6. Figure below shows the drive train of a bicycle whose wheels are 70.0 cm in d

Question

6. Figure below shows the drive train of a bicycle whose wheels are 70.0 cm in diameter and having pedal cranks that are 18 cm long. The cyclist pedals at a steady angular rate of 100.0 rev/min. The chain engages with a front sprocket 14 cm in diameter and a rear sprocket 6.00 cm in diameter.

(a) Calculate the speed of a link of the chain relative to the bicycle frame.

(b) Calculate the angular speed of the rear sprocket.

(c) Calculate the angular speed of the bicycle wheels.

(d) Calculate the speed of the bicycle relative to the road.

(e) Will the speed of the bicycle relative to ground decrease, stay the same or increase if the rear sprocket diameter is changed to 10 cm(assume everything else remains the same)?

(f) Identify, draw(figure below) and write down the algebraic expression of the second law for the forces on the bycicle+person(assume the bicycle is speeding up)

(g) Write down the torque relative to the center of mass of the bycicle+person assuming rotational equilibrium relative to the center of mass.

Explanation / Answer

a) radius = 7 cm = 0.07 m

V(link) = 0.07 * 100*2*pi/60 = 0.733 m/s

b)

angluar speed = v(link)/radius
  
= .733 /0.03 = 24.43 rad/s = 233.33 rev/min

c)

angular speed of the bicycle wheels = angular speed of rear sproket

= 24.43 rad/s = 233.33 rev/min

d)

speed of bicycle = 24.43*0.35 = 8.55 m/s

e)

if the rear sproket is changed to 10cm the speed of bicycle DECREASES

f)here,

if the force of friction is f ,

and acceleration of man+bicycle = a

then ,

f = (Mman + Mbicycle) * a

g) torque = 0 ..as the bicycle is not accelerating

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