First slide

Coefficient of restitution

Question

A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is

Moderate

A

$h (\frac{1 + e^{2}}{1 - e^{2}})$
B

$h (\frac{1 - e^{2}}{1 + e^{2}})$
C

$\frac{h}{2} (\frac{1 - e^{2}}{1 + e^{2}})$
D

$\frac{h}{2} (\frac{1 + e^{2}}{1 - e^{2}})$

Solution

Particle falls from height ft then formula for height covered by it in nth rebound is given by
$h_{n} = {he}^{2 n}$
where e = coefficient of restitution, n = No. of rebound
Total distance travelled by particle before rebounding has stopped:
$\begin{array}{l} H = h + 2 h_{1} + 2 h_{2} + 2 h_{3} + 2 h_{n} + \dots \dots \\ = h + 2 {he}^{2} + 2 {he}^{4} + 2 {he}^{6} + 2 {he}^{8} + \dots \dots \end{array}$
$\begin{array}{l} = h + 2 h (e^{2} + e^{4} + e^{6} + e^{8} + \dots \dots) \\ = h + 2 h [\frac{e^{2}}{1 - e^{2}}] = h [1 + \frac{2 e^{2}}{1 - e^{2}}] = h (\frac{1 + e^{2}}{1 - e^{2}}) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App