Two objects, of masses m 1 = 460.0 g and m 2 = 504.9 g, are connected by a strin

Question

Two objects, of masses m1 = 460.0 g and m2 = 504.9 g, are connected by a string of negligible mass that passes over a pulley with frictionless bearings. The pulley is a uniform 53.0-g disk with a radius of 3.96cm. The string does not slip on the pulley.

acceleration m/s2 tension N Two objects, of masses m1 = 460.0 g and m2 = 504.9 g, are connected by a string of negligible mass that passes over a pulley with frictionless bearings. The pulley is a uniform 53.0-g disk with a radius of 3.96cm. The string does not slip on the pulley. (a) Find the accelerations of the objects. (b) What is the tension in the string between the 460.0-g block and the pulley? (Round your answer to four decimal places.) What is the tension in the string between the 504.9-g block and the pulley? (Round your answer to four decimal places.) By how much do these tensions differ? (Round your answer to four decimal places.) (c) What would your answers be if you neglected the mass of the pulley?

Explanation / Answer

resolve force components on blocks

for m1

T1-m1g=m1a

T1-460.9*10-3*9.8=0.4609a

m2g-T2=m2a

504.9*10-3*9.8-T2=0.5049a

add above equations

T1-T2+0.422=0.9658a

T2-T1=0.422-0.9658a

apply moment equation

T2-T1=Ia/R2

I=MR2

T2-T1=Ma

0.422-0.9658a =0.053a

a=0.414m/s2

b)

T1=4.7N

T2=4.73N

differ by0.021N

C)

IF WE NEGLECT MASS OF PULLEY TENSIONS ARE APROXIMATELY EQUAL

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