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

AI Thread Summary
The discussion revolves around calculating the work done by a net force on a moving object with a mass of 4.0 kg, transitioning from an initial velocity of (11.0i + 20.0j) m/s to a final velocity of (16.0i + 32.0j) m/s over 2.0 seconds. The first equation for work, W = (1/2)(m)(V2^2 - V1^2), was used to find the work done as 1518 J, but confusion arose regarding the requirement to provide multiple answers. Participants clarified that the integral method for calculating work involves using the net force and distance traveled, which requires determining acceleration and distance using kinematic equations. Additionally, it was noted that the calculated net force was incorrect, prompting further discussion on how to accurately derive it. The conversation highlights the complexities of applying different work equations in physics.
WahooMan
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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?
 
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Any help at all would be appreciated..
 
WahooMan said:

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.
 

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