Impact of a ball due to gravity and momentum

[lacrias]

Just a quick question of of curiosity. It's basic physics but I can't remember it

Lets say you have two balls of equal mass about 3 meters up on a ledge. You let one drop straight down, it hits the ground and stops. The other one is pushed forwards with a speed of let's say 1m/s and then hits the ground further out and continues to roll.

Which ball takes more impact? If I remember correctly, each ball has separate x and y components so they both would land with the same impact, but I am not sure. Can anyone please elaborate?

Thank you!

 

[Astronuc]

Both have the same vertical velocity, but the one with a horizontal velocity has a little more kinetic energy. Velocity is a vector and horizontal and vertical components add.

The impulse from vertical impact would be the same, but horizontal compenent would provide a shear component to the impact.

If the collisions were purely elastic, but with friction, the ball with the horizontal component would spin, but both balls would bounce back to the same height.

Without friction, the ball with the horizontal velocity would not have spin but would continue to travel horizontally at the same speed (assuming we neglect air resistance).

 

[m2003]

I would like to first clarify that the term "impact" can have different meanings in this context. If we are talking about the force exerted on the ground by the ball, then both balls would have the same impact since they have the same mass and are falling from the same height. This is because the force of gravity is the same for both balls, regardless of their initial horizontal velocity.

However, if we are talking about the impact on the ground in terms of displacement or distance traveled, then the ball with the initial horizontal velocity will have a greater impact. This is because the ball will have both a vertical and horizontal component of velocity, meaning it will travel a greater distance upon hitting the ground compared to the ball that is just dropped straight down.

In terms of momentum, both balls will have the same initial momentum when they are released from the ledge. However, the ball with the initial horizontal velocity will have a greater change in momentum upon hitting the ground, as it will experience a change in both its vertical and horizontal components of velocity.

Overall, the key concept here is that the horizontal velocity of the ball does not affect the force of gravity acting on it, but it does affect its displacement and change in momentum upon impact. I hope this helps to clarify your understanding of the impact of a ball due to gravity and momentum.