Question

A 1 Kg ball falls from a height of 25 cm and rebounds upto a height of 9 cm. The coefficient of restitution is

Answer 1

Umm.. I got it this. I'll solve it though if any one else needs it.

Final velocity of the ball will be 2.21 m/s [using \(\sf V^2=U^2+2aS\)]

Similarly, the ball's initial velocity after the collision will be 1.32 m/s [ [using \(\sf V^2=U^2+2aS\)]

Coefficient of restitution = \(\sf \frac{relative~velocity~after~the~collision}{relative~velocity~before~the~collision}\)

Since, ground is our frame of reference, relative velocities before and after collision will become 2.21 and 1.32


Substituting the values you get 0.6

Answer 2

I got 0.6 doing a different way.

Answer 3

You should not have solved it without someone posting :(

Answer 4

@shalante ,Why don't you post your way too, we will all get to learn different ways c:

Answer 5

@Abhisar
I'll post in a while since I am in class right now.

Answer 6

It is just the kinetic and potential energy way

It is an isolated system so
\[\Delta KE +\Delta PE=0\]
\[\frac{ 1 }{ 2 }mv _{f}^2-\frac{ 1 }{ 2 }mv _{i}^2+mgh _{f}-mgh _{i}=0\]
\[\frac{ 1 }{ 2}mv _{i}^2+mgh _{i}=\frac{ 1 }{ 2 }mv _{f}^2+mgh _{f}\]
Cancel all m
\[\frac{ 1 }{ 2 }v _{i}^2+gh _{i}=\frac{ 1 }{ 2}v _{f}^2+gh _{f}\]
L
In a coefficient of restitution, when an object collides with a fixed object, the formula becomes similar to this
\[coefficient of restiuition=\frac{ final velocity after collision }{ final velocity before collision }\]

Convert 25 cm to 0.25 m and 9 cm to 0.09 m and since acceleration is in meters
Time to plug and chug!
To get final velocity before collision let \[v _{i}=0m/s, g=9.8 m/s ^{2} h _{i}=0.25m, h _{f}=0m\]
Solve for final velocity
So final velocity before collision is 2.21m/s

To get final velocity after collision let \[v _{i}=0m/s, g=-9.8m/s^2, h _{i}=0m, h _{f}=0.09m\]
So final velocity before collision is 1.32m/s

\[COR=\frac{ 1.32m/s }{ 2.21m/s }-0.6\]

Answer 7

Oops meant to be
\[COR=\frac{ 1.32m/s }{ 2.21m/s }=0.6\]
Made a typo by putting a subtraction sign when it is supposed to be an equal sign.
Well, this way is longer, but probably more useful in other problems that a bit similar to this where your formula does not work.

Answer 8

Cool c: