Newton's Third Law of Motion

Momentum and collisions
Tow types of collisions can take place between objects, elastic and inelastic. We will look at the definitions of each later but for the moment it is necessary to stress that, whenever objects collide in the absence of an external force the net momentum of both objects before collision is equal to the net momentum of the objects after collision.
When objects collide without been permanently deformed or generating heat the collision is said to be elastic. Take the example of two billiard balls colliding. We see that momentum is transferred completely from one billiard ball to the other. If the balls have the same mass then the speed of the first ball will be the same as that of the second ball.

 

 

If the objects differ in mass so will their speeds differ after collision. Let's not forget that the net momentum of both balls should be the same before and after collision. So of the 10 g blue ball travelling at an unknown velocity strikes the stationary 1 g orange ball, the orange ball will surely have to travel at a greater velocity after the collision in order for the net momentum to be the same.

Consider the animation on the right showing an elastic collision between two objects. What is the initial velocity of the blue ball?

Momentum is conserved, so the net momentum before collision equals the net momentum after collision. Since the orange ball is stationary its momentum is 0. The only momentum of the system before collision is due to the moving blue ball. So we can write the expression below.

Mass(blue ball) X velocity(blue ball) = Mass(orange ball) X velocity(orange ball)

=> 0.01 Kg X V(blue ball) = 0.001 Kg X 30 m/s

=> V(blue ball) = (0.001 Kg X 30 m/s) 0.01 Kg

=> V(blue ball) = 3 m/s
A collision which results in objects becoming distorted and generating heat is known as an inelastic collision. However, the conservation of momentum still applies.
Consider the animation on the right showing an inelastic collision between two objects. If the orange ball has a mass of 6 kilograms can you predict the mass of the blue ball?

Momentum is conserved, so the net momentum before collision equals the net momentum after collision. Since the blue ball is stationary its momentum is 0. The only momentum of the system before collision is due to the moving orange ball. So we can write the expression below.

Mass(coupled balls) X velocity(coupled ball) = Mass(orange ball) X velocity(orange ball)

=> Mass(coupled balls) X 1 m/s = 6Kg X 2m/s

=> Mass(coupled balls)= (6Kg X 2m/s) / 1 m/s

=> Mass(coupled balls)= 12 Kg

=> so the blue ball also has a mass of 6 Kg.

1) Look at the video on the right. It shows collisions on a frictionless surface. Two skaters of different mass approach each other on a collision course. After collision the speed of the skater with the larger mass is 0 while the lighter skater is pushed backwards.

a) What should the lighter skater do to prevent being pushed backwards?

b) Why is weight training essential for rugby players?

Consider a skater approaching another skater, who is stationary, on a collision course. One weighs 120 kg and travels at 3 m/s while the other weighs 80 kg and travels at 0 m/s.

2) What is the total momentum of the system before the collision?

3) What is the total momentum after the collision?

4) If at the end of the collision the larger skater has a speed of 0 m/s what is the speed of the smaller, 80 kg, skater?