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September 3rd, 2015, 12:09 PM   #1
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M1 - Potential energy

Points A, B and C on the wire have coordinates (0, 0), (3, 3), and (6, 6). A m-kg bead is projected along the wire from A with speed u ms$^{-1}$ so that it has enough energy to reach B but not C. Prove that 8.16 < u < 10.95 and that the speed at B $\geqslant$ 2.58 ms$^{-1}$.

If u = 10, the bead comes to rest at a point D between B and C. Find
(a) The greatest speed of the bead between B and D.
(b) The coordinates of D.
What happens after the bead reaches D?

The answer for (a) is 6.83ms$^{-1}$ and for (b) is (5.7, 5).

Last edited by skipjack; September 3rd, 2015 at 02:49 PM.
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September 7th, 2015, 04:57 AM   #2
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Some hints:

For the first part, use conservation of energy: the initial kinetic energy will be transferred to gravitational potential energy as it rises up the wire.

KE = GPE

$\displaystyle \frac{1}{2}mu^2 = mg\Delta h$

$\displaystyle \frac{1}{2}u^2 = g\Delta h$

I think you have a typo in the question as well: I think it is the speed at A which has a constraint $\displaystyle u \ge 2.58 ms^{-1}$. To make this proof, consider the case where $\displaystyle v = 0$ at B. Use conservation of energy whenever you can because the equations are easier to solve than the SUVAT equations.

For the second part:

a) Since the only acceleration in this situation is the deceleration due to gravity, the greatest speed will be the one when the bead reaches B. Just solve a SUVAT equation to get the answer here.

b) v = 0 at D... use conservation of energy again or a SUVAT equation with a little bit of trigonometry to get the horizontal and vertical distances.

It should be pretty obvious what happens when the bead reaches D...

Give me a shout if you're still having trouble.

Last edited by Benit13; September 7th, 2015 at 04:59 AM.
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September 10th, 2015, 12:15 PM   #3
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I'm still struggling.. no matter how i try it i still land up in a mess!
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September 11th, 2015, 01:42 AM   #4
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Quote:
Originally Posted by Jmun View Post
I'm still struggling.. no matter how i try it i still land up in a mess!
Which part specifically do you find difficult? Can you post your attempt?
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