Answer to Question #241846 in Mechanical Engineering for Papi Chulo

Question

A light 300mm diamter pulley is held stationairy and carries a 10kg mass haning on a light cord passing around the pulley. Find the vertical acceleration of the mass when the pulley is released. Frictional torque is the pulley bearings is 3N.m.

Clearly show the following value

E_k=?

E_p=?

E=?

Energy equation=??

v=??

Answer 1

$\textsf{ diameter} = 300\text{ mm}\\ \textsf{ radius} = 150\text{ mm} = 0.15\text{ m}\\ \tau_f = 3\text{ N.m}\\ \textsf{m} = 10\text{ kg}$

$I = 1/2 mr²\\ I =1/2×10 ×(0.15)² = 0.1125\\ \tau = I\alpha \\ \alpha =3/0.1125 = 26.67\text{ rad/s²}\\ \textsf{} \\ \textsf{but, } a = r\alpha\\ a = 0.15 × 26.67 = 4\textsf{ m/s²}\\ a_T =( 9.81 -4)\text{ m/s²} = 5.81\text{ m/s²}$