Question

In: Physics

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy...

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy is rotational? (Note: the moment of inertia of a cylinder of mass M and radius R rotating about its central axis is 0.5MR².)

A 1/3

B 2/3

C 1/2

D 1/4

E 3/4

2. A public art installation consists of three 25-kg glass sculptures hung side-by-side with steel wires of length 1.00 m, 2.00 m and 3.00 m. If the wires all have the same diameter, which one stretches the greatest distance?

A All three wires will stretch the same distance.

B The 1.00-m wire will stretch the greatest distance.

C The 2.00-m wire will stretch the greatest distance.

D The 3.00-m wire will stretch the greatest distance.

E There is not enough information to say.

Expert Solution

(1)

Correct Option: A 1/3

The moment of inertia of the cylinder is

Let v be translation speed of the cylinder and be the angular speed of the cylinder. For rolling without slipping motion,

The rotational kinetic energy of the cylinder is

The translation kinetic energy of the cylinder is

Total kinetic energy of the cylinder is

The fraction of rotational energy is

(2)

Correct Option: D The 3.00-m wire will stretch the greatest distance.

The change in length of a wire of length L and cross-sectional area A when it is stretched by force F is given by

Each sculpture has mass m=25kg, the force applied by each of the three sculpture is the same.

F=W=mg

The diameter of each wire is same, so they all have the same cross sectional area.

The three wires are made of steel, so Young's modulus for the three wires is the same.

Quantities F, A, and Y are same for the three wires. So, the change in length is directly proportional to the length of the wire L. Longer the wire, more will be the stretch. Therefore, 3.00-m wire will stretch the greatest distance.

genius_generous answered 2 years ago

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