The document summarizes concepts related to forces and motion. It defines key terms like work, kinetic energy, and potential energy. It provides formulas for calculating work, kinetic energy, and gravitational potential energy. Examples are given to demonstrate applying the concepts and formulas to solve physics problems involving changes in kinetic and potential energy.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2. 5
5.1 W F F Nm
(J)
F
W = Fs
s
F F
¬ ?
F ?
¬ F F ?
¬ F F F? ?
¬ F F F F F
F? ?
- F F F F F
F
θ F cosθ W = F cosθ s
s
- F F F F F
F F
F
fs W = - fs s
s mg s W= -Fs
F
.=
- F F F s (W = Fs ) s
F F www.schoolDD.com 1
3. - F F F F
F1= 0 F2
W= x
x
- F F ( +,-) F
FW=F Fs
F 1
3 F F1= 20 , F2 = 5 F3= 6 F F
5
. F1 , F2 F3
.
F2
F1
F3
60°
5.0
.
F1 F F1 F F F F1cos60
F 5.0 m
W1 = F1 cos60 s1
= 20(1/2) 5
W1 = 50 N-m (J) Ans
F2 , W2 = F2 s2
= 5(0) ( F2 )
F
W2 = 0 J Ans
F3 , W3 = F3 s3
= -6(5) ( F3 )
W3 = -30 J Ans
F F www.schoolDD.com 2
4. .
F1+ F2+ F3 , W = W1+ W2+ W3
= 50 + 0 + (-30)
W = 20 J Ans
W =F Fs
= (F1 cos60 - F3) s
= (20(1/2) 6) 5
W = 20 J Ans
F 2
F 10 2.5 F
F F F
F
a=0 F
mg F .
2.5 m
F a=0
= ma F F = mg = 10(10) = 100 N
= 2.5 m
W = Fs
= -100(2.5) ( F )
W = -250 J Ans
¬ F F F F F F
F F 10 m F F ?
¬ F F F F
F ?
F F www.schoolDD.com 3
5. F 3
F F F F
4 F F F 10 F F
2
0.5 /
a = 0.5 F F F
T 10
mg
W = Fs F s F F F
= ma
F mg T = ma
4(10) T = 4(0.5)
T = 38
W = Fs
= -38(10)
W = -380 J Ans
F 4
25 10
2 F . 0.1 F
F F F
F sin37
F = 25 N F = 25
37°
10 kg 37°
f F cos37
mg
f=0
= ma
F F cos37 = ma
25(4/5) = 10 a
a = 2 m/s2
F F www.schoolDD.com 4
6. s s = ut + ½ at2
= 0 + ½ (2)(22)
F
s=4 m
W = F s = F cos37 s
= 25(4/5)(4)
W = 80 J Ans
f = µN = µ(mg - F sin37)
= 0.1(10(10) 25(3/5))
f = 8.5 N
= ma
F F cos37 - f = ma
(20-8.5) = 10 a
a = 1.15 m/s2
s s = ut + ½ at2
= 0 + ½ (1.15)(22)
s = 2.3 m
W = F F s = (F cos37 f) s
= (20-8.5)(2.3)
W = 26.45 J Ans
F 5
F F 100 F F F 5 F F F 8
F 10 F F 20
F = 100 N
5.0 m
N
4.0 m
θ 2F cosθ
θ f 10.0 m
5.0 m 4.0 m
mg
F = 100 N
W = F F s = (2F cosθ f) s
= (2(100)(3/5)-20)(10)
W = 1000 J Ans
F F www.schoolDD.com 5
7. F 6
F F F F F 40 37
3 F F F 60
F F F
N
3.0 m 3.0 m
f
37° 37°
F F
mg sin37 mg cos37
mg
F F F F
F = mg sin37 + f
= 40(10)(3/5) + 60
F = 300 N
W = Fs ( s = 5 m)
= 300(5)
W = 1500 J Ans
F 7
40 30 F 4 F
F 2 F
t=2 t=2
a
N
F = 40 F = 40
30° 30°
mg sin30 mg cos30
mg
W=Fs , FF s
= ma
F - mg sin30 = ma
F F www.schoolDD.com 6
8. 40 4(10)(1/2) = 4a
a = 5 m/s2
s s = ut + ½ at2
= 0 + ½ (5)(22)
s = 10 m
W = Fs ( s = 10 m)
= 40(10)
W = 400 J Ans
F 8
F F 5 50 FF F F
FF
3.0
2.0
5.0
F F F 2 F F F F (3 ) F F
(2 )
F F 3
F F1= mg (3/5) F F F F F
F ( F F )
F1 = 50(10)(3/5) = 300 N
s1 = 3/2 = 1.5 m ( cm. F F )
F
W1 = F1 s1
= 300(1.5)
W1 = 450 J
F F F 2
F2 = mg (2/5)
F2 = 50(10)(2/5) = 200 N
s2 = 3.0 m ( cm. F F F F 3 m)
W2 = F2 s2
= 200(3.0)
F F www.schoolDD.com 7
9. W2 = 600 J
W = W1 + W2
= 450 + 600
W = 1050 J Ans
F 9
F 5x5 3 2 F
( F F =1 / F )
F
cm.
