have made during this time? 4. A uniform frictionless pulley has the shape of a

Question

have made during this time? 4. A uniform frictionless pulley has the shape of a uniform solid disk of mass 2 50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the system is released from rest How far must the stone fall so that the pulley has 4.50 J of kinetic energy? What percent of the total kinetic energy does the pulley have? a. b. Calculate the moment of inertia of a uniform, solid disk with mass M and radius R for an axis perpendicular to the plane of the disk and passing through its center. 5. n. Th @ em" w

Explanation / Answer

Here ,

let the angular speed of the pulley is w

speed of the block is v

as the ropes is not slipping

v = r * w

for energy of pulley = 4.50 J

4.50 = 0.5 * (I * w^2 )

4.50 = 0.5 * 0.5 * 2.50 * 0.20^2 * w^2

w =13.42 rad/s`

speed of block , v = 0.20 =13.42 = 2.684 m/s

Now ,using conservation of energy

0.5 * mv^2 + 0.5 I*w^2 = m * g * h

0.5 * 1.50 * 2.684^2 + 4.50 = 1.50 * 9.8 * h

h = 0.66 m

b)

percentage of KE of pulley = kinetic energy of pulley * 100/total kinetic energy

percentage of KE of pulley = 4.50 *100/(1.50 * 9.8 * 0.66) = 46.38%

the percentage of KE of pulley is 46.38 %

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