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, similar to what is shown in (Figure 1) . The pulley is a uniform disk with mass 10.0 kg and radius 31.0 cm and turns on frictionless bearings. You measure that the stone travels a distance 12.5 m during a time interval of 2.50 s starting from rest.

a)Find the mass of the stone. Express your answer with the appropriate units.

b)Find the tension in the wire. Express your answer with the appropriate units.

Explanation / Answer

Rotational KE of pulley = 0.25MV² = (0.25)(10.0)V² = 2.5V² {where V = max speed of stone}
max KE of stone = 1/2mV² = (0.5)mV²
Vavg of stone = 12.5/2.50 =5 m/s
V = max speed of stone = 2Vavg = 10 m/s
GPE of stone = mgh = m(9.81)(12.5) = 122.625m J
122.625m = 2.5V² + 0.5mV² = 2.5(10)² + 0.5m(10)² = 250 + 50m
72.625m = 250
m = 3.44 kg ANS*
acceleration of m:
d = 1/2at²
12.5 = 0.5a(2.5)²
a = 4 m/s²
Tension in wire = m(g-a) = 3.44(9.81-4) = 19.98 N ANS

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