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The figure shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.8 m, its inner radius R1 is R2/2, its mass M is 8.0 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular speed of 7.6 rad/s with a cat of mass m = M/4 on its outer edge, at radius R2. By how much does the cat increase the kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius R1?

Sagot :

The cat increase the kinetic energy of the cat-ring system is  42.4 J.

Mass of the merry-go-round = M = 7.6 kg

Outer radius of the merry-go-round = R2 = 0.9 m

Inner radius of the merry-go-round = R1 = R2/2 = 0.9/2 = 0.45 m

Moment of inertia of the merry-go-round = I

I = 3.8475 kg.m2

Mass of the cat = m = M/4 = 7.6/4 = 1.9 kg

Initially the cat is sitting at the outer edge that is at a distance of 'R2' from the center.

Initial moment of inertia of the system = I1

I1 = I + mR22

I1 = 3.8475 + (1.9)(0.9)2

I1 = 5.3865 kg.m2

Initial angular speed of the system =  title=View image!

1 = 7.6 rad/s

Now the cat walks to the inner edge of the merry-go-round therefore it is at a distance 'R1' from the center.

New moment of inertia of the system = I2

I2 = I + mR12

I2 = 3.8475 + (1.9)(0.45)2

I2 = 4.23225 kg.m2

New angular speed of the system =

I = I2

(5.3865)(7.6) = (4.23225)2

= 9.673 rad/s

Initial kinetic energy of the system = E1

E2 = 198 J

Amount by which the kinetic energy of the system increases =

E = E2- E1

title=View image!

E = 198 - 155.6

ΔE = 42.4 J

Amount by which the kinetic energy of the system increases when the cat crawls to the inner edge = 42.4 J.

Kinetic Energy:

Kinetic energy is the energy that an object possesses due to its motion. It is defined as the work required to accelerate an object of specified mass from rest to a specified velocity. After the body acquires this energy during acceleration, it retains this kinetic energy as long as the velocity does not change.

Learn about Kinetic Energy here:

https://brainly.com/question/25959744

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