# Homework Help: Frictional energy transfer

1. Feb 28, 2008

### nick_d_g

Hi there
As part of a group project, we are using a clutched flywheel to power a buggy.
The flywheel spins freely on an axel, on which is a fixed disc, which is pressed against the flywheel using a spring. This is the format of a basic disc clutch.
Power is dissipated from the flywheel to the clutch disc, and hence to the wheels.
At t=0, the flywheel is spinning with w(0), and the clutch disc, and hence wheels are stationary.
As energy is transfered to the clutch, and hence the wheels, the buggy will speed up. After time t, the flywheel and buggy wheels will have the same angular velocity and will 'lock'.

Known variables are:
I - Inertia of flywheel
u(k and s) - (myu) coefficient of friction between clutch disc and flywheel (kinetic and static)
N - Normal force applied to clutch disc from spring
r0 and r1 - inner and outer radius of clutch disc
R - equivalent net radius of clutch disc
w(0) - Initial angular velocity of flywheel
m = mass of buggy
r(w) - radius of buggy wheels

Using the eqn.
(1) F = u(k) . N
the force of the clutch disc opposing motion of the flywheel can be calculated.

Then, using:
(2) R = r(2)^3 - r(1)^3 (<- division)
r(2)^2 - r(1)^2
gives us the equivalent net radius (R), i.e. where the forces can be modelled as acting.

The work done by the flywheel on the clutch disc is:
W = f.x
= u(k).N.R (Note, this is the ammount of work per radian of flywheel rotation)

This can then be related to the KE of the buggy:
KE = 0.5 x m x v^2

= 0.5 x m x [r(w)]^2 x [w]^2

But, the work done is greater than the KE delivered to the buggy, due to losses in friction.
Does anybody know how we can calculate this energy loss??

We know that the clutch will 'lock' with the flywheel when they have the same angular velocity (w). we need to calculate the energy loss between the start and when this occurs.

Many Thanks to all who read this
Nickx