Simple work and variable position question

AI Thread Summary
The discussion focuses on calculating the work done by a variable force on a particle with a given position function. The user attempts to derive the work using the formula W=F*s and integrates the position function to find the work over the time interval of 1.49 seconds. They express concern about the accuracy of their solution, particularly regarding the assumption of gravitational force. Another participant suggests finding the force from the second derivative of the position function instead of relying on gravity. The conversation emphasizes the importance of correctly interpreting the problem's conditions to arrive at the right answer.
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Homework Statement


A one-dimensional force acts on a particle of mass m = 6.26 kg in such a way that its position is given by:

x = 0.484t^3 - 33.6t

Find W, the work done by this force during the first 1.49 s.


Homework Equations


W=F*s
W=mgs
Integration


The Attempt at a Solution


I just wanted to know whether I'm solving this correctly because I only have one more chance to input an answer in my online homework system (as those of you who have been helping me probably know by now. :frown:

Anyhow, this is what I've done.

W=Fs
F=mg
W=mgs
**Because the position is variable but the mass and gravity are constant, we integrate the formula given, and we get:

W=mg*∫x.dx= (.121t^4) - 16.8(t^2), from 0s to 1.49s

We come to:

W=mg*(-36.7)
W=6.26*9.81*(-36.7)= (-2253.8) J

Did I do this properly?
 
Physics news on Phys.org
The problem does not say that the particle is subjected to gravity. F=ma, and the acceleration is second derivative of position. Find the force from the given x(t) function.

ehild
 
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