Question
Asked Oct 16, 2019

Two buckets of mass ?1=19.3 kg and ?2=12.3 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.93 kg and a radius of ?p=0.450 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction.

The buckets are released from rest and begin to move. If the larger bucket is a distance ?0=1.85 m above the ground when it is released, with what speed ? will it hit the ground?

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2
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1 2

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Expert Answer

Step 1

Let the tension in the string 1 and string 2 be denoted as T1 and T2 and their respected masses be denoted as m1 and m2.

Let the mass and radius of the pulley be denoted as mp and rp .

The moment of inertia I of the pulley about an axis passing through its center of mass is expressed as,

1
-m r
2
2
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1 -m r 2 2

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Step 2

The equations governing the motion of the masses and the pulley are ,

mg Tma
T2-m,g m,a
1
(T-7)7,
m.r
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mg Tma T2-m,g m,a 1 (T-7)7, m.r

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Step 3

Here α is the angular acceleration of the pulley.

The relation between the linear a...

a ar
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a ar

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