# Relationship between work and potential energy

1. Jan 20, 2007

### lzh

1. The problem statement, all variables and given/known data
At time ti, the kinetic energy of a particle is
35.5 J and its potential energy is 8.16 J.At
some later time tf , its kinetic energy is 9.38 J.
If only conservative forces act on the parti-
cle, what is its potential energy tf ? Answer
in units of J.
If the potential energy at time tf is 6.95 J,
what is the work done by the nonconservative
forces acting on the particle? Answer in units
of J.

2. Relevant equations
W=F*displacement*cos(theta)

3. The attempt at a solution
For the first part of the question, because there were only conservative forces, the sum of kinetic and potential must be same for both ti and tf. And i know that i have the right answer for that. But for the second part, where force isn't conserved, that would not be the case:
I CANNOT take the sum of 35.5 and 8.16 and subtract 6.95 like i did for the first part.
I dont think i completely understand the concept here, so i'd appreciate any help.

Last edited: Jan 21, 2007
2. Jan 20, 2007

### Decan

You're missing a relationship between work and energy. W = ______

Fill in the blank and you should have your answer. Hint (you're not looking for W = Fd)

3. Jan 20, 2007

### lzh

work is kinetic energy here, right?

4. Jan 20, 2007

### Decan

and what else...

5. Jan 20, 2007

### PhanthomJay

No. When non-conservative forces act, total mechanical energy is not conserved. How much energy did you start with? What did you end up with? Can you explain this?

6. Jan 20, 2007

### lzh

well, I started with 43.66J. But i dont know how much ends up being left.

7. Jan 20, 2007

### lzh

wait... can this possibly be right?:
W=KE+PE

8. Jan 20, 2007

### Decan

That's my line of thought...work done by non conservative forces= change in kinetic energy + change in potential energy

9. Jan 20, 2007

### lzh

so does the answer to this part end up the same as first part of the question?

10. Jan 20, 2007

### PhanthomJay

No. The initial mechanical energy,
(KE + PE)_initial, is 43.66J. The final mechanical energy, (KE + PE)_final, is 16.33J. The difference between the two represents the change in the total mechanical energy of the system , which is, as stated above, equal to the work done by the non-conservative forces.

11. Jan 21, 2007

### lzh

would the change in mechanical energy be negative?
-27.33J in this case.
because +27.33J is wrong, according to my hw service

Last edited: Jan 21, 2007
12. Jan 21, 2007

### Decan

Assuming you did the calculation right, the work should be negative.