A 45 N brick is suspended by a light string from a 2.0 kg pulley. The brick is r

Question

A 45 N brick is suspended by a light string from a 2.0 kg pulley. The brick is released from
rest and falls to the floor below as the pulley rotates through 5.0 rad. The pulley may be
considered a solid disk ? 2 ?
2
I ? 1MR of radius 1.5 m.
a. Draw a free body diagram for the brick and the pulley in the space provided. (3)
b. What is the pulley’s angular acceleration as the brick falls? (5)
c. What is the total kinetic energy of the system at the instant the pulley has
undergone an angular displacement of 2.0 rad? (8)
Free Body Diagrams
Brick Pulley

Explanation / Answer

Lets say the brick weighs m
the pulley weighs M
and has a radius R
The rotational inertia of the pulley is J

A)Part a is obvious but can't be shown without a diagram.

B)Use Toque and force equation for brick and pulley system and use a = R

Suppose Tesion in string to be T

Mg- T = Ma

TR = J*

a = R

Solve the 3 equation to get

C)Imagine the pulley is rotating at w rad/s. Then the total kinetic energy would be

Ek = 1/2 J w^2 + 1/2 m (wR)^2
(the brick is travelling at wR m/s)

Substitute w = 2 to find the answer of part C

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