- #1

lightofthemoon

- 12

- 0

## Homework Statement

A solid spherical ball of mass 0

**.**75 kg and radius 5

**.**0 cm is thrown onto a horizontal surface with coefficient of kinetic friction

*μ*. It’s initial velocity at time

*t*= 0 is horizontal and its initial angular velocity is zero. After rolling with slipping for a time

*t*1 = 0

**.**76 seconds, the ball begins to roll without slipping with angular speed ω1 = 120 rad/s. It continues to roll without slipping up a short ramp of height

*h*= 16 cm

What is the value of μ?

## Homework Equations

KE = .5mv^2 = 5Iω^2

f= μN

T=Fr=Iα

vf=vi +at

## The Attempt at a Solution

I was thinking about solving this problem with conservation of energy.

.5mv^2 + .5Iω^2 - μmgd = .5mv^2 + .5Iω^2

However, we don't know the initial velocity, or the distance that the ball traveled with slipping.

In order to solve for initial velocity I thought about using one of the four kinematic equations. However, for each of the equations where are at least 2 unknowns.

So I also tried using forces to solve this problem as well.

Acceleration due to friction

f= μN

ma= μN

a=μg

Rotational acceleration

T=Fr=Iα

α= 5μg / 2r

Then I'd use the equation vf=vi +at and it's rotational equivalent. But this is where I'm stuck again, because there are also 2 unknown variables.