A quantity called the coefficient of restitution is a common measure of the elas
ID: 2170433 • Letter: A
Question
A quantity called the coefficient of restitution is a common measure of the elasticity of a collisionThis coefficient is
CR = -(v1f - v2f)/(v1i - v2i)
There will be two objects colliding, a dropped ball and the Earth. The Earth does not change its motion measurably upon collision, so we can take v2f = v2i =0. Then:
CR = -v1f/v1i or CR = |v1f/v1i|
You are not be measuring the speeds directly, but rather measuring the height the ball is dropped from and the height it bounces back up to.
a) How is the height the ball is dropped from (hdrop) related to v1i, the speed just before it hits the ground?
b) How is the height the ball bounces back to (hbounce) related to v1f, the speed just after it hits the ground?
c) Using your answers to the previous two questions, derive an expression for the coefficient of restitution in terms of hdrop and hbounce instead of v1f and v1i.
**Please help!!! I will vote lifesaver, thank you!**
Explanation / Answer
we know v^2=u^2+2ah when the ball is dropped from its u=0,h=hdrop,v=v1i,a=g so v1i=sqrt(2*g*hdrop) similarlly for the second part u=v1f,v=0,a=-g,h=hbounce putting all in euation we get 0=v1f^2-2*g*hbounce =>v1f=sqrt(2*g*hbounce) CR=|v1f/v1i| putting value of v1i and v1f CR=|sqrt(hbounce/hdrop)|