Two pails hang from opposite ends of a rope suspended over a flywheel, as shown

Question

Two pails hang from opposite ends of a rope suspended over a flywheel, as shown here. Assume that the rope does not slip on the pulley, that the bearing of the pulley axle exerts negligible friction, and that the pulley wheel has considerable mass. Starting in the positions shown, the pails are released from rest. Construct a free-body diagram for each pail. Use the lengths of your force arrows meaningfully-to indicate their relative magnitudes. Construct a free-body diagram for the flywheel. (You may assume that its axle is supported by a single pin.) Use the lengths of your force arrows meaningfully-to indicate their relative magnitudes. Describe the rotational motion of the flywheel after the pails arc released from rest. Explain/show your reasoning with words and/or equations.

Explanation / Answer

first the mechanism :
since the mass of pail 1 is more (its 2m) when released from rest the fly wheel will rotate towards left i.e mass 1 will go down
mass 2 (which has m ) will go up
for part 1)
u draw 2 arrows one below 2m mass and other below m mass
these arrows indicate that they have a force of gravitation on them
force on mass 2m = 2mg
and on m = mg
and the second force in the picture is tension (t)
the tension in the string will be same so t1 = t2
= 2m1m2/(m1+m2) *g = 4/3mg




so draw a line above 2m and below 2m

tension = 4/3mg and force of gravity = 2mg

and draw a line above m and below m tension = 4/3mg and force of gravity = mg

b)the axle has a force = 3mg on the pin

so draw 3 lines one above and 2 on the sides (1 left and 1 right ...name them t )

c)the wheel will rotate towards left with acceleration = m1-m2/(m1+m2) *g = g/3

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