A stone is suspended from the free end of a wire that is wrapped around the oute

Question

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, as shown in the figure (see the figure ). The pulley is a uniform disk with mass 10.3 kg and radius 46.0 cm and turns on frictionless bearings. You measure that the stone travels a distance 13.0 m during a time interval of 2.70 s starting from rest.

Find the mass of the stone.
Take the free fall acceleration to be 9.80;{ m m/s^{2}}.

Find the tension in the wire.
Take the free fall acceleration to be 9.80;{ m m/s^{2}}.

Explanation / Answer

The acceleration along the y-direction is a = 2 y / t^2 = 2 * 13 / 2.7^2 = 3.566 m/s^2 Torque on the pulley torque = T * R = I * @ ==> T * R = 0.5 M R^2 * (a / R) ==> T = 0.5 m a = 0.5 * 10.3 * 3.566 = 18.36 N The equation of motion along the vertical direction is mg - T = ma ==> m = T / g-a = 18.36 / 9.8 - 3.566 = 2.945 kg

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