Physics Quiz 6 [Archive]

Ether

21-12-2011, 09:32

Same as specified here (http://www.chiefdelphi.com/forums/showpost.php?p=1092535&postcount=1) and here (http://www.chiefdelphi.com/forums/showpost.php?p=1092585&postcount=3), except the wheels are at the corner of a rectangle (i.e. trackwidth is not necessarily equal to wheelbase).

Let f = trackwidth/wheelbase ≠ 1

Ninja_Bait

21-12-2011, 19:10

Part A:
1. Fy=Tau/r
2. Distance from wheel to CoM = sqrt(trackwidth^2+wheelbase^2)/2 and from now on is d
3. Fydsin(angle included) = Fxdsin(other angle included) because net torque is zero.
4. Fy(trackwidth/d) = Fx(wheelbase/d)
5. Fx = Fy/f = Tau/rf
6. |F| = |Fx + Fy| = Tau*sqrt(f^2 + 1)/rf

Part B:
1. muN<Tau*sqrt(f^2+1)/rf
2. Tau>muNrf/sqrt(f^2+1)

Ether

21-12-2011, 20:25

4. Fy(trackwidth/d) = Fx(wheelbase/d)
5. Fx = Fy/f

How did you get from step4 to step5

Ninja_Bait

21-12-2011, 20:28

How did you get from step4 to step5

Divide both sides by Wheelbase/d and then... oh shoot... that should say Fx=Fyf=Tauf/r. Then F=Tau*sqrt(f^2+1)/r. Also, the answer to B should be Tau>muNr/sqrt(f^2+1)

Or you just invert the definition of f so that it is now WB/TW and then my original answers are right.

Thank you for the correction.

Ether

21-12-2011, 20:48

Tau>muNr/sqrt(f^2+1)

Nice work.

Solution attached.