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M1 - Pulleys watch

1. Two particles P and Q have masses 3m and 5m respectively. They are connected by a ligth inextensible string which passes over a smooth light pulley fixed at the edge of a pulley. The coefficient of friction between P and the table is 0.6. The system is released from rest with the string taut. For the period before Q hits the floor or P reaches the pulley.

a). Write down an equation of motion for each particle seperately

b). Find, in terms of g, the accceleration of Q

c). Find, in terms of m and g, the tension in the string

When Q has moved a distance h, it hits the floor and the string becomes slack. Given that P remains on the table during the subsequent motion and does not reach the pulley.

d). Find, in terms of h, the distance moved by P after the string becomes slack until P comes to rest.
2. You have given no indication of what you have tried which is why you have had no answers, probably.

Common errors here; students try to treat the system as if it were in equilibrium, which it isn't, both masses are accelerating. Another mistake is to stick N (for Newtons) all over the place in the equations so that it looks like there is a variable called N. Do not put units into equations.

To start you off, for particle P, there is a tension in the string pulling it across the table and a Friction in the opposite direction.
As the table is horizontal the reaction force R=3mg. These two forces combine to equal 3ma.

Thus the equation of motion for P is

As the string is inextensible, the Tension at the other end of the string is the same (although in the opposite direction)

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Updated: March 2, 2016
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