DYNAMICS & NEWTON’S LAW Topics:  Force  Newton’s Law of Motion  Application of Newton’s Law

1.Kinematics: is the branch of mechanics which studies a motion that is observed based on physical quantities such as position, distance, displacement, speed, velocity and acceleration with no consider on what causes the motion (force). Examples: Uniform rectilinear motion of a particle Accelerated uniform rectilinear motion Vertical motion Parabolic motion etc

2.Dynamics: is the branch of mechanics concernings motion of object with regard to what causes the motion (force). Examples: Motion of object on a smooth plane Motion of object on a rough plane Motion of object on an inclined plane Motion of object that connected by a pulley Lift etc

Force  is a quantity that can change the state of motions (e.g., golf game), forms (e.g., bread batter making) and sizes (e.g.,spring) of an object.  force can be a push or a pull upon an object.

The first Newton’s Law In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line). V= 0 a = 0 At rest GLB

The 2 nd Newton’s Law So, What will happen, if the resultant of Force is not ZERO ?

m F F a a = ? a~F a ~ 1/m

For example :

Sample problem What is the acceleration resulted when a force resultant of 12 N is applied to an object which is 6 kg in mass? Solution:

3. Newton’s Third Law If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1: F action = - F reaction

application Normal force Weight On horisontal plane : N = W θ w w cosθ θ w sinθ N On inclined plane : N = W cosθ

W = mg N

w w’ T T T = W F fkfk

There two kinds of frictional force Static frictional force: is a frictional force exerts on the object which is at rest. Kinetic frictional force: is a frictional force works on the moving object. f s = static frictional force (N) f k = kinetic frictional force (N) μ s = coefficient of static friction μ k = coefficient of kinetic friction μ s > μk, So … fs > fk 0 ≤ μ ≤ 1 μ = 0 (smooth) μ > 0 (rough)

Friction force F fs maks

Friction force F fs maks If F < fs maks  at rest If F = fs maks  Exactly will be move If F > fs maks  Object is moving fs maks = μ s N

Sample Problem Calculate the acceleration of system, if Force applied is : (g=10m/s 2 ) a. 50 N b. 52 N c. 60 N d. 70 N e. 61 N 12 kg F μS= 0,5 μk = 0,3

Sample problem A car is 800 kg in mass, from rest it is accelerated with a constant acceleration, after 2 seconds the car travels at a distance of 20 m. Determine the force resulted by the car if during the motion it experiences the frictional force of 200 N! Solution: Because a = constant, then the car moves in accelerated uniform rectilinear motion, therefore the acceleration (a) can be determined by;

Sample problem: Determine the normal force of cube A, B, and C, if m = 10 kg and g = 9.8 m/s 2 ! N=? w m A w m B w m C 20 N 15 N

 Cube A Solution: Because on cube A exerts no outside force, N = w = m.g = (10kg)(9.8m/s 2 ) = 98 N  Cube B Because on cube B works an outside force of 20 N, N = Ʃ F = w + F = m.g + F = (10kg)(9.8m/s 2 ) + 20 N = 118 N

 Cube C Because on cube C works an outside force of 15 N, N = Ʃ F = w - F = m.g - F = (10kg)(9.8m/s 2 ) - 15 N = 83 N

Problem 1 3 kg 7 kg Calculate the acceleration of system and stress of string (percepatan system dan tegangan tali ) if flour is smooth ( jika lantai licin ) g = 10 m/s 2

Answer 3 kg 7 kg w=mg = 30N W 2 =70N N Because the floor is smooth, μ=0, f s =0

Problem 3 kg 7 kg Calculate the acceleration of system and stress of string (percepatan system dan tegangan tali ) if flour is rough ( jika lantai kasar ) g = 10 m/s 2 μ s =0,4 μ k =0,3

Answer 3 kg 7 kg w=mg = 30N W 2 =70N N μ s =0,4, f smaks =0,4.70 = 28N μ s =0,4 μ k =0,3 f k =μ k.N = 0,3.70=21N

Problem 2 Determine the acceleration (a) and tension of each string ! m 1 = 4 Kg m 2 = 6 Kg There isn’t Friction between string and pulley

Determine the acceleration (a) and tension of each string ! If the inclined plane is smooth. ( g = 10 m/s 2 ) 3Kg 2Kg 30 o

Answer 3Kg 2Kg 30 o W1 T W2 w2sin30 o w 2 cos30 o T

Tension of string (T) 3Kg 2Kg 30 o W1 T W2 w2sin30 o w 2 cos30 o T