Elastic Collision 5: Acceleration at B & Magnitude Explained

[Karol]

Homework Statement

A ball bounces on the floor with elastic collisions like in the drawing.
The collisions take a short time in comparison to the travel between the collisions.
What is the direction of the acceleration at point B?
Why is the magnitude of the acceleration at point B bigger than at point A?

Homework Equations

In elastic collision with the floor the rebound velocity is the same as the approach velocity and energy is conserved.

The Attempt at a Solution

Because the ball travels to the right with identical loops the horizontal velocity is conserved so only the vertical component of the hit velocity changes direction, so the acceleration is directed upwards.
The ball has to acquire vertical velocity and just because it is said the time for the collisions is short i can assume the acceleration is higher than g, which is at point A, but i feel this explanation isn't good.

 

[ehild]

Homework Statement

A ball bounces on the floor with elastic collisions like in the drawing.
The collisions take a short time in comparison to the travel between the collisions.
What is the direction of the acceleration at point B?
Why is the magnitude of the acceleration at point B bigger than at point A?

Homework Equations

In elastic collision with the floor the rebound velocity is the same as the approach velocity and energy is conserved.

The Attempt at a Solution

Because the ball travels to the right with identical loops the horizontal velocity is conserved so only the vertical component of the hit velocity changes direction, so the acceleration is directed upwards.

It is on the opposite way: If friction can be ignored, the floor exerts only perpendicular ( vertical) force on the ball.

The ball has to acquire vertical velocity and just because it is said the time for the collisions is short i can assume the acceleration is higher than g, which is at point A, but i feel this explanation isn't good.

It is good... but you need to be a bit more accurate. The ball has a downward vertical component of velocity before hitting the floor, and it changes into vertically upward. So the vertical component of velocity changes from -v_y to v_y, and it happens in a very short time. The average acceleration is a=Δ v_y/ Δt= 2v_y/Δt. If Δt is very short it can be quite high value, much bigger than g.

ehild

 

[_N3WTON_]

Also you may want to note that velocity is not a conserved quantity. The i component of velocity remains constant, but it is not conserved.

 

[Karol]

It isn't written in the question that friction can be neglected.
What do you mean i component of velocity? for example the x component? and why isn't velocity preserved, if all i components, x y and z remain constant?

 

[ehild]

It isn't written in the question that friction can be neglected.

It was written in the problem that the collisions were elastic. There is no loss of KE in elastic collision. So friction can not take part.

ehild