# Help with Impulse, Free-Fall, and Momentum?

1. Dec 3, 2011

Hello everyone.

In Physics class, we did a lab where we dropped golf balls into a box of sand from a height of 9 ft (or 2.743 meters). The golf ball had a mass of .046 kg. We were not allowed to time the drop so these were the only givens. We also measured the depth of the "crater" the golf ball made in the sand. The depth was .0174 meters.

The first question asked for the acceleration of the ball while slowing down in the sand.

The second asked for the time to stop in the sand.

The third asked for the impulse the sand applied to the golf ball.

For the first question, I used the equation $v=\sqrt{2gh}$ to find the final velocity of the ball. Plugging in the number 2.743 m for h, I got about 7.34 m/s for vf.

I then used the equation vf2= vi2 + 2aΔx to find the acceleration. I assumed, since the ball was dropped, the golf ball had an initial velocity of 0 m/s. I used 2.743 m + depth for Δx.

After plugging in everything and solving, I found the acceleration to be 9.75 m/s2

I then used the acceleration to solve for time:
a= $\frac{Δv}{Δt}$.

I found t to be .75215 seconds.

For Impulse, I used the equation I=FΔt, and since ƩF=ma, I solved for F, which was about .449 Newtons, and got impulse to be .337 Ns upward (since it asked the impulse the sand applied to the ball).

Then it asked another question relating to the lab:

Assuming a refrigerator-sized meteorite (100 kg) strikes a sand desert on the earth at a terminal velocity of 300 m/s, predict the crater's depth based on data gathered in this lab.

I feel like there's not enough information to solve this problem. Is there something I'm missing?

I first found the Impulse by multiplying the terminal velocity with the mass (would it be right to assume that the meteorite started at rest?). The impulse I calculated came out to be 30000 Ns.

I used $v=\sqrt{2gh}$ again to find the h, and it came out to be 4587.16 m but I'm clueless as what to do next.

I really appreciate anyone's help--it's been giving me a lot of trouble.

Thank you.

2. Dec 3, 2011

### Staff: Mentor

Okay.
They're looking for the acceleration of the ball while slowing down in the sand. So the distance involved is the depth of the crater, and its initial velocity should be the velocity the ball achieved during its fall from 9ft to the sand's surface. You'll have to redo your calculations from this point.

3. Dec 3, 2011

So vi would be 7.34 m/s and v final would be 0 m/s? If so, would it make sense for the acceleration to be more than gravity?

4. Dec 3, 2011

### Staff: Mentor

Yes, and I would expect it to be MUCH greater than g. After all, g 'happened' over 9 feet and gave you a velocity change of about 7 m/s, now you're going to remove all that velocity (kinetic energy) over a short distance of less than an inch, and in much less time.

5. Dec 3, 2011

Thank you very much for all your help. I can get the three questions above but I'm still having trouble with the meteorite one.

6. Dec 3, 2011

### tamir102

y dont u ratio everything... to the size of the golf ball and solve like u did the golf ball problem

7. Dec 3, 2011

### Staff: Mentor

It's pretty difficult extrapolating from one test case! If you had data for crater size and depth for many drop heights (potential energies) , then you might stand a chance of making an informed extrapolation.

As it is you'll have to decide what factor(s) you think will influence the crater depth that you can scale appropriately. Since you're only given estimates for size, mass, and speed of the meteorite, presumably the factors will be related to them.

8. Dec 3, 2011

^There were three trials, all of which gave a result of .0174 meters as the depth.

A hint the professor gave was that one thing would be exactly the same between both trials, but I'm not sure what. It seemed like she emphasized the word sand, so I would guess impulse but wouldn't a larger mass yield a larger impulse?

9. Dec 3, 2011

### Staff: Mentor

Yes, they've made it clear that sand is common in the scenarios. But it might be beyond the scope of the question to try to draw conclusions from things like sand density or viscosity without some major investigation!

I admit that I don't know what your teacher had in mind. But I have a strong feeling that it will be related to energy and force.

Maybe it would be worthwhile to list the things that one might compare between the scenarios, and contemplate their relationships to energy and forces.