Help me with This Bouncing Ball Problem

[bloodhound]

Because i am doing a project on bouncing balls, i am also looking at a situation where the ball bounces down a stair.

 

What i need, is to find out the required value of e for this question

 

 

ok , u have a ball bouncing down a stair. forget about the horizontal stuff, u can either think of it as looking head on to the stairs. or imagine a ball bouncing on a surface, but after each bounce the surface moves down a fixed height. basically a stair. u get me rite.

 

 

if u look at the graph. we DROP a ball at rest from height H, and the ball as coeff of restitution e, all i want is the condition for e so that the blue heights are equal. or equivalently the brown heights are equal. i would prefer the blue heights.

 

Take the height of the steps to be "a" or any letter u like

 

anyway . cheers

[swansont]

If you want the bounce height relative to the stairs to be equal, then the ball has to lose the energy it gained in one step on each bounce. So if the height of a step is a, it loses mga of energy in each bounce.

[bloodhound]

but what is the condition of e so that it loses mga of energy each bounce

[lqg]

but what is the condition of e so that it loses mga of energy each bounce

because the collision with the stairs isnt absolutely elastic nor is it plastic the one that lasts is non elastic in this case e is between 0 and 1: 0<e<1

[Dave]

Euhm, the co-efficient of restitution is always inbetween 0 and 1.

[swansont]

but what is the condition of e so that it loses mga of energy each bounce

 

e is the fraction of the original energy (measured above the first step, or mgH) that is retained. You should be able to set up a simple equation with that information.

[bloodhound]

i am too lazy to work it out myself. someone do it for me

[Dave]

rofl, the idea is that we give you clues to help you work it out yourself ;-)

[bloodhound]

ok. ill have a go then.