Work and energy (change in potential)

[lemin_rew]

Homework Statement

part a and b are solved(is it correct), but I am not sure how to solve part c.
A single constant force F = (3.02i + 5.45j)N acts on a 3.69kg particle.

a) Calculate the work done by this force if the particle moves from the origin to the point having the vector position r = (1.97i - 2.77j)m

b) What is the speed of the particle at r if its speed at the origin is 3.51m/s?

c)What is the change in the potential energy of the system?

Homework Equations

The Attempt at a Solution

a) F dot r = (3.02i + 5.45j) dot (1.97i +-2.77j) = (3.02x1.97)+(5.45x -2.77)= -9.15J

b)1/2mvi^2 - (F dot r) = 1/2mvf^2
(0.5x3.69kgx3.51^2 - 9.15J = 1/2(3.69kg)vf^2
v= 2.71m/s

c)W= Ek-Eg
-9.15J = 1/2mvf2-1/2mvi2 - Eg
-9.15J = 1/2(3.69kg)(2.71^2-3.51^2) - Eg
Eg= 0.033J
can anyone tell me what I am doing wrong for part c?

 

[haruspex]

I think the result you got in part (c) should have been zero. What you actually got looks like rounding error.
I would have thought that the lost KE has all gone into the PE (i.e. total conserved), no? A uniform force field would be conservative.