- #1

- 1

- 0

**
**

1. Homework Statement

1. Homework Statement

A solid sphere (mass of m, radius of r and I=2/5 mr

^{2}) is rolling without slipping on

a rough surface with a speed of v. A ramp (mass of 2m and angle of θ) rests on a

smooth surface and is free to slide on the surface. As the ball rolls up the ramp, the

ramp begins to move. Provide all answers in terms of the given variables and any

fundamental constants.

A. What will be the speed of the ball/ramp when the ball reaches its highest point on

the ramp?

B. What distance L will the ball roll up the incline?

C. What will be the speeds of the ball and the ramp after the ball rolls back down off

of the ramp?

## Homework Equations

Conservation of Momentum, Conservation of Energy

## The Attempt at a Solution

A. mv=(m+2m)v

mv=3mv

v

_{f}=1/3v

B.

we now have v

_{f}which is v/3 we can solve

ΣE

_{i}=1/2 Iω

^{2}+1/2mv

^{2}=

1/2(2/5mr

^{2})(v/r)

^{2}+1/2mv

^{2}=

1/5mr

^{2}+1/2mv

^{2}=7/10mv

^{2}

ΣE

_{f}=mgh+1/2*3mv

_{f}

^{2}=

mgh+1/2*3m(v/3)

^{2}=

mgh+1/6mv

^{2}=7/10 mv

^{2}

h=8v

^{2}/15g

L=(8v

^{2}/15g) cscΘ

c. I would like guidance on how to solve c.

I know it uses energy, but I'm stuck on this one

Last edited: