3. Consider the bicycle shown in Figure Q3 below. The total mass of the bicycle

Question

3. Consider the bicycle shown in Figure Q3 below. The total mass of the bicycle and the rider is 89 kg and the position of the centre of mass is as indicated in the figure. If the coefficient of friction between the road and the tyre is 0.8, calculate the maximum deceleration that can be achieved? Remember that the deceleration must not be so large that the rider is thrown over the handlebars. What is the difference in the stopping differences between braking with: the front brake only: front and rear brakes; and rear brake only? 3 COM, center of mass2 17 inches (432 mm) 42 inches (1,067 mm) Figure Q3

Explanation / Answer

3. in the given problem

masso f cycle and rider, m = 89 kg

uk = 0.8

for maximum decelration will be when the normal reaction of the rear tyre becomes zero

in this case from moment balance about the first tyre

m*a*45 = mg*(42 - 17)

hence

a = 0.5556g = 5.45 m/s/s

in this case

maximum deceleration achieved = uk*mg/m = uk*g = 7.848 m/s/s, which will tip over the cycel

hence

a = 5.45 m/s/s

for both the brakes applied case, again the maximum accelration wil lbe calculated by taking the rear tyre normal reaction force to be 0

so the limit will again be a = 5.45 m/s/s

lets find maximum decelration from the kinematics

then

a = uk(N1 + N2)/m = uk(mg)/m

hence again the maximum possibke deceleration will be 5.45 m/s/s

when only fron brake is applied, the front tyre becomes locekd and skids, causing the bike to tip over if maximum deceleration is reached

when both breakes are applied, even though the limit of maximum acceleratin is still the same to prevent tipping over, due to friction on both the tyres, till the time the bike hasnt tipped over, the friciton in the rear tyre is poresent and the normal reaction keeps the limit on limiting acceleration

when front brake is not applied, the front tyre never locks, so net moment aboutg the center of the front tyrew is always zero and hecne the bike cannot tip over

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