A bicycle wheel (hoop) with a mass of 4.1 kg and a radius of 0.14 m is on the to

Question

A bicycle wheel (hoop) with a mass of 4.1 kg and a radius of 0.14 m is on the top of a hill. The hill has a height of 34 m . The bicycle wheel (hoop) is initially at rest at the top of the hill and then rolls without slipping down to the bottom of the hill.

Part A

Which of the following is the correct formual for the moment of intertia for a bicycle wheel (hoop)?

2/3MR^2
1/3MR^2
1/2MR^2
MR^2
2/5MR^2

Part B

What is the moment of intertia for the bicycle wheel (hoop)?

Part C

What is the velocity of the bicycle wheel (hoop) at the bottom of the hill?

Part D

If the bicycle wheel (hoop) does not roll, but instead slips so that it slides down the hill, what is the velocity at the bottom of the hill?

Explanation / Answer

here,

mass , m = 4.1 2g

radius , r = 0.14 m

height , h = 34 m

A)

the moment of intertia for a bicycle wheel (hoop) is M*R^2

B)

the moment of intertia for the bicycle wheel (hoop) is M*R^2

C)

let the velocity of the bicycle wheel (hoop) at the bottom of the hill be v

using consrevation of energy

potential energy lost = kinetic energy gained

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

m * g * h = 0.5 * m * v^2 + 0.5 * (m*r^2) * (v/r)^2

g * h = v^2

9.8 * 34 = v^2

v = 18.25 m/s

the velocity of the bicycle wheel (hoop) at the bottom of the hill is 18.25 m/s

D)

if the wheel does not rolls, there is no rotational energy

so ,

potential energy lost = kinetic energy gained

m * g * h = 0.5 * m * v^2

9.8 * 34 = 0.5 * v^2

v = 25.81 m/s

the velocity at the bottom of the hill is 25.81 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.