# A rod kept inside a cart

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1. Mar 12, 2016

### Titan97

1. The problem statement, all variables and given/known data

A rod of mass m is attached on the ceiling inside a cart of mass 6m kept at rest. Length of rod is L. Find the velocity of rod with respect to cart when the rod becomes vertical after releasing it. The rod is free to rotate about its point of suspension.

2. Relevant equations
Conservation of energy and momentum

3. The attempt at a solution
With respect to earth, let velocity of center of mass of rod be $v_1$ and velocity of cart be $v_2$.
Using COE,
$$mg\frac{l}{2}=\frac{1}{2}mv_1^2+\frac{1}{2}(6m)v_2^2$$
Since centre of mass remains at rest, $mv_1=6mv_2$
$$V_1=\sqrt{\frac{7}{6}gl}$$
So $v_{\text{rel}}=\frac{v}{6}+v$
But I am not getting the correct answer.

Last edited: Mar 12, 2016
2. Mar 12, 2016

### TSny

Is one end of the rod attached to the ceiling of the cart so that the rod is free to rotate about this end?
Did you account for all of the KE of the rod?

Also, the problem statement doesn't specify which point of the rod is used when finding the "velocity of rod with respect to cart".

Last edited: Mar 12, 2016
3. Mar 12, 2016

### Titan97

@TSny question edited. They have used concept of reduced mass to solve it. But wrong in my method?

4. Mar 12, 2016

### TSny

You have left out some of the KE of the rod.

5. Mar 12, 2016

### Titan97

Oh. Is it the rotational kinetic energy?

6. Mar 12, 2016

Yes.

7. May 8, 2016

### conscience

Hello , I get $\frac{\sqrt{21gl}}{5}$ as the answer .Is this what I should be getting ?

8. May 8, 2016

### TSny

Yes, I believe that is the correct speed of the center of the rod relative to the cart when the rod is vertical.

9. May 8, 2016

### conscience

Thanks

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