Physics Homework Help?

Question

A thin hoop of negligible width is rolling on a horizontal surface at speed v = 3.8 m/s when it reaches a 15 ∘ incline.

Part A

How far up the incline will it go?

 

Part B

How long will it be on the incline before it arrives back at the bottom?

 

Answer 1

(a)

Step 1:

The hoop rolling on a horizontal surface at speed is .

The hoop inclined at an angle is .

The potential energy of the hoop at inclination is .

The kinetic energy of the hoop is .

Substitute and .

.

The kinetic energy of the hoop is .

Step 2:

Law of conservation of energy: .

.

The hoop inclined up is .

Solution:

The hoop inclined up is .

Answer 2

(b)

From part (a) : The hoop inclined up is .

Initial velocity is zero.

The distance along the inclination is .

Substitute and .

.

Substitute  and .

.

The total time taken for the hoop : .

The total time taken for the hoop is .