# Calculus-based physics mechanics

1. Sep 11, 2004

### dqasem

Calculus-based physics....mechanics

I'm having a little trouble with this problem...

"A small glass ball is projected straight up in an evacuated tube (no air resistance) and then falls back down. During its motion it passed both an upper and a lower timer that are separted by a distance H.

Let TsubL be the time interval between the two passes across the lower timer, and TsubU be the time interval between the two passages across the upper timer.

Find an expression for the acceleration of gravity, g, in terms of H, TsubL, and TsubU.

Any help would be appreciated, but thorough explanation would be a plus. Thanks everybody.

2. Sep 11, 2004

### Tide

For any given vertical location the time interval between (upward and downward) crossings is $\Delta t = \frac {2v}{g}$. If the initial speed is $v_0$ then, for a given height, $v = \sqrt {v_0^2 - 2gy}$ and using the information provided we have
$$g^2 T_L^2 = 4 \left( v_0^2 - 2g y_L \right)$$
$$g^2 T_U^2 = 4 \left( v_0^2 - 2g y_U \right)$$
Now subtract the equations and solve for g!

3. Sep 11, 2004

### dqasem

Thanks a lot Tide, but I don't think I am allowed to use acceleration due to gravity in the equations, because i am trying to define g. It's like using a word in its own definition. I don't think my teacher will let it fly.

4. Sep 11, 2004

### Tide

I don't think that is what your teacher means. He or she is asking you to calculate the value of g which means it becomes an unknown value in your equations and you must solve for it. That is what is meant by "find an expression for."