# Work done by a varying force of a block

1. Sep 29, 2010

### eventob

1. The problem statement, all variables and given/known data
A block with mass 5.00kg, moves along the x-axis with zero friction. The block experiences a net force Fx that varies with it's position x. When x=0, v (initial speed) is equal to 2.0 m/s

Find the work done on the block when it is displaced from x=0 to x=8

What is the final speed at x=8

This is not the original problem statement ... I had to translate it to English in order to post it here. :p

Se attached image for the graph of the relationship between the force and displacement.

2. Relevant equations

3. The attempt at a solution
Calculated the area in the trapezoid, and subtracted the area of the triangle. 30J-5J=25J, I think this is right answer?

Then I used the relation between work and kinetic energy

W=delta K=(1/2)m*v_f^2 - (1/2)m*v_i^2
where the subscript i and f stands for initial and final speed

Solved this for v_f and got the answer 3 m/s

Are these answers correct? Unfortunately, I don't have the answers, since this is a problem I got from my physics professor, not from the textbook.

Thanks in advance. :)

#### Attached Files:

• ###### graph.jpg
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2. Sep 29, 2010

### kjohnson

Yes, you calculated the area under that curve correctly and applied the work energy theorem (work=change in kinetic energy) to calculate the final velocity at x=8. Everything seems fine to me.