Answered

Explore a vast range of topics and get informed answers at IDNLearn.com. Our community is ready to provide in-depth answers and practical solutions to any questions you may have.

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

#SPJ4

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.