An object is acted on by the force shown in the picture shown below:
What is the final position of the object if its initial position is x = 0.50 m and the work done on it is equal to -0.29 J?
Initial position = Xi = 0.5 m
Work = W = -0.29 J
Force = F
displacement = d
Final position = Xf = ? m
W = F(d - Xi) + F(d-d) + F(Xf - d)
W = Fd
The Attempt at a Solution
I worked on the first part of this problem, where work was equal to 0.12 J and the initial position was 0.5 m, using this equation:
0.12 = 0.8(0.5 - 0.5) + 0.4(0.75-0.5) + 0.2(Xf - 0.75)
I assumed, since W = Fd, and displacement can't have a negative value, Force would have to have a negative value to get a negative value for Work. Using this logic, I modified the original equation to use a negative Force:
W = -F(d - Xi) - F(d-d) - F(Xf - d)
Using this equation, I went through these steps:
1. Plug in values
-0.29 = -0.8(0.5 - 0.5) - 0.4(0.75-0.5) - 0.2(Xf - 0.75)
-0.29 = 0 - 0.1 + 0.15 - 0.2Xf
3. Subtract 0.15 and add 0.1 to both sides
-0.34 = -0.2Xf
4. Divide both sides by 0.2
1.7 = Xf
However, the answer I got for the final position (1.7), was incorrect. I'm assuming my initial logic using negative values for force was incorrect, but I'm not sure how else I would solve the problem with a negative work value.
Any help is appreciated. Thanks!