In this near-earth situation, the pulley has mass 0.63kg, radius 0.32m, and enco

Question

In this near-earth situation, the pulley has mass 0.63kg, radius 0.32m, and encounters a frictional torque of 0.29 about the pulley axle. The hanging mass is 3.4kg, the mass on the plane is 1.6kg, the plane is inclined above horizontal and has kinetic frictional coefficient of 0.15. Use dynamics to determine the system acceleration, string tensions, and speed after the mass on the plane has moved 0.83m.

In this near-earth situation, the pulley has mass 0.63kg, radius 0.32m, and encounters a frictional torque of 0.29 about the pulley axle. The hanging mass is 3.4kg, the mass on the plane is 1.6kg, the plane is inclined above horizontal and has kinetic frictional coefficient of 0.15. Use dynamics to determine the system acceleration, string tensions, and speed after the mass on the plane has moved 0.83m.

Explanation / Answer

Let tension in string be T1 and T2, T1 for block on plane and T2 for hanging mass

equations for the system will be as follows:

m1gsin(theta) - T1 = m1a

(T1 - T2)*R = I*(a/R) (I of pulley = .5mR^2)

T2 - m2g = m2a

frictional torque is given so:

I*(a/R) = .29

a= 2.87

now using third equation:

T2 - m2g = m2a

T2 = 43.07N

(T1 - T2)*R = .29

T1 = 43.97

now speed of mass:

v^2 = 2*2.87*.83

v = 2.18m/sec

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