# Momentum problem: object struck with stick

oneamp

## Homework Statement

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)?

## 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

Homework Helper
Gold Member
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.

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

Mentor
What did I do wrong?
Units. I suspect that you converted to seconds, when the equation was meant to be in ms.

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.

Mentor
I integrated with limits of 0 to 0.00274, so it's in seconds.
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.)

oneamp
Thank you.