You and your bicycle have a combined mass of 75.0 kg, locatedat the center of ma

Question

You and your bicycle have a combined mass of 75.0 kg, locatedat the center of mass as shown. In the diagram below the dimensions b = .595 m, c = .465 m, and h = .990 m. You are moving at 6.00 m/s to the left when you engage only the rear brake, locking the wheel. The wheel has a radius of .370 m.

a. If uk is .35, what is your stopping distance?

b. What are the normal forces at A and B?

c. Repeat part (a) assuming you lock only the front wheel.

d. What are the normal forces at A and B?

e. What "magic" speed will be the barrier between the rear tire leaving the ground and not leaving the ground?

Explanation / Answer

let the normal reaction btwn the ground and the back wheel be = f2

let the normal reaction btwn the ground and the front wheel be = f1

f1+f2 = mg

frictional force = f2 x uk

torque about .com due to friction and f2 = f2(0.465) + f2(uk)(0.990)

torque about .com due to f1 = f1(0.595)

these two should be equal

so f1(0.595) = f2(0.465 + 0.990x0.35) => f1 = (1.36)f2

f1+f2 = mg

f2 = 311.44

f1 = 423.55

friction = 0.35xf2=109.00

acc = 1.4533

stopping dist= v^2 /2a = 12.38 m

c) now the friction = f1(uk)

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