# Homework Help: Energy of a System

1. Dec 16, 2013

### haha1234

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I have tried to solve this two question.
For question 13, I've plotted a graph.Is it correct?
But I can't find the answer by calculating the area under the line.

For question 11,What is the cosθ

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Last edited: Dec 16, 2013
2. Dec 16, 2013

### CAF123

You are plotting F(x) = 2x + 4, which has a non zero F intercept. But your method of finding the work done between those two values of x is correct. Alternatively you could just do the computation W = ∫Fdx, which is equivalent to your method.

In the next question, cosθ represents the cosine of the angle between the force and displacement vectors.

3. Dec 16, 2013

### haha1234

For this question, why the change in potential energy is not equal to zero?

4. Dec 16, 2013

### CAF123

Why do you think it should be zero?

5. Dec 16, 2013

### haha1234

Since the object only moves in x direction:shy:

6. Dec 16, 2013

### CAF123

The key point here is that the force is a function of x. Since V = -W, and W was non zero, we already know that the change in potential energy is similarly non zero.

If you consider an object acted on upon by gravity moving only along the x axis. Gravity points downwards so the angle between the force vector and displacement is 90 degrees and hence W = F.dx = 0 and correspondingly the change in potential energy of the object is zero. The force in this case, though, is not a function of x.

7. Dec 16, 2013

### haha1234

Sorry,but what is v?
And how to find the potential energy?

8. Dec 16, 2013

### CAF123

V is potential energy here, perhaps you use U.

To elaborate on my example earlier, a block attached to a spring undergoes a restoring force F= -kx when it is displaced some x. We can talk about the potential energy stored in the spring even though the problem is 1 dimensional.

9. Dec 16, 2013

### haha1234

How to find the cosθ?
Is the direction of F show as follow?
And what is the direction of the displacement vector?

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10. Dec 16, 2013

### nasu

The work of what force is required by the problem?

11. Dec 17, 2013

### CAF123

cosθ is the angle between the force vector acting on the particle and and the displacement vector of the particle. The question asks about one particular force and so you have to first identify it's direction. It is not as you have shown it.
Consider first the path OAC. This is made of two segments OA and AC. The particle travels from O to C. Consider each segment separately.