Spring elastic potential, removing mass

[HaoPhysics]

Homework Statement

5 identical masses M are suspended by a spring stretched a distance of L. If 3 of these masses are removed, what is the potential energy stored in the spring?

2. Relevant diagram
So L is the distance stretched with 5 masses.
Let L2 be the distance stretched with 2 masses remaining.
L2 < L since the spring would "shrink" if it had to hold up less mass.
L2 = (2/5)L

The potential energy is E = ½(k*x²)

The Attempt at a Solution

The answer which the book gives is (5/2)MgL
Which would make sense if we are measuring the potential energy when the spring is holding 5 masses.

Since F = 5Mg = kx, and x = L, so E = ½(k*x²) = ½(5MgL) = (5/2)MgL
​

But isn't the question asking the potential energy when the spring is holding 2 masses?
As I understand it, the potential energy would change:

F = 2Mg = kx, and x = (2/5)L, so E = ½(k*x²) = ½(4/5MgL)=(2/5)MgL

Which answer should it be?​

 

[Doc Al]

Your answer sounds right to me. Where did you get this problem?

 

[HaoPhysics]

Your answer sounds right to me. Where did you get this problem?

http://imgur.com/a/2k2WV

Answer key says (3) is correct.

 

[Doc Al]

Answer key says (3) is correct.

Could be a typo. Note that (2) cannot be correct -- the units are off. Only (1), (3), and (5) have proper units.

 

[haruspex]

Could be a typo. Note that (2) cannot be correct -- the units are off. Only (1), (3), and (5) have proper units.

Yes, that is almost surely right, but I note that the question is not entirely clear. It does not say "3 masses are removed and the system allowed to come to equilibrium again". If the string is cut between the second and third mass from the top then, in that instant, the PE is still what it was with all 5. On the other hand, that would make the answer 3, not 2.

 

[Doc Al]

Yes, that is almost surely right, but I note that the question is not entirely clear. It does not say "3 masses are removed and the system allowed to come to equilibrium again".

Agreed. The question not clear.

If the string is cut between the second and third mass from the top then, in that instant, the PE is still what it was with all 5. On the other hand, that would make the answer 3, not 2.

I thought of that, but dismissed it as being too sneaky without bothering to do the calculation. You know what, I think that's the "correct" interpretation after all -- it's a trick question!

 

[HaoPhysics]

Agreed. The question not clear.I thought of that, but dismissed it as too sneaky without bothering to do the calculation. You know what, I think that's the "correct" interpretation after all -- it's a trick question!

It indeed is a very tricky question! And also, very asinine! Because there is no point in saying "after 3 masses are removed" if we're still regarding the 5 mass system!

Hope the AP Physics C exam won't be like that.