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**Problem:**

A conservative force F is acting on a particle that moves vertically. F can be expressed as (3y-6) j head N, y is in m and j head is a unit vector along vertical direction.

a) Calculate the potential energy associated with F, with the potential energy set to zero at y=0.

b) At what values of y will the potential energy be maximum?

**Relevant equations:**

U(y) = - integral of F(y)

**Attempt at the solution:**

a) When F = 0, y = 2

U = - [integrate 0 to 2] (3y-6) = 6J

b) PE is maximum when F = 0. From (a), when F = 0, y = 2.

I am not familiar with this kind of questions. Could someone please tell me if it's correct?