An exercise bike has the basic construction of a bicycle with a heavy disk wheel

Question

An exercise bike has the basic construction of a bicycle with a heavy disk wheel. In addition to friction in the bearings and the transmission system, resistance to pedaling is provided by two narrow friction pads that push with equal force on each side of the wheel. The coefficient of kinetic friction between the pads and the wheel is 0.4, and the pads provide a total retarding force of 20 N tangential to the wheel. The pads are located at a position 0.3 m from the center of the wheel. The distance, recorded on an odometer, is considered to be the distance that a point on the wheel 0.3 m from the center moves. The pedals move in a circle of 0.15 m in radius and complete one revolution, while a transmission system allows the wheel to rotate twice.

A cyclist pedals continuously for 20 minutes, registering 4800 m on the odometer.

(a) What is the magnitude of the normal force pushing each friction pad onto the wheel?

(b) Which is the radial acceleration of the part of the wheel that passes between the friction pads?

(c) If the wheel has a kinