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

1. Abhisar

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

2. anonymous

I got 0.6 doing a different way.

3. anonymous

You should not have solved it without someone posting :(

4. Abhisar

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

5. anonymous

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

6. anonymous

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

7. anonymous

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.

8. Abhisar

Cool c: