Work Done by a General Variable Force

AI Thread Summary
To calculate the net work done on an 8 kg brick moving along the x-axis with a variable force, one method involves finding the area under the acceleration vs. position graph. Initially, there was confusion about the calculation, but it was resolved by correcting an input error. Another approach discussed involves using the slope of the acceleration graph, which relates to the force acting on the brick. This method simplifies the calculation by directly connecting the slope to the force without needing to find the area. Understanding both methods provides a comprehensive view of solving work done by a variable force.
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A 8 kg brick moves along an x axis. Its acceleration as a function of its position is shown in Figure 7-37. What is the net work performed on the brick by the force causing the acceleration as the brick moves from x = 0 to x = 8.0 m?

07_34.gif


What I tried to do is find the area and multiply by the mass, but it doesn't work.

Please help.


Edit: Never mind it worked. I just typed it in wrong. But I have another concern.

Is there any additional ways to solve this problem other than the one I mentioned? I was looking at someone else's work and that person did something with the slope. How does that work?
 
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By looking at it I could see that if they take info from the slope they would appear to be taking a longer route, finding the slope just cancels the displacements.
 

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