A mass m 1 = 14.5 kg and a mass m 2 = 11.0 kg are suspended by a pulley that has

Question

A mass m1 = 14.5 kg and a mass m2 = 11.0 kg are suspended by a pulley that has a radius of 9.8 cm and a mass of 2.9 kg (see figure). The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. Treating the pulley as a uniform disk, determine the tension in the right cord.  https://general.physics.rutgers.edu/gifs/CJ/9-10.gif

A mass m1 = 14.5 kg and a mass m2 = 11.0 kg are suspended by a pulley that has a radius of 9.8 cm and a mass of 2.9 kg (see figure). The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. Treating the pulley as a uniform disk, determine the tension in the right cord. https://general.physics.rutgers.edu

Explanation / Answer

this is the classics atwoods machine.

setup equations of motion:
m=mass
a=acceleration
g=gravity
T=tension

m1a1=m1g-T
m2a2=m2g-T

T is the same in both equations from newtons third law

and by the same principle, a1= -a2

substitute those equivalences and simplify you end up with:

a1=(m1g-m2g)/m1+m2

now we can find T only in terms of masses and g

T=m1g-m1a1=2m1m2g/(m1+m2)

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