Can Physics Concepts Clarify These Energy and Force Problems?

[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?

 

[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.

 

[musicfairy]

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

 

[LowlyPion]

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

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.