Calculating Work Done by Non-Constant Force Using Integration

[kopinator]

A 2.3 kg block is acted upon by a horizontal force F(x) = 25.0 - 10.0x where the force is measured in Newtons if x is measured in meters. The coefficient of kinetic friction between the block and the flat surface is 0.21. The block is initially at x = 0 m. What distance must the block travel if the net work done on the block by F(x) and friction combined is to be exactly zero?


Work=Fd
Force(friction)=mu x mg



The net work has to equal 0 so i set up the problem like this:
Wnet= Wfriction-Wf(x)=0
Wf(x)=Wfriction
F(x)d=Ffd (the d's cancel out)
25-10x=mu x mg (plug in numbers and solve for x)
x=2.026 m
I feel like I'm on the right track of how to solve the problem but my x is wrong.

 

[SammyS]

A 2.3 kg block is acted upon by a horizontal force F(x) = 25.0 - 10.0x where the force is measured in Newtons if x is measured in meters. The coefficient of kinetic friction between the block and the flat surface is 0.21. The block is initially at x = 0 m. What distance must the block travel if the net work done on the block by F(x) and friction combined is to be exactly zero?

Work=Fd
Force(friction)=mu x mg

The net work has to equal 0 so i set up the problem like this:
Wnet= Wfriction-Wf(x)=0
Wf(x)=Wfriction
F(x)d=Ffd (the d's cancel out)
25-10x=mu x mg (plug in numbers and solve for x)
x=2.026 m
I feel like I'm on the right track of how to solve the problem but my x is wrong.

F(x) is not constant, so the work done by F(x) is not simply F(x)d .

You must integrate F(x)dx.