Question

MR A pulley of mass 3M and radius R is mounted on ftictionless bearings and supported by a stand of mass 4M at rest on a table as shown to the right. The rotational inertia of this pulley about its axis is (3/2)MR2. Passing over the pulley is a massless cord supporting a block of mass M on the left and a block of mass 2M on the right. The cord does not slip on the pulley, so after the block-pulley system is released from rest, the pulley begins to rotate, and the tension Ti in the cord on the left side is not the same as the tension Tg on the right. R ЗМ A) Write the equations of translational motion (Newton's second law) for each of the two blocks and the analogous equation for the rotational motion of the pulley in terms of the above variables. B) Solve the equations in part A) for the acceleration of the blocks in terms of g. c) Determine the tensions T and Tg in terms of M and g. 2M 4M

Answer 1

a I = 3,2 m R² 3 m R La Imq mg I - Img FB. D og am ang - TR = 2m 9 - F. B.D of m To mag = m 9 - F-B.D of disc Tnet - IL TR-TR = 3 m R² &

(Te) R = 3m R² TR-T 2 2ma - a = R2 12 = 2/2 @ ' @ uby hq . puo a= (am-m) g amt mt 3 m a = mg 6mtom D bub - wb о Ве

TR= 2 mg - 2m.a TR = am 1g-a) TR = 2m (g-29) TR = -ang [TR= angH negative sing Indicat the upward direction. Te = (atom = (29+9) m Te = 3mg]h