2.0 m
3.0 m
2.0 m
5.0x5.0 m mg
cm. cm.
F = mg
F = 1x103(5x5x2)(10) = 5x105 N
s = 2.0 m
W =Fs
= 5x105(2.0)
W = 1x106 J Ans
F 10
F F 0.4 F 10 F F
0.1 F F
u = 10 v=0
t = 0.1
m
F m
s
W = F s -------1
F F = ma ( a v = u + at a = (v-u)/t
F F www.schoolDD.com 8
10. F = m (v-u)/t
F = 0.4(0-10)/(0.1) = - 40 N
s s = (u + v)/2 x t
s = (10 + 0)/2 x 0.1
s = 0.5 m
F F, s 1, W =Fs
= - 40 (0.5)
W = - 20 J Ans
F 11
F F F s
F (N)
10
F 0 --> 4 m F
F F = 10 N
s (m)
2 4 6 8
-10
F . F F s . F
W = W0◊4 + W4◊6 + W6◊8
= (10 x 40) + (1/2 x 2 x 10) + (1/2 x 2 x -10)
W = 40 J Ans
,, ,,
5.2 P F F F F / F (W)
P= P= = = Fv ( v )
¬ F F F F F
F
F F www.schoolDD.com 9
11. F 12
F 1 10 20 F
m
F s = 10
a=0 t = 20
m
mg
P = W/t
= ( F v a=0 F = mg )
=
=
P = 5x103 W Ans
F 13
F F 37 ° F
F F 15 20
F (N)
F 10
37°
s s (m)
5 10 15
P = W/t -------1
F W = (F cos37) s
= Fs cos 37 ( = . F x cos 37 )
= ½ x (15 + 10) x10 x (4/5)
W = 100 J
F W 1, P = 100/20
P = 5 W Ans
F F www.schoolDD.com 10
12. F 14
F 100 30 ° F 0.01 m/s F .
F F F 1/ F
N v = 0.01
F
f
mg sin30
mg cos30
mg
30°
P = W/t = F v -------1
Fv F F = ma
F - mg sin30 - f = 0 ( v a = 0, f = µN = µmg cos 30 )
F 100(10)(1/2) (1/ )(100)(10)( /2) = 0
F = 1000 N
F F 1, P = 1000 (0.01)
P = 10 W Ans
F F www.schoolDD.com 11
13. 5.3
5.3.1 F Ek F F (J)
v m F v
2
m
Ek = mv F F 1/2 mv2
F F kg m2/s2 = kg m/s2 m
=Nm=J F
5.3.2. F Ep F F
F F (J) F
1. F F F
m
m F F F
Ep = mgh h F F F F
h F F mgh
F F F F kg m/s2 m =
Nm=J F
F F
2. F F
m F F
Ep = kx2 F x
F F F F
k F 2
1/2 kx
F F F N/m m2 =
x Nm=J F
5.4. F
F F F
= F
- W1→2 = F F
F F www.schoolDD.com 12
14. = F 1 ( Ep1 + Ek1 )
= F 2 ( Ep2 + Ek2 )
W1→2 = F 1 2
F F F
1. F F ( F F )
u=0
1 m
=
Ep1 + Ek1 = Ep2 + Ek2
h mgh + 0 = 0 + ½ mv2
v mgh = ½ mv2
2 m
v =
2 m Ep1 + Ek1 = Ep2 + Ek2
h 0 + ½ mu2 = mgh + ½ mv2
u ½ mu2 = mgh + ½ mv2
1 m
2.
