Two golf balls of equal size and mass are released simultaneously from the roof of a building. One of the balls has a smooth surface while the other one has grooves on it. They then hit on a hard and horizontal plane on the floor. Assume that the golf balls are not worn after colliding with the hard plane and the effect of air resistance is considered, describe and explain which ball can reach a greater height after rebound.

it would have to be a very tall building to notice these effects.

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So does it mean that the ball with grooves can reach a higher velocity and rebound to a greater height?

To determine which ball can reach a greater height after rebound, we need to understand the concept of conservation of energy. The total mechanical energy of a system remains constant when only conservative forces, such as gravity, are acting on it.

When the golf balls are dropped from the roof, they possess potential energy due to their height above the ground. As they fall, this potential energy is converted into kinetic energy, which is the energy of motion. When the balls hit the hard and horizontal plane on the floor, some of their kinetic energy is converted into other forms of energy, such as sound and heat.

The key factor here is that the golf balls remain intact and are not worn after colliding with the hard plane. This means that both balls experience the same amount of kinetic energy loss upon impact.

Now, let's consider the smooth-surfaced ball first. Due to its smooth surface, it encounters minimal friction during the collision, resulting in a smaller loss of kinetic energy. Consequently, a significant amount of kinetic energy can be converted back into potential energy, allowing the ball to rebound to a greater height.

On the other hand, the ball with grooves on its surface experiences more friction during the collision due to increased contact area. This higher friction results in a larger loss of kinetic energy. As a result, less kinetic energy is available to convert back into potential energy, thus limiting the height it can reach after rebound.

In conclusion, the golf ball with the smooth surface can reach a greater height after rebound compared to the one with grooves, due to its ability to conserve more of its initial kinetic energy.