A block is attached to a rope. The other end of the rope is then attached to a p

Question

A block is attached to a rope. The other end of the rope is then attached to a pulley (a solid disk of mass 12.0 kg and radius 27.0 cm). The pulley is then turned (about a frictionless axis through its center) so that the rope "winds up" and the block is suspended in the air. (Figure 1). Finally, the system is released from rest at the moment shown in the figure and it is observed that during the next 4.00 s the block falls 12.7 m. Compute the tension in the rope while the box is falling. Express your answer with the appropriate units. T = Compute the mass of the box. Express your answer with the appropriate units. M =

Explanation / Answer

applying d =u t + a t^2 /2

12.7 = 0 + a 4^2 / 2

a = 1.5875 m/s^2

For pulley, net torque = I alpha

R T = ( M R^2 / 2) (a / R)

T = M a / 2

(A) T = 12 x 1.5875 / 2

= 9.525 N

(B) on block,

Fnet = m a

mg - T = m a

m ( g - a) = T

m (9.8 - 1.5875 ) = 9.525

m = 1.16 kg

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