Ind the distance traveled by the ball

[corpuzdawn]

A ceramic ball of mass m falls form rest a distance h[0] above a horizontal ceramic surface. The subsequent motion of the ball is purely vertical, bouncing ONLY on one spot on the surface. If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.


is the distance traveled 0? because the ball only bounces at one spot?

 

[cepheid]

is the distance traveled 0? because the ball only bounces at one spot?

NO, they want you to find the vertical distance traveled by the ball.

 

[rcgldr]

If the coefficient of restitution between the ball and surface halves after every bounce.

My guess is this should be "the coefficient of restitution results in the height of the ball being halved after every bounce". The coeffiecient is constant, but the height of the ball is halved on each bounce. If the coefficient is halved, then you'd need to know the initial coefficient of restitution on the first bounce.

 

[sophiecentaur]

My guess is this should be "the coefficient of restitution results in the height of the ball being halved after every bounce". The coeffiecient is constant, but the height of the ball is halved on each bounce. If the coefficient is halved, then you'd need to know the initial coefficient of restitution on the first bounce.

Take care here.
If the coefficient of restitution is 0.5 then the velocity will be halved. What does that say about the Kinetic Energy remaining and what does that say about the Height of the subsequent bounce?

 

[corpuzdawn]

Take care here.
If the coefficient of restitution is 0.5 then the velocity will be halved. What does that say about the Kinetic Energy remaining and what does that say about the Height of the subsequent bounce?

if the velocity is halved.. the KE is also halved... which means... the height is quartered?

 

[sophiecentaur]

What is the formula for ke?

 

[corpuzdawn]

oops. sorry. KE= [1/2]mv^2 so... the KE is quartered?

 

[sophiecentaur]

That's better. So height is a quarter, too. Mgh = KE

 

[corpuzdawn]

so that's the answer? the distance traveled is... h[0]/4

 

[sophiecentaur]

Yep.
That 50% gives an over-optimistic view of what's really going on. In fact, 3/4 of the original energy's lost.

 

[rcgldr]

My guess is this should be "the coefficient of restitution results in the height of the ball being halved after every bounce". The coeffiecient is constant, but the height of the ball is halved on each bounce. If the coefficient is halved, then you'd need to know the initial coefficient of restitution on the first bounce.

If the coefficient of restitution is 0.5 then the velocity will be halved. What does that say about the Kinetic Energy remaining and what does that say about the Height of the subsequent bounce?

Sorry for my somwhat confusing response, C_r (coefficient of restitution) = ratio of (speed after bounce) / (speed before bounce) or sqrt( (height after bounce) / (height before bounce) ).

The issue I was trying to point out is tha the OP states that C_r is halved on each bounce, versus stating that the speed or the height was being halved on each bounce. My guess is that the original problem meant that the speed (C_r = .5) or the height (C_r = sqrt(.5) ~= .7071) was halved on each bounce, not the C_r itself.

 

[sophiecentaur]

Absolutely. The COR can hardly change on each bounce.

 

[corpuzdawn]

That's better. So height is a quarter, too. Mgh = KE

why is KE=mgh? is it PE=mgh?

 

[sophiecentaur]

mass X g X height ? Not familiar?

btw, if they had wanted the aswer for "distance traveled" to be zero, they would probably have said "displacement" which is a vector quantity. Distance is a scalar.

 

[corpuzdawn]

sorry... but I always thought that mgh is PE. why is KE=mgh again?

 

[sophiecentaur]

Oh I see what you mean. The KE becomes mgh (at the top) was what I meant. (conservation)