ﻣﯿﺰان‬ ‫ﻋﻠﻰ‬ ‫ﯾﻘﻒ‬
٥٠٠‫ﻛﺠﻢ‬ ‫ث‬٠‫ﻋﻠﻰ‬ ‫وأﺛﺮ‬‫ﻗﺪرھﺎ‬ ‫ﻷﻋﻠﻰ‬ ‫ﺷﺪ‬ ‫ﻗﻮة‬ ‫اﻟﻤﺼﻌﺪ‬٦٠٠‫ﻓﺄوﺟﺪ‬ ‫ﺟﻢ‬ ‫ث‬
)١() ‫اﻟﻤﯿﺰان‬ ‫ﻗﺮاءة‬٢‫اﻟﺤﺮﻛﺔ‬ ‫ﺑﺪء‬ ‫ﻣﻦ‬ ‫ﺛﺎﻧﯿﺘﯿﻦ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺼﻌﺪ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫واﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻋﺠﻠﺔ‬ (
‫ﰈ‬‫د‬ ‫ك‬ < ‫س‬
‫ﺇ‬‫س‬ ‫ھﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫وﻣﻌﺎدﻟﺔ‬ ‫ﻷﻋﻠﻰ‬ ‫اﻟﺤﺮﻛﺔ‬–‫ﺟـ‬ ‫ك‬ = ‫د‬ ‫ك‬‫ش‬
-٠.٦×٩.٨=٥٠٠‫ﺟـ‬ )+٩.٨(
‫ﺇ‬= ‫ﺟـ‬١.٩٦‫ث‬ / ‫م‬٢
‫ﺇ‬‫ع‬ = ‫ف‬٠+ ‫ن‬‫؛‬!٢‫ن‬ ‫ﺟـ‬٢
=٠+‫؛‬!٢×١.٩٦×٤‫ــــــــــــــــ‬ =‫م‬‫د‬ ‫ك‬
‫ﰈ‬‫ﻓﻘﻂ‬ ‫اﻟﺮﺟﻞ‬ ‫وزن‬ ‫ھﻰ‬ ‫اﻟﻤﯿﺰان‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻘﻮة‬
‫ﺇ‬‫ر‬–‫ﺟـ‬ ‫ك‬ = ‫د‬ ‫ك‬‫ﺇ‬( ‫ﺟـ‬ + ‫د‬ ) ‫ك‬ = ‫ر‬
= ‫ر‬٨٠)٩.٨+١.٩٦= (٩٤٠.٨‫ﻧﯿﻮﺗﻦ‬
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــ‬‫ــــــــــــــــــــــــــــــــ‬
‫ﻛﺘﻠﺘﮭﻤﺎ‬ ‫ﻛﺮﺗﺎن‬١٠، ‫ﺟﻢ‬٥‫أﻣﻠﺲ‬ ‫أﻓﻘﻰ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﺤﺮﻛﺎن‬ ‫ﺟﻢ‬‫وﺳﺮﻋﺘﮭﻤﺎ‬ ‫ﻣﺘﻀﺎدﯾﻦ‬ ‫اﺗﺠﺎھﯿﻦ‬ ‫ﻓﻰ‬٤، ‫م/ث‬
٦‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫وارﺗﺪت‬ ‫ﻓﺎﺻﻄﺪﻣﺘﺎ‬ ‫م/ث‬٢‫م/ث‬٠‫أوﺟﺪ‬
)١() ‫ﻣﺒﺎﺷﺮة‬ ‫اﻟﺘﺼﺎدم‬ ‫ﺑﻌﺪ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻜﺮة‬ ‫ﺳﺮﻋﺔ‬٢‫اﻟﻜﺮﺗﯿﻦ‬ ‫ﻣﻦ‬ ً‫ﺎ‬‫أﯾ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﺪﻓﻊ‬ (
)٣‫اﻟﺘ‬ ‫(ﻗﻮة‬‫ﺗﻼﻣﺴﮭﻤﺎ‬ ‫زﻣﻦ‬ ‫ﻛﺎن‬ ‫إذا‬ ‫اﻟﻜﺮﺗﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﻀﺎﻏﻂ‬‫؛‬!٥‫ﺑﺎﻟﻨﯿﻮﺗﻦ‬ ‫ﺛﺎﻧﯿﺔ‬
)٤‫اﻟﺘﺼﺎدم‬ ‫ﻧﺘﯿﺠﺔ‬ ‫اﻟﻤﻔﻘﻮدة‬ ‫اﻟﺤﺮﻛﺔ‬ ‫طﺎﻗﺔ‬ ‫اﺣﺴﺐ‬ (
)١(‫ك‬١‫ع‬١‫ك‬ +٢‫ع‬٢‫ك‬ =١‫ع‬١‫ك‬ +٢‫ع‬٢
‫ﺇ‬)١٠×٤+(٥)-٦= (١٠‫ع‬١
/
+٥)٢(+٤‫م/ث‬٦‫م/ث‬
‫ﺇ‬‫ع‬/
١=٠‫ﺇ‬‫ﺑﻌ‬ ‫ﺳﻜﻨﺖ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻜﺮة‬‫اﻟﺘﺼﺎدم‬ ‫ﺪ‬~~
)٢(‫ﻣﻨﮭﻤﺎ‬ ‫ﻷى‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺘﻐﯿﺮ‬ = ‫اﻟﺪﻓﻊ‬١٠‫ﺟﻢ‬٥‫ﺟﻢ‬
‫ك‬ = ‫د‬١‫ع‬ )١
/
-‫ع‬٢(‫ع‬١
/
-٢‫م/ث‬
=١٠)٠-٤(
=-٤٠‫ﺟﻢ‬٠= ‫/ث‬ ‫م‬-٤٠٠٠‫ﺟﻢ‬٠‫ﺳﻢ/ث‬)٤(‫اﻟﺤﺮﻛﺔ‬ ‫طﺎﻗﺘﻰ‬ ‫ﻣﺠﻤﻮع‬ = ‫اﻟﻤﻔﻘﻮدة‬ ‫اﻟﺤﺮﻛﺔ‬ ‫طﺎﻗﺔ‬
)٣(‫ق‬ = ‫د‬×‫ن‬‫اﻟﺘﺼﺎدم‬ ‫ﻗﺒﻞ‬–‫ﺑﻌﺪ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫طﺎﻗﺘﻰ‬ ‫ﻣﺠﻤﻮع‬
٤٠٠٠=٥×‫؛‬!٥] =‫؛‬!٢‫ك‬١‫ع‬١
٢
+‫؛‬!٢‫ك‬٢‫ع‬٢
٢
[-]٠‫ك‬ +٢‫ع‬٢
٢
[
‫ﺇ‬= ‫ق‬٢٠٠٠٠‫داﯾﻦ‬]=‫؛‬!٢×١٠×١٦+‫؛‬!٢×٥×٣٦[-]‫؛‬!٢×٥×٤[
‫ﺇ‬= ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺘﻀﺎﻏﻂ‬ ‫ﻗﻮة‬٠.٢‫ﻧﯿﻮﺗﻦ‬=١٦٠( ‫ث‬ /‫)م‬ ‫ﺟﻢ‬٢
‫ﻋﺸﺮ‬ ‫اﻟﺴﺎدس‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
٧.٨٤
٢
‫ﻋﺸﺮ‬ ‫اﻟﺴﺎﺑﻊ‬ ‫اﻟﺴﺆال‬
‫اﻟﺤــــــــــﻞ‬
٨٠
www.mathtop4.alafdal.net