# Momentum problem: object struck with stick

1. Oct 15, 2013

### oneamp

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

A stationary 1.67 kg object is struck by a stick. The object experiencees a horizontal force given by F = at - bt^3, where t is the time in milliseconds from the instant the stick first contacts the object. if a = 1500 N/ms and b = 20 N / ms^3, what is the speed of the object just after it comes away from the stick (t = 2.74 ms)?

2. Relevant equations

3. The attempt at a solution

I integrated to come up with the impulse J_x. Then I added it to p_0 = 0. The integral solved at the limits of 0 to 0.00274 = 0.005631. I divided this by the mass 1.67 to get the velocity. This gave v = 0.003372 which is not right...

What did I do wrong?

Thanks

2. Oct 15, 2013

### CWatters

I'm rusty but shouldn't you divide by the mass before integrating or doesn't that make a difference?

Newton says

Force = mass * acceleration
so
acceleration = force / mass

Then integrate to give velocity.

3. Oct 15, 2013

### oneamp

I'm integrating to get an impulse, then using it to get velocity from the momentum equation. The problem is about momentum.

4. Oct 15, 2013

### Staff: Mentor

Units. I suspect that you converted to seconds, when the equation was meant to be in ms.

5. Oct 15, 2013

### oneamp

I integrated with limits of 0 to 0.00274, so it's in seconds. So that result should be J_x, and dividing out mass should give velocity. I don't see where I could have messed up units, offhand.

6. Oct 15, 2013

### Staff: Mentor

Yes, but the t in the equation is in ms. Look at the units of the parameters a & b.

For you to use seconds you must first convert the equation to use seconds. (Or just stick to ms.)

7. Oct 15, 2013

Thank you.