How Is Work Calculated When a Force Varies with Position?

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AI Thread Summary
The force acting on an object is defined by the equation Fx = 10x - 2.0x² N, and the task is to calculate the work done as the object moves from x = -1 to x = +6. The correct approach involves integrating the force equation over the specified limits rather than differentiating it. The integration should be performed from x = -1 to x = +6 to find the total work done. The initial attempt yielded an incorrect value due to improper limits and differentiation instead of integration. Properly applying the integration will yield the correct work done by the force.
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Homework Statement


A force acting on an object moving along the x-axis is given by Fx = 10x-2.0x2 N where x is in m. How much work is done by this force as the object moves from x = -1 to x= +6

Distance = 7 m

Homework Equations


Work = Force * Distance cosine theta

The Attempt at a Solution


The equation for force is already given so I found force by integrating the equation Fx = 10x-2.0x2 to get Fx = 10-4.0x then I substituted the x for 7 to get -18 Joules. The problem I have is that the answer I got isn't among the options.
 
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You differentiated instead of integrated.
 
and Put the limits for x properly from -1 to +6, (Wx=+6 - Wx=-1)
 
Yuqing said:
You differentiated instead of integrated.

mukundpa said:
and Put the limits for x properly from -1 to +6, (Wx=+6 - Wx=-1)

Oh, I see thanks.
 

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