posted by nikhil on .
Two masses m and 2m are attached with each other by a rope passing over a frictionless and massless pulley. If the pulley is accelerated upwards with an acceleration ‘a’, what is the value of T?
If the pulley is accelerated at rate a, it is the same as if the weights became m(g +a) and 2m(g+a), in a coordinate system moving with the pulley, with gravitational accleration g + a.
There would be additional acceleration of the weights at a rate
a' = (g+a)(m/3m) = (g+a)/3
(2m would accelerate at rate a' down and m would accelerate up)
For the cable tension, let us apply Newton's second law to 2m.
2m*(g+a)-T = 2m*a' = 2m*(g+a)/3
T = 2m*(g+a)(2/3)= (4m/3)(g+a)