A massless rope that is tied to a 17kg block is draped over a pulley. The 29kg p

Question

A massless rope that is tied to a 17kg block is draped over a pulley. The 29kg pulley has a radius 18cm and the pulley rotates s.t. the rope does not slip on the pulley. The right side of the rope is pulled down with a tension of 431 N. What is the acceleration of the block? You may treat the pulley as a disk. Ignore any frictional torque in the axle.

Please explain all steps!!!!

A massless rope that is tied to a 17kg block is draped over a pulley. The 29kg pulley has a radius 18cm and the pulley rotates s.t. the rope does not slip on the pulley. The right side of the rope is pulled down with a tension of 431 N. What is the acceleration of the block? You may treat the pulley as a disk. Ignore any frictional torque in the axle. Please explain all steps!!!!

Explanation / Answer

let m1 = 17 kg

m = 29 kg

let T1 is the tension in the left side and T2 is the tension in the right side.

T2 = 431 N

I = 0.5*m*R^2

= 0.5*29*0.18^2

= 0.47 kg.m^2

let a is the acceleration of the block.

net force acting on block,

Fnet = T1 -m1*g

m1*a = T1 - m1*g

T1 = m1*a + m1*g --(1)

net torque acting on the pulley,

Torque = T2*R - T1*R

I*alfa = T2*R - T1*R

I*a/R = T2*R - T1*R

I*a/R = T2*R - (m1*a+m1*g)*R

a*(I/R + m1*R) = T2*R - m1*g*R

a = (T2*R - m1*g*R)/(I/R + m1*R)

= (431*0.18 - 17*9.8*0.18)/(0.47/0.18 + 17*0.18)

= 8.4 m/s^2 <<<<<--------------Answer

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