Physics Quiz 7

[Ether]

Figure1 attached shows the top view of a vehicle with standard wheels
attempting to rotate counter-clockwise but not yet moving because the
torque being applied to the wheels is too low. The +Y axis is the
"forward" direction.

Assume the following:

- Four identical standard non-steerable wheels of radius "r"

- Wheels are located at the corners of a rectangle

- Axis of each wheel is parallel to the X-axis

- Coefficient of friction "mu" is the same in all directions

- The same magnitude torque "tau" is being applied to each wheel

- Let f2 = trackwidth/wheelbase

- The right wheels are being torqued “forward”

- The left wheels are being torqued “backward”

- The vehicle is in static equilibrium

- CoM aft of CoG. Vehicle is on a flat, level floor.

- Let f1 = (distance from CoG to CoM)/(distance from CoG to the point midway between rear wheels)

- Let W be the weight of the vehicle.

- Fn is the total friction reaction force of the floor on the bottom of wheel #n,
and Fnx Fny are its components. n= 1,2,3,4.


Problem:

Find the torque tau in terms of mu, r, W, f1, and f2 required to break the
static friction and start the vehicle rotating.