An object of mass M = 12.5 kg is attached to a cord that is wrapped around a whe

Question

An object of mass M = 12.5 kg is attached to a cord that is wrapped around a wheel of radius r = 11.5 cm (see figure). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2 and the incline makes an angle ? = 37.0° with the horizontal. Assume the axle of the wheel to be frictionless.


(a) Determine the tension in the rope.
.
Your response differs from the correct answer by more than 100%. N

(b) Determine the moment of inertia of the wheel.
kg · m2

(c) Determine the angular speed of the wheel 3.00 s after it begins rotating, starting from rest.
rad/s

Explanation / Answer

Please check my calc.

for the mass on the incline, Fnet=ma or

mg(sin370)-T = ma      where m=12.5 kg amd a = 2

thus, T = 12.5(9.8sin370 - 2) = 48.72234 N

for wheel (pulley) net=I where the torque net is tension times the radius

so, TR=I. but =a/R so TR2=Ia or I = TR2/a = (48.72234)(.115m)2/ 2 = .322 kgm2

c)   from kinematics: v = v0 + at   where v0 = 0 , a = 2 and t = 3   we get v = 6 m/s

but = v/r so = 6/.115 = 0.019167 rad/s

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