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# Applied Maths watch

1. Two weights P and Q hang in equilibrium from a string which passes over a rough circular cylinder in a plane perpendicular to the axis, which is horizontal. If P is on the point of descending, what weight may be added to Q without causing it to descend?
2. What is the coefficient of friction?
3. just µ
4. Let W be the weight that is added at Q. Then

P = Q exp(pi*mu)
Q + W = P exp(pi*mu)

W
= P[exp(pi*mu) - exp(-pi*mu)]
= Q[exp(2pi*mu) - 1]

(I'm not sure whether the question wants us to express W in terms of P or in terms of Q.)
5. (Original post by Jonny W)
Let W be the weight that is added at Q. Then

P = Q exp(pi*mu)
Q + W = P exp(pi*mu)

W
= P[exp(pi*mu) - exp(-pi*mu)]
= Q[exp(2pi*mu) - 1]

(I'm not sure whether the question wants us to express W in terms of P or in terms of Q.)
thanks i was confused about which way to express W also, i thought that i had perhaps missed something obvious, but expressing both ways is probably best just to make sure both are covered! thanks

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