to discuss the conservation laws

Newton’s laws of motion, in particular the second law, govern the instantaneous behavior of a system. They relate the forces that are acting at any instant in time to the resulting changes in motion. Conservation laws involve a different approach to mechanics, more of a “before –and – after” look at systems.

In order to discuss the conservation laws, we introduce new physical quantity, i.e linear momentum (abbreviated as p). This physical quantity will be useful in understanding collisions (automobile collisions as a special case). It is a vector. It is defined to be the product of mass (m) of an object and its velocity (v). For example, the momentum of a bicycle and rider with a total mass of 80 kilograms and a speed of 10 m/s is:

p = mv = (80 kg)( 10 m/s) = 800 kg m/s.

Newton’s Second law of Motion (alternate form): The net external force acting on an object equals the rate of change of its linear momentum.

Force = (change in momentum)/ (change in time).

Let us try to understand Example 3.1 (Page 89):

Let’s estimate the average force on a tennis ball as it is served. The ball’s mass is

0.06 kilograms, and it leaves the racket with a horizontal speed of 40 m/s. High

speed photographs indicate that the contact time is about

5 milliseconds (0.005 sec).

Because the ball starts with zero horizontal speed (and hence zero momentum), its change in momentum is

= (0.06 kg) (40 m/s) = 2.4 kg m/sec.

We define an isolated system as a system where there are no outside forces causing changes in the linear momenta of the objects. For example, once the cue ball on a pool table has been shot (given some momentum), the pool table and the balls form an isolated system.

The Law of Conservation of Linear Momentum states that the total linear momentum of an isolated system remains constant. The most important use of this law is in the analysis of collisions. Two billiard balls colliding, a traffic accident, and two skaters running into each other are familiar examples of collisions. We will limit our examples to collisions involving only two objects that are moving in one dimension (along a line)

The following statement is the key to applying the law of conservation of linear momentum to a collision: The total linear momentum of the objects in a system before the collision is EQUAL to the total linear momentum after the collision.

Let us try to understand one application of this principle, i.e an automobile collision.

1. Before the collision means the situation before the two objects have collided.
2. After the collision means the situation where the collision has taken place and the objects have moved away or they have stuck together.

This type of analysis is routinely used to reconstruct traffic accidents. It can be used to determine whether a vehicle was exceeding the speed limit before a collision.