Question

An m = 13.6 kg mass is attached to a cord that is wrapped around a wheel of radius r = 11.3 cm (see the figure below).


The acceleration of the mass down the frictionless incline is measured to be a = 1.98 m/s². Assuming the axle of the wheel to be frictionless, and the angle to be theta= 33.0^o determine the tension in the rope.

An m = 13.6 kg mass is attached to a cord that is wrapped around a wheel of radius r = 11.3 cm (see the figure below). . The acceleration of the mass down the frictionless incline is measured to be a = 1.98 s-. Assuming the axle of the wheel to be frictionless, and the angle to be 6 = 33.0° determine the tension in the rope. Submit Answer Tries 0/8 Determine the moment of inertia of the wheel. Submit Answer Tries 0/8 Determine angular speed of the wheel 2.16 s after it begins rotating, starting from rest. Submit Answer Tries 0/8

Determine the moment of inertia of the wheel.

Determine angular speed of the wheel 2.16 s after it begins rotating, starting from rest.

Answer 1

here,

mass of cord , m = 13.6 kg

r = 11.3 cm = 0.113 m

acceleration , a = 1.98 m/s^2

theta = 33 degree

the tension in the rope , T = (m * g * sin(theta) - m * a)

T = 13.6 * ( 9.81 * sin(33) - 1.98) N

T = 45.7 N

let the moment of inertia be I

acceleration , a = net force /effective mass

a = ( m * g * sin(theta) /(m + I/r^2))

1.98 = ( 13.6 * 9.81 * sin(33) /(13.6 + I/0.113^2))

solving for I

I = 0.295 kg.m^2

the moment of inertia of the wheel is 0.295 kg.m^2

at t = 2.16 s

the angular speed , w = w0 + alpha * t

w = 0 + (a/r) * t

w = 0 + (1.98/0.113) * 2.16 rad/s

w = 37.8 rad/s