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# Dynamics

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### Dynamics

1. 1. OBJECTIVES: In this chapter we will learn :Some important kinds of Forces such as ; NORMAL & FRICTION Forces The Laws of MotionHow to solve dynamics problems by the Laws of Motion
2. 2. DYNAMICS 1. NORMAL Force: is the relation between FORCE & is REACTION Force, perpendicular to MOTION the surface that the action force is applied FORCE: is the Effect that can destroy,stop or move the objects. Since it shows a DIRECTION. Then itis a VECTOR Quantity. THE KINDS OF FORCES
3. 3. FRICTIONAL FORCE• Frictional force: It is an important force which only acts when two objects are touching and are applying force to one another.• It is a force that slows down moving objects and brings them to rest.• It always acts in a direction opposite to the direction of the force applied to the object.• Walking is possible only on a frictional surface.• Water also applies a frictional force to the objects moving in it.• Frictional force does not depend on the area of the rubbing surfaces. The frictional force between the object and the table depends on two factors; a. The weight of the object.b. The roughness of the surfaces rubbing together.
4. 4. 2. FRICTION Force: Ex: Find the friction F F N force in both case.is REACTION Force, formed Nin opposite direction to theaction force applied. F f max   .N  W  mg W  mg N W  F N W  F Re ady to Move F f max  .W  F  F f max  .W  F  No Motion F ext F f F f maxFf FNET  Fext  F f max F f max Between twoF f max surface, there is Static Kinetic a maximum value Friction of Friction Force. Friction Fext Let us write an equation about this maximumfriction force between two surface. F f max F f max  N  const N We call this constant as the coefficient offriction, µ between two surface F f max   .N
5. 5. 3. TENSION Force: Planet Field Strength Mass Weightis ACTION-REACTION Force, Mercury 3,78 N/kg X 40 kg = 151 Nformed along stretch Force Venus 8,94 N/kg X 40 kg = 358 Napplied. Earth 10 N/kg X 40 kg = 400 N Moon 1,7 N/kg X 40 kg = 67 N Mars 3,79 N/kg X 40 kg = 152 N Jupiter 25,4 N/kg X 40 kg = 1067N Saturn 10,7 N/kg X 40 kg = 428 N Uranus 9,2 N/kg X 40 kg = 368 N Neptune 12 N/kg X 40 kg = 480 N Pluto 0,3 N/kg X 40 kg = 12 N Ex: What is the weight of an object on the Moon which has the weight on Earth as 100N ? W  mg  100 N  10m  m  10kg4. GRAVITATIONAL Force: W  mg  10.1,7  17 Nis Natural Attractive Field Force, betweentwo bodies that appears as the WEIGHT. 5. MAGNETIC Force: 6. ELECTROSTATIC Force: FG FG FG FG 7. NUCLEAR Force:We define the Gravitational Field as; . FG . g FG  W  W  m.g m .
6. 6. LAWS OF MOTION II-) ACTION PRINCIPLE:I-) INERTIA PRINCIPLE: If the NET FORCE is not ZERO on an object ; Either the object will be accelerated or deceleratedINERTIA: is the tendency to keep the initialposition F NET  a FNET m a m 2 FNET 2a 3FNET m 3a FNET  const  mass(m) aPRINCIPLE: If the NET FORCE is ZERO onan object ; Either the object stops or FNET  m.amoves steadily (with constant velocity) III-) ACTION-REACTION PRINCIPLE: If an object applies a Force on another object. The Other One replies with the same Force in opposite direction
