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# 2 Potential Energy questions

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1. Some of you may have noticed that I've been posting quite frequently for help with questions involving Potential/Kinetic Energy. It is a topic I've been struggling with a little, but this should be the last time for a while that I'll be needing help with it.

1)
A smooth wire is bent into the shape of the graph of for , the units being metres. Points A, B and C on the wire have coordinates . A bead of mass kg is projected along the wire from A with speed so that it has enough energy to reach B but not C. Prove that is between and .

If , the bead comes to rest at a point D between B and C. Find the greatest speed of the bead between B and D,

AnswerSo I assume that if the bead has enough energy to reach B but not C, then it's fair to model that as . Doing the algebra gives me , giving me . So my upper value is correct, but not the lower one, and I'm quite confused as to why.

For the next part, I assumed that the greatest speed of the bead between B and D would be the speed of the bead as it just passes B (as the graph of always as a positive or flat gradient). The answer is apparantly , and I don't have any idea how they got that.

So now for question 2
2 A block of mass is placed on a rough horizontal table. A string attached to the block runs horizontally to the edge of the table, passes round a smooth peg, and supports a sphere of mass attached to its other end. The motion of the block on the table is resisted by a frictional force of magnitude , where . The system is initally at rest.
a) Show that when the block and the sphere have each moved a distance , their common speed is given by
b) Show that the total energy lost by the sphere as it falls through the distance is

AnswerNow I can manage part a: , so . This is easy enough to rearrange to make the subject and get the expression in part a).

Part b is giving me problems. I assume the energy lost is equal to , which is equal to , but when I substitute in the answer for from part a) I just get a mess that no matter how I try to tidy up never looks anything like the expresssion I should be ending up with.

Help would be extremely appreciated.
2. hmmm, I get 7.85 as well
3. If you graph the curve, you'll see that in order to reach B, it must go over a hump earlier on, which is higher than B.

Edit: If you don't want to sketch the curve, the fact that the gradient of the curve at B is negative, will also tell you that there is a hump prior to B.
4. (Original post by ghostwalker)
If you graph the curve, you'll see that in order to reach B, it must go over a hump earlier on, which is higher than B.

Edit: If you don't want to sketch the curve, the fact that the gradient of the curve at B is negative, will also tell you that there is a hump prior to B.
Ahhhhhhh I differentiated and sketched x + sinx so missed that
5. Can anyone help with the second one?
6. (Original post by Julii92)
Can anyone help with the second one?

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7. (Original post by TenOfThem)

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Right! Thank you (And Ghostwalker)

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