A particular double pulley consists of a small pulley of radius 20 cm mounted on

Question

A particular double pulley consists of a small pulley of radius 20 cm mounted on a large pulley of radius 50 cm, as shown in the figure. The pulleys rotate together, rather than independently. A block of mass m-3.00 kg hangs from a string wrapped around the large pulley, while a second block of mass M-7.00 kg hangs from the small pulley. Each pulley has a mass of 0.500 kg and is in the form of a uniform solid disk. Use g 10 m/s2. (a) What is the magnitude of the acceleration of the block attached to the large pulley? m/s2 (b) What is the magnitude of the acceleration of the block attached to the small pulley? m/s2

Explanation / Answer

Ans)

The two pulleys are fixed together as a solid body.

Given data is small pulley radius r=20cm

Large pulley of radius R=50cm

Block of mass m=3kg

Second block of mass M=7kg

Mass of each pulley N=0.5kg

And use g=10m/s2

a)the acceleration of the block attached to the large pulley

A=2R(Rm-rM)g/[N(r2+R2)+2(R2m+r2M)]

A=[2x50((50x3)-(20x7))x10]/[0.5(400+2500)+2((2500x3)+(400x7))]

=(100(-10)x10)/(1450+20600)

=-90000/12050

A= 0.4535 m/s2

negative is for direction

b)the acceleration of block attached to the small pulley

a=rA/R

=(20x7.47)/(50)

a=0.1814 m/s2

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