7. 7. INCLINED PLANE: Along x-axis, There is motion. W . sin   F R Fnet  ma y N Ff Fnet  FR  Ff  W . sin   Ff  ma mg sin   .mg cos   ma W . sin  W . cos   a  g.sin    cos   x W If there is no FRICTION, then take;  0 a  g. sin  Object is sliding down.Along y-axis, There is no motion. Fnet  0 F f   .N N  W . cos   0 F f   .mg cos  N  mg cos 
8. 8. LIFT PROBLEMS: B- The Lift accelerated downward or decelerated upward ;Let us look at the cases by both the observersinside the Lift and outside the Lift FNet  0A- The Lift accelerated upward or decelerateddownward ; T  W  F fic.  0 FNet  0 T  W  F fic. F ficT  W  F fic.  0 T  mg  ma T a T  W  F fic. T  m g  a  T  mg  ma W  mg T  m g  a  T FNet  ma FNet  ma   a T  W  m.a F fic T  W  m.  a W  mg T  mg  ma T  mg  ma T  m g  a  T  m g  a 
9. 9. Apparent WeightW = mg W = m(g+a) W = m(g-a) Weightless
10. 10. Ex.:What is the acceleration of the object, a=? Ex.:A force of 10N is applied on the mass of   the 2kg with and angle of 370. If the coefficient N a of friction between mass and surface is 0.1, what  is the acceleration of the mass in m/s2 ? m=10 kg F  100 NFf     a   0,5 N FY F  10 N    W m=2 kg 37 0 Ff FX Along y-axis; There is no MOTION, ay=0           0,1FNet  0  N  W  0  N  W  mg N  100 N  FX  F.cos37 0  10 N .0,8  8 N   W FY  F.sin370  10 N .0,6  6 N Along x-axis; There is MOTION, a=ax     Along y-axis; There is no MOTION, ay=0 FNet  ma F f  N           FNet  0  N  FY  W  0  N  W  FY F  F f  ma  0,5.100 N  N  20 N  6 N  14 N 100 N  50 N  10kg.a  50 N Along x-axis; There is MOTION, a=ax     a  5m / s 2 FNet  ma   F f  N  FX  F f  ma  0,1.14 N 8 N  1,4 N  2kg.a  1,4 N a  3,3m / s 2
11. 11. Ex.: Two masses which are contact with each other Ex.: Three masses are connected with ropes. Aare pushed by a force of 20 N. What force does the force of 280 N acted on the masses as shownmass A apply to the mass B when coefficient of in the figure. Find the tensions in the rope T1friction between the masses and the surface; µ=0 ,T2 . and µ=0.1?   N1   N3 N2 a N1 a   m3  20kg  m  20kg  m1  30kg  N2 T2 2 T1 F  280N   F  20 N m1=3kg R    m2=2kg Ff 3  Ff 2  Ff 1   0,2   W3 W2  Ff 1  Ff 2    W1 W1 W2 F f 1  N1  0,2.300 N  60 N  Along y-axis; There is no MOTION, ay=0 Ff 2  N 2  0,2.200 N  40 N    FNet  0 F f 3  N 3  0,2.200 N  40 N        N1  W1  30 N F f 1  N1  0,1.30 N  3N For all system; FNet  mT a             N 2  W2  20 N F f 2  N 2  0,1.20 N  2 N F  Ff 1  Ff 2  Ff 3  m1  m2  m3 .aAlong x-axis; There is MOTION, a=ax 280 N  (60 N  40 N  40 N )  (30  20  20)kg .a     FNet  mT a FNet  mT a a  2m / s 2        F  m1  m2 a  F  F f 1  F f 2  m1  m2 a For m3 ; For m 2 ; 20 N  5kg .a 20 N  5 N  5kg.a     FNet  m3a FNet  m2a   a  4m / s 2 a  3m / s 2        T2  Ff 3  m3.a T1  T2  Ff 2  m2 .a  For Reaction Force, For Reaction Force, T2  40 N  20kg.2m / s 2 T1  80 N  40 N   20kg .2m / s 2R; Choose one of the   R; Choose one of the T2  80 N T2  200 Nmasses, ex; m2 masses, ex; m2        FNet  R  m2 a FNet  R  F f 2  m2 a   R  2kg.4m / s 2  8 N R  2 N  2kg.3m / s 2  8 N
12. 12. Ex.: Two masses are F ? Ex. ( Atwood Machine) :connected to each other When the system isas shown in figure are released , find the tensionpulled up by force F. If in the rope in N, T= ? the tension in the cord m1  5kg a For all system;is 42N what is the   force F? W1 FNet  mT a     For m 2 ; FNet  m2a  T  42N  a W1  W2  m1  m2 .a     T T  W2  m2 .a  150 N  50 N  (15kg  5kg ).a T m2  3kg 42 N  30 N  3kg.a a  5m / s 2   m2  5kg m1  15kg a  4m / s 2  W2 For m1 ; FNet  m1a       For all system; FNet  mT a W1  T  m1.a W2 W1        F  W1  W2  m1  m2 .a 150 N  T  15kg .5m / s 2   F  50 N  30 N   5kg  3kg .4m / s 2 T  75N  F  112 N
