Blocks of mass m1=0.13 kg and m2=0.34 are connected by a massless string that sl

Question

Blocks of mass m1=0.13 kg and m2=0.34 are connected by a massless string that slides over a frictionless pulley. Mass m1 slides on a horizontal, frictionless surface. Mass m2 is released when the blocks are at rest.

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(a) Assume the pulley is massless. What is the magnitude of the acceleration of m1 and the tension in the string?
a=
T=


(b) Now, lets say the pulley has a mass of 0.26 kg and can be modeled as a hollow, thin cylinder of radius R=0.011 m. Find the acceleration of m1, the tension of the upper section of string, and the tension of the lower section of string. You should check that your answers for these three quantities agrees with the answers to part a in the limit that the mass of the pulley goes to zero. Also, it is worth noticing that for a hollow cylinder of radius R rotating about its axis, every bit of mass is a radius R from the axis of rotation.
a=
Tupper=
Tlower=

Explanation / Answer

Applying the Newton's 2nd law of motion, T = m1a ------------ (1) m2g - T = m1a --------------- (2) From equation (1)&(2) a (m1+m2) = m2g a = m2g/(m1+m2)    = 0.34*9.8/(0.47)    = 7.08 m/s^2 the magnitude of the acceleration of m1 is 7.08 m/s^2. the tension in the string, T = 0.13*7.08                                              = 0.921 N

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