A ball is dropped down to the floor and bounces back up to the same height. (we are assuming a "perfect" ball.) What is the change in the momentum?
the change would be ZERO right? If the momentum was zero to begin with then there is zero change.
Yes,
gravity does positive work on the way down and negative on the way back up leading to net zero
That is correct. The change in momentum would be zero. Since the ball starts with zero momentum when it is dropped, and when it bounces back up to the same height, it comes to a stop momentarily before reversing direction, its final momentum is also zero. Therefore, the change in momentum is zero.
Indeed, the change in momentum would be zero in this scenario.
To understand why, let's first define momentum. Momentum is the product of an object's mass and its velocity. In equation form, momentum (p) can be expressed as:
p = m * v
Where "p" is momentum, "m" is mass, and "v" is velocity.
When the ball is dropped from a certain height, it gains downward velocity due to the force of gravity acting on it. As it falls and eventually reaches the floor, its velocity increases, resulting in a non-zero momentum. When the ball bounces back up, it loses its downward velocity and gains upward velocity, but its mass remains the same.
However, since the ball reaches the same height as its initial drop, the magnitude of its velocity is the same in both directions – downward and upward. As momentum is a vector quantity, it takes into account both the magnitude and direction. Therefore, if the magnitudes of the velocities are the same, the momenta in both directions cancel out, resulting in a net change of zero.
In simple terms, when the ball bounces back up to the same height, it gains an equal amount of momentum in the opposite direction. Thus, the change in momentum is zero.