How Do You Calculate Potential Energy with a Constant Force?

[maniacp08]

A constant force Fx = 6N is in the +x direction.

A) Find the potential energy function U(x) associated with this force if U(Xo) = 0.

B) find a function U(x) such that U(4.0m) = 0

C) Find a function U(x) such that U(6.0) = 14J

I know that if PE is known then the F can be found by the derivative of the PE.
I know that if F is known then the PE can be found by integrating the force.

Since the force Fx is given to be 6N
the integral of 6 = -6x + C
Is that PE function for the force Fx?

Im not sure what A means

but is B 0 = -6(4) + C
C = 24?

and C is 14 = -6(6) + C
C = 50

Thanks for your help.

 

[Redbelly98]

You have correctly found the constant C, for parts B and C. So you should be able to write the full expression for U(x).

Part A is done the same way.

 

[maniacp08]

Thanks! I get it but I have 1 similar problem but I am confused from the context of the problem, if you could help, it be great.The force acting on an object is given by Fx = a/x^2. At x = 5.0m, the force is known to point int the -x direction and have a magnitude of 25N. Determine the potential energy associated with this force as a function of x, assuming we assign a reference value of -10J at x = 2.0m for potential energy.

I know given the force I can take the integral to find the potential energy which is
integral of a/x^2 since a is a constant I can take it out so it be negative
integral of 1/x^2 dx = 1/x + C = a/x + C

The problem is, they are giving me the other information of
x = 5.0m
force known to point in -x direction
-10J
x = 2.0

I do not know what to do with these info. I know they are important. Can someone guide me please, thanks so much.

 

[maniacp08]

Anyone?

 

[Redbelly98]

You can use the given numbers to get a and C.

For example,
F = a/x^2
You can find a, because you know that F = -25N when x = 5.0m

Then use your equation for potential energy, and the information about the potential at x=2.0m, to find C.