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Title: GR8677.034
Post by: conantee on January 02, 2010, 06:46:53 AM
Question 34-36
The potential energy of a body constrained to move on a straight line is kx^4 where k is a constant. The position of the body is x, its speed v, its linear momentum p, and its mass m.

34. The force on the body is
(A) \frac{1}{2} mv^2
(B) -4kx^3
(C) kx^4
(D) -\frac{kx^5}{5}
(E) mg


Title: Re: GR8677.034
Post by: conantee on January 02, 2010, 07:01:21 AM
The only thing you need for this question is just dimension of force.
(A) and (C) is surely wrong since they are energy.
(E) is wrong since gravity comes from nowhere in this problem.
Now, kx^4 has dimension of energy, which is equivalent to dimension of work done by force for some distance.
Hence, the force should be in dimension of energy/distance. So, it should have term kx^3

The correct answer is (B). 86 of 100 got this right.

Physics behind it: if you can remember the concept of conservative force. You can use the fact that force is the space coordinate directive of potential energy.