# Landing Airplane Wheel

1. Sep 19, 2011

### diracy

1. The problem statement, all variables and given/known data
Consider a wheel of a landing airplane. The wheel has mass M, radius
R, and moment of inertia around its axis $\alpha$MR^2.
The wheel lands on the ground with horizontal
velocity v, but does not rotate before it touches the ground.
(a) Calculate the velocity of the wheel when it stops slipping. Assume that the wheel presses on
the ground with force Mg and the coecient of friction is . Once the wheel no longer slips it
moves with constant velocity. (b) Find the length of the skid mark this wheel would leave on the
runway. (c) Compute the amount of energy lost to friction by subtracting the nal kinetic energy
of rotation and linear motion from the kinetic energy of the wheel before it hit the ground. (d)
Compare the energy loss to Mg times the length of the skid mark. (These two should not be
the same!) (e) Figure out how to calculate the energy loss by multiplying the friction force by a
distance. Figuring out which distance it is requires some thought if you haven't seen this before

2. Relevant equations

3. The attempt at a solution

I was able to do (a), (b), and (c) but I am stuck with d and e. Can someone give me some guidance?

Last edited: Sep 19, 2011
2. Sep 20, 2011

### diracy

any help here?