What is the Work Done by Force F on a Moving Object?

[WahooMan]

Homework Statement

A 4.0 kg object moving in two dimensions initially has a velocity V1 = (11.0i + 20.0j)m/s. A net force F then acts on the object for 2.0s, after which the object's velocity is V2 = (16.0i + 32.0j)m/s. Determine the work done by F on the object. Enter your answers numerically separated by a comma.

Homework Equations

W = (1/2)(m)(V2^2 - V1^2)
or
W = (Integral from A to B) of F * dl

The Attempt at a Solution

I tried the first equation and got

W = (1/2)(4.0)(1280 - 521) = 1518J

but my instructions are to enter my answers (plural) separated by a comma, which I can't figure out because I don't understand why I would have two answers.

Also, I don't quite understand how to do the integral equation. Would A = 0s and B = 2.0s? How do you integrate 13.0 N (what I got for the net force) with respect to l?

 

[WahooMan]

Any help at all would be appreciated..

 

[PhanthomJay]

Homework Statement

A 4.0 kg object moving in two dimensions initially has a velocity V1 = (11.0i + 20.0j)m/s. A net force F then acts on the object for 2.0s, after which the object's velocity is V2 = (16.0i + 32.0j)m/s. Determine the work done by F on the object. Enter your answers numerically separated by a comma.

Homework Equations

W = (1/2)(m)(V2^2 - V1^2)
or
W = (Integral from A to B) of F * dl

The Attempt at a Solution

I tried the first equation and got

W = (1/2)(4.0)(1280 - 521) = 1518J
but my instructions are to enter my answers (plural) separated by a comma, which I can't figure out because I don't understand why I would have two answers.

Yes, good, this is correct. I don't know what that comma is all about, either.

Also, I don't quite understand how to do the integral equation. Would A = 0s and B = 2.0s? How do you integrate 13.0 N (what I got for the net force) with respect to l?

This is the harder way to do it, but if you are integrating an Fdx term, the integral must be from x =0 to x = x, but since the force is constant, the work done is just F_net(d), where d is the distance traveled in 2 seconds. That involves the use of F_net =ma to find the acceleration, and then using the kinematic equations of motion to find d. Your calc for the net force, however, is incorrect.