An Atwood machine consists of blocks of masses m1=40.0kg and m2=60.0kg attached

Question

An Atwood machine consists of blocks of masses m1=40.0kg and m2=60.0kg attached by a cord running over a pulley as in the figure. The pulley is a solid cylinder ( I=0.5MR^2 ) with mass M=20.0kg and radius r=0.8m. The block of mass m2 is allowed to drop and the cord turns the pulley without slipping. Assuking the pulley is frictionless.

a) Write simplified equations (should be three equations) with all known parameters substituted to find tension of the string of the left hand side (T1), tension of the string of the right hand side (T2) and linear acceleration 'a' of the system. You don't have to solve the above equation. Hint: Define positive direction before you start the problem.

For parts (a) (b) (c) and (d) assume: 'a'=2.0 m/s^2

b) Find the magnitude of the angular acceleration of the pulley

c) If the m1 mass initially stays rest close to ground, how far will it rise within 10.0 seconds?

d) What is the velocity after 10.0 seconds?

Explanation / Answer

positive follows arrows

so for m1

T1 - m1g = m1a
T1 - 392.4 = 40 a

for m21
m2g - T2 = m2a
588.6 - T2 = 60 a

for the pulley
r T2 - rT1 = 0.5 M R^2 alpha

T2 - T1 = 0.5 M a
T2 - T1 = 10 a
b) alpha = a R = 2*0.8 - 1.6

c) y = v0 t + 1/2 a t^2 = 0.5*2*10^2 = 100 m

d) v = a t = 2*10 = 20 m/s

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