Question

1. imagine that two balls are covered in tape with the sticky side out. when one ball is rolled into the other, they stick together. model this collision below. how would the motion of the balls change?

Explanation:

Step1: Identify the type of collision

This is an in - elastic collision (since the balls stick together).

Step2: Apply the law of conservation of momentum

Let the mass of the first ball be $m_1$ with initial velocity $v_1$ and the mass of the second ball be $m_2$ with initial velocity $v_2$. According to the law of conservation of momentum $m_1v_1 + m_2v_2=(m_1 + m_2)v_f$, where $v_f$ is the final velocity of the combined balls.

Step3: Analyze the change in motion

If one ball was initially at rest ($v_2 = 0$), then $m_1v_1=(m_1 + m_2)v_f$, and $v_f=\frac{m_1}{m_1 + m_2}v_1$. The combined balls will move with a slower velocity than the initially moving ball. In general, the two balls combine into one object with a combined mass, and their overall motion is determined by the initial momenta of the individual balls. The direction of motion of the combined balls is the same as the direction of the net initial momentum of the two - ball system.

Answer:

The two balls combine into one object with a combined mass. Their motion is determined by the law of conservation of momentum. If one ball was initially at rest, the combined balls will move with a slower velocity than the initially moving ball. The direction of motion of the combined balls is the same as the direction of the net initial momentum of the two - ball system.