A bicycle rider pumps steadily to maintain a constant speed of 16 km/hr. Calcula

Question

A bicycle rider pumps steadily to maintain a constant speed of 16 km/hr. Calculate the maximum and minimum magnitudes of the absolute velocity of the pedal A (i.e the velocity with respect to a fixed frame on the ground). Note Diameter of front and back gear are 170 and 70 mm respectively. The wheels have diameter 660 mm, and the pedels make a circle with radius 160 mm.

A bicycle rider pumps steadily to maintain a constant speed of 16 km/hr. Calculate the maximum and minimum magnitudes of the absolute velocity of the pedal A (i.e the velocity with respect to a fixed frame on the ground). Note Diameter of front and back gear are 170 and 70 mm respectively. The wheels have diameter 660 mm, and the pedels make a circle with radius 160 mm.

Explanation / Answer

v = 16 km/hr = 4.44 m/s

radius of wheel =0.33 m

wheel and back gear = v/r = 4.44/0.33 = 13.47 rad/s

for the back and front gears, b db = f df

13.47*70 = f * 170

f = 5.546 rad/s

so, max speed of the pedal = f*r + 4.44

= 0.89 + 4.44

= 5.33 m/s

= 19.19 km/hr

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