13. 13. Ex.: Find acceleration of the system and T1 & T2 Ex.: When the system is released, what is theWhen the coefficient of friction between 10kg of Acceleration of the system. The coefficientmass and the surface,µ=0 and µ=0.1? of friction is µ=0,1.   m3  10kg   a  T2 T1 a N  m1  2kg T     W1sin 370 2.10.0,6  12 N . T2 T1 m2  2kg  F f  N  0,1.16 N  1,6 N W1. cos 370  m1  6kg W1 370m2  4kg  W2  20 N N  W1. cos 37  2.10.0,8  16 N 0    W1  W2 For all system; FNet  mT a       W2  W1. sin 37  Ff  m1  m2 .a 0For all system; FNet  mT a    20 N  12 N  1,6 N  (2kg  2kg ).a W1  W2  m1  m2  m3 .a a  1,6m / s 2 60 N  40 N  (6kg  4kg  10kg ).a a  1m / s 2 For m1 ; For m 2 ;     FNet  m1a FNet  m2a       W1  T1  m1.a T2  W2  m2 .a  60 N  T  6kg .1m / s 2 T2  40  4kg.1m / s 2   T1  54 N T2  44 N
14. 14. Ex.: Find the velocities of the objects K and L Ex.: In the figure the coefficient of kinetic friction isshown in figure .3 seconds later, after they are  µ for all interacting surfaces. Find the accelerationsreleased.   N of the blocks a. a1 m1  4kg  N1  W1  m1g T1 N1 N 2 N 2  W1  W2  m1  m2 g       a2  2a1 T1 Ff T a       T1   0,1 W1  Ff 1  m1 F  T2  2T1 T f1 a  F f  N W1 m F  T2  0,1.40 N   2  Ff 2 W2 a2 m2  8kg  4N   F f 1  N1  10m1 Ff 2  N 2  10m1  m2   W2 For m1 ; For m 2 ; For m1 ; For m 2 ;         FNet  m1a FNet  m2a FNet  m1a1 FNet  m2a2               T  Ff 1  m1.a F  T  Ff 2  Ff 1  m2 .a T1  Ff  m1.a1 W2  T2  m2 .a2  F  Ff 1  m1a  Ff 2  Ff 1  m2 .a T1  4  4a1 80  T2  8.a2 F  m1g  m1a  m1  m2 g  m1g  m2 .a  40  T1  8.a1 80  2T1  8.2a1 12a1  36 F  m1g  m1a  m1g  m2 g  m1g  m2 .a a1  3m / s 2 a2  6m / s 2 F  3m1g  m1a  m2 g  m2 .a v1  a1.t v2  a2 .t F  3m1  m2 g  m1  m2 .a  3m / s 2 .3s  6m / s 2 .3s F  3m1  m2   18m / s a g  9m / s m1  m2 
15. 15. Ex.: The objects K and L are released in africtionless system as shown in figure. Find thetension T on the rope which joins the objects K andL . mK=mL=1kg  T   a  NK NL K   WK . sin 530 L  WK . cos 530  0 WL . cos 370  WL . sin 37 WK 0  0W 53 37 L  For all system; FNet  mT a    WK sin 530  WL sin 370  mK  mL .a 10.0,8  10.0,6  (1kg  1kg ).a a  1m / s 2
16. 16. CHECKING OF UNDERSTANDING (HOMEWORK) The Answers of them should be placed just after this Chapter before the Next Chapter.1. What is Force? How many kinds of Forces are there?2. Why do we need to use the kind of ``NORMAL FORCE``?3. What are the factors that the force of friction depends on?2. What is the difference between uniform motion and uniformly accelerated motion?3. Driving on an icy high way is particularly dangerous. Why?4. What is INERTIA and its Principle? Give some examples5. You hit a ball with your foot. Since the forces are F and –F can you say the total force is zero? Then why does the ball start to move?6. The x-component of the projected objects is always constant , why?7. Mostly which Law of Motion is used to solve Dynamics Problems?8. What is Atwood Machine? And how do we find the acceleration of it?9. Can we feel ``Weightlessness`` on Earth? How?
17. 17.  00 F ext F ext