# Energy questions

1. Oct 21, 2008

### musicfairy

Here's some mcs and I need someone to check my answers.

1. A student holds one end of a string in a fixed position. A ball of mass 0.2 kg attached to the other end of the string moves in a horizontal circle of radius 0.5 m with a constant speed of 5 m/s. How much work is done on the ball by the string during each revolution?
(A) 0 J
(B) 0.5 J
(C) 1.0 J
(D) 2π J
(E) 5π J

It's A because if it's a circle it does no work.

2. For a particular nonlinear spring, the relationship between the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation F = kx2. What is the amount of work done by stretching the spring a distance x0?
(A) kx03
(B) 1/2 kx0
(C) 1/2 kx03
(D) 1/3 kx02
(E) 1/3 kx03

It's E. I'm supposed to integrate, right?

Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s.

3. What is the total kinetic energy of the two-puck system before the collision?
(A) √13 J
(B) 5.0 J
(C) 7.0 J
(D) 10 J
(E) 11 J

B. I solved for K of each and added them.

4. A 1000 W electric motor lifts a 100 kg safe at constant velocity. The vertical distance through which the motor can raise the safe in 10 s is most nearly
(A) 1 m
(B) 3 m
(C) l0 m
(D) 32 m
(E) l00 m

C. I set mgh/t = 1000 and solved for h.

And here's the odd ball question.

15. A conservative force has the potential energy function U(x), shown by the graph
above. A particle moving in one dimension under the influence of this force has kinetic energy
1.0 joule when it is at position x1 Which of the following is a correct statement about the motion of the particle?

(A) It oscillates with maximum position x2 and minimum position x0.
(B) It moves to the right of x3 and does not return.
(C) It moves to the left of x0 and does not return.
(D) It comes to rest at either x0 or x2.
(E) It cannot reach either x0 or x2.

This one I know the answer to, but have no idea how to get there. The answer is E. Why? Can someone please explain?

I thought I'm supposed to add up U and K to find E, so I added 2 + 1 = 3 J. This obviously is wrong. What's the correct approach to this problem?

Last edited: Oct 21, 2008
2. Oct 21, 2008

### LowlyPion

I didn't check them all that closely, but for 3) your math doesn't add up exactly right. KE = mv2/2

For the last one, your particle only has 1 Joule in its KE energy bank account and it would need 2 J to climb out of the potential well. The proper way of looking at it as far as this problem is (-2J +1J) can't get higher than -1 J.

3. Oct 21, 2008

### musicfairy

Thanks a lot. I didn't realize you could have -U.

4. Oct 21, 2008

### LowlyPion

Well you do when you are on top of the hill and you want to know the potential energy of a cart at the bottom that you need to get up.

Basically, like most things it's relative.

Cheers.

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