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 travelled 0? because the ball only bounces at one spot?

cepheid

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

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.

sophiecentaur

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

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

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

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)