Question

Two identical objects (such as billiard balls) have a one-dimensional collision in which one is initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. Show that both momentum and kinetic energy are conserved.

a) Momentum is conserved, kinetic energy is not.

b) Kinetic energy is conserved, momentum is not.

c) Both momentum and kinetic energy are conserved.

d) Neither momentum nor kinetic energy are conserved.

Answer 1

Both momentum and kinetic energy are conserved.

Step-by-step explanation:

In this situation, we have a one-dimensional collision between two identical objects, one initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. In this case, both momentum and kinetic energy are conserved.

Momentum is conserved because the total momentum before the collision is equal to the total momentum after the collision. Since one object is initially motionless, its momentum is zero. The other object has momentum, and after the collision, it becomes stationary while the previously stationary object gains the same momentum.

Kinetic energy is conserved because the objects have the same mass and the moving object transfers its entire kinetic energy to the previously stationary object, making it move with the same speed as the originally moving object.