u=0
1 m =
Ep1 + Ek1 = Ep2 + Ek2
h v
mgh + 0 = 0 + ½ mv2
2 m mgh = ½ mv2
θ
F F www.schoolDD.com 13
15. 3.
u=0 s
1 m W1◊2 =
h f Ep1 + Ek1 f s = Ep2 + Ek2
v
mgh + 0 f s = 0 + ½ mv2
2 m mgh f s = ½ mv2
θ
4.
v2
2
=
r
Ep1 + Ek1 = Ep2 + Ek2
+
0 + ½ mv12 = mgh + ½ mv22
½ mv12 = mg(2r) + ½ m v22
1
v1
=
u=0
Ep1 + Ek1 = Ep2 + Ek2
1 mgh + 0 = 0 + ½ mv2
h
2 mgh = ½ mv2
v
5.
m u=0
1
=
h Ep1 + Ek1 = Ep2 + Ek2
m v=0 mg(h+x) + 0 = ½ kx2 + 0
m x mg(h+x) = ½ kx2
2 k
F F www.schoolDD.com 14
16. 6.
m u=0
1
W1◊2 =
h
Ep1 + Ek1 f x = Ep2 + Ek2
m mg(h+x) + 0 f x = 0+0
f m x mg(h+x) = fx
2
v=0
7. F F
1 2
W1◊2 =
u f
v=0 Ep1 + Ek1 f x = Ep2 + Ek2
m x 0 + ½ mu2 f x = 0 + 0
½ mu2 = f x
F 15
F 1 20
. F F
. F
u=0
m
h = 20
v
m
. Ep = ? F
Ep = mgh
= 1(10)(20)
Ep = 200 J Ans
F F www.schoolDD.com 15
17. . Ek = ?
Ek = ½ mv2 -----1
Fm v v2 = u2 + 2as
= 0 + 2(10)(20)
v = 20 m/s
F v 1, Ek = ½ (1)(202)
Ek = 200 J Ans
F F F F F F
F
F 16
5 F 100 N/m F 7 F F
F
k =100
0.07 - 0.05 = 0.02 m
0.05 Ep = ½ kx2
= ½ (100)(0.022)
Ep = 0.02 J Ans
0.07
F 17
0.1 F 100 N/m F 20 F
F F F F F F
. . A, B, C, D E
. F EF
B
O
D
u = 0 0.2 1.0
0.5 vF = 0
k = 100 A C E F
10.0
F F www.schoolDD.com 16
18. . v A , vB , vC , vD , vE = ?
F F F F F
F = Epo = ½ kx2
= ½ (100)(0.22)
=2 J
O --> A = F
2
2 = ½ mvA
2 = ½ (0.1)( vA2)
vA = 6.3 m/s Ans
O --> B =
2 = mgh + ½ mvB2
2 = 0.1(10)(1) + ½ (0.1)( vB2)
vB = 4.5 m/s Ans
O --> C =
2 = ½ mvC2
2 = ½ (0.1)( vC2)
vC = 6.3 m/s Ans
O --> D =
2 = mgh + ½ mvD2
2 = 0.1(10)(0.5) + ½ (0.1)( vD2)
vD = 5.5 m/s Ans
O --> E =
2 = ½ mvE2
2 = ½ (0.1)( vE2)
vE = 6.3 m/s Ans
. W E◊ F = ?
O --> F - WE◊ F =
2 - W E◊ F = 0
WE◊F = 2 J Ans
F F O F F E --> F F
F F
F F www.schoolDD.com 17
19. F 18
m F F F F .
0.4
u=0
m
A
v=0
2.0
m m
B f C
s=?
A --> C - WB ◊ C =
mgh - f s = 0
mgh - µmg(s) = 0
s = h/µ = 2/0.4
s = 5 m Ans
F 19
F F F F F 1 .
0.1 F
. F F
. F
A
u=0 vD = 0
D
0.50
hmax
f
B 1.0 C
. hmax = ?
A --> D - WB ◊ C =
mgh - f s = mghmax
F F www.schoolDD.com 18
20. mgh - µmg(s) = mghmax
hmax = h - µ(s) = 0.5 0.1(1)
hmax = 0.4 m Ans
. F
F F
= WB◊ C
mgh = fs
mgh = µmg(s)
s = h/µ = 0.5/0.1
s = 5.0 m
- F F C F s = 5.0 m Ans
¬ - F F B ?
F 20
F 1.0 F 1 / F F
k = 100 / F F
v=1
k =100
m
x
m
F F F F
F =
½ mv2 = ½ kx2
1.0(12) = 100(x2)
x2 = 1/100
x = 0.1 m Ans
F F www.schoolDD.com 19
21. F 21
F 0.2 60 F
60° l = 2
u=0
h
v
F F F F F
F =
mgh = ½ mv2
v2 = 2gh = 2g(l l cos60)
v2 = 2(10)(2-2(1/2))
v = m/s Ans
F 22
1 F F F F
F 0.10 F F F F
F F
k
m
x1 = 0.1 m
x2 = ?
m
F F F
F F = mg
kx1 = mg
k = 1(10)/0.1 = 100 N/m
F F F F F F
F =
mgh = ½ kx2
1(10) x2 = ½ (100)( x22)
x2 = 0.2 m Ans
F F www.schoolDD.com 20
22. F 23
10 1000 F 1
F ( F F )
m u=0
F F F F
h =1000 W1◊2 =
mg(h+x) f x = 0
m
mg(h+x) = f x
f x =1.0
m 10(10)(1000+1) = f (1)
v=0 f = 100100 N Ans
F 24
F 1 µk = 0.5 37 F F F k = 100
N/m F 1.0 F F F
1.0
u=0
m x=?
v=0
m
37°
F F F F F F F F
F W1◊2 =
mgh f s = ½ kx2
mg (1+x) sin37 - µmg cos37(1+x) = ½ kx2
1(10)(1+x)(3/5) 0.5(1)(10)(4/5)(1+x) = ½ (100) x2
6(1+x) 4(1+x) = 50 x2
25 x2 x 1 = 0
x =
x = 0.22 m Ans
F F www.schoolDD.com 21
23. F 25
F m F F F h F F F
r F F
A u=0
m m
N=0
h 2r v
B
h m
r
+ 2r mg
A --> B
F F F F F A F F B
F =
mg (h-2r) = ½ mv2
2g (h-2r) = v2 ----1
F B F F N=0
mg F F F
Fc =
mg =
v2 = r g
F v2 = r g 1, 2g (h-2r) = r g
h = r Ans
5.6
F F F F
F F F
F = F
F F www.schoolDD.com 22
24. F F
F = F
Eff
F F F F 100 F %
Eff = F
x 100
F
F
W F = Fs
F W F = mgh
s s = h
h m
F Eff = 100 % , W F = W F
m F s = mgh
F = mg
mg FF
W F = Fs
W F = mgh
s s = 2h
F Eff = 100 % , W F = W F
F s = mgh
m F
h F = mg/2
F
m
mg
F F www.schoolDD.com 23
25. F
s
h m
mg W F = Fs
W F = mgh
F Eff = 100 % , W F = W F
F s = mgh
s m F = mg
F s>h
F h
m
mg
R
W F = Fs
r F W = mgh
F
s s =2 R h =2 r
h m F Eff = 100 % , W F = W F
Fs = mgh
m
F = mg
mg F R>r
F
r W F = F (2 r)
W F = mgh
m F
F Eff = 100 % , W F = W F
mg F (2 r) = mgh
h
F = mg
F r>h
F F www.schoolDD.com 24
