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Impulse and Momentum: A Physics Lesson with Exercises, Assignments of Physics

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2020/2021

Uploaded on 05/27/2021

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LESSON 5: IMPULSE AND MOMENTUM
Introduction
The law of conservation of energy, which discussed in the previous lesson is one of several great
conservation laws in physics. Among the other quantities found to be conserved is linear momentum.
I this lesson, conservation of linear momentum and energy will be used to analyze collisions.
Collisions as between billiard or pool balls that illustrates vector law very effectively. The total vector
momentum before collision equals the total vector momentum after collisions.
Learning Outcomes
After successful completion of this lesson, you should be able to:
 Relate Newton’s second Law of Motion to impulse and momentum.
 Calculate the impulse of a force and relate it to the change in momentum.
 Distinguish between internal and external forces among interacting bodies.
 Recognize when momentum is conserved.
Apply the impulse momentum relation and the conservation of momentum to a variety of
problems involving collisions (elastic and inelastic) and other kinds of interaction between bodies.
Discussion
5.1 Linear Momentum
Momentum is a property related to an object’s motion and mass. The faster the object moves and
the larger its mass, the greater is its momentum. It is the tendency of an object to continue moving at
constant velocity and thereby encountering difficulty in bringing the object to rest. The linear
momentum p is defined quantitatively as the product of its mass m and velocity v:
Momentum = p = mv
The Unit Of Momentum is
Since velocity is a vector quantity having magnitude and direction, momentum is also a vector
quantity with magnitude and direction. The direction of an object’s momentum equals the direction of
its velocity.
5.2 Impulse
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LESSON 5: IMPULSE AND MOMENTUM

Introduction The law of conservation of energy, which discussed in the previous lesson is one of several great conservation laws in physics. Among the other quantities found to be conserved is linear momentum. I this lesson, conservation of linear momentum and energy will be used to analyze collisions. Collisions as between billiard or pool balls that illustrates vector law very effectively. The total vector momentum before collision equals the total vector momentum after collisions. Learning Outcomes After successful completion of this lesson, you should be able to:  Relate Newton’s second Law of Motion to impulse and momentum.  Calculate the impulse of a force and relate it to the change in momentum.  Distinguish between internal and external forces among interacting bodies.  Recognize when momentum is conserved.  Apply the impulse — momentum relation and the conservation of momentum to a variety of problems involving collisions (elastic and inelastic) and other kinds of interaction between bodies. Discussion 5.1 Linear Momentum Momentum is a property related to an object’s motion and mass. The faster the object moves and the larger its mass, the greater is its momentum. It is the tendency of an object to continue moving at constant velocity and thereby encountering difficulty in bringing the object to rest. The linear momentum p is defined quantitatively as the product of its mass m and velocity v : Momentum = p = mv The Unit Of Momentum is Since velocity is a vector quantity having magnitude and direction, momentum is also a vector quantity with magnitude and direction. The direction of an object’s momentum equals the direction of its velocity. 5.2 Impulse

Impulse is the product of a force acting on an object and the time that the force acts. An impulse causes the object’s momentum to change: Impulse J = F • t An equation relating the impulse of a force and the subsequent change in momentum of the object on which the force acts is derived using Newton’s Second Law of Motion and kinematics: Rearranging the terms or 5.3 Conservation of Linear Momentum As two colliding bodies interact with each other, they exert forces on each other. These are internal forces if we take the two bodies together as our system. At the same time, they may be acted upon by other external forces such as friction. The total linear momentum of a system is conserved if there is no additional external force present before, after and during the collision. The total linear momentum of a system remains constant. 5.4 Collisions When two bodies collide, internal forces are external during the short time of impact. These forces may be conservative or dissipative. If the forces are conservative, the collision is said to be elastic. In

Sample Problems with Solutions:

  1. A 2200 kg car at 35 strikes a stationary 1500 kg car and the two locked bumpers. a) What is their final common velocity just after collision? b) What percentage of the initial energy is dissipated in the collision? Given: m1 = 2200 kg , m2 = 1500 kg V1 = 35 , V2 = 0 m1V1 + m2V2 = m1U1 + m2U U1 = U2 = U

 hence, 59.5% of initial energy remains kinetic energy, and 40.5% of initial energy was dissipated during collision

  1. Suppose that in the first example, the cars have spring loaded bumpers, so that collision is perfectly elastic. a) What is the velocity of each car after the collision? b) What are the final momenta and energies? Solution: from momentum conservation
  1. A body of mass 100 g with a velocity of 10 cm/s hits another identical body at rest, and the two recoil as shown. Find U1 and U
  2. A bullet weighing 0.02 lb is fired with a nozzle velocity V1 = 2700 ft/s into a ballistic pendulum weighing 20 lbs. Find the maximum height through which it rises. Given: m1 = 0.02 lb m2 = 20 lbs U1 = U2 = U V1 = 2700 ft/s V2 = 0 ft/s
  1. A 1.5 kg ball moving at 2.0 m/s to the right collides head on with a 1.0 kg ball moving at 3.0 m/s to the left. The coefficient of restitution is 0.70. Find the speed and direction of the balls after collision.
  1. A steel ball of mass 0.514 kg is fastened to a cord 68.7 cm long and is released when the cord is horizontal. At the bottom of its path, the ball strikes a 2.6e-kg steel block initially at rest on a frictionless surface. The collision is elastic. Find (a) the speed of the ball and (b) the speed of the block, both just after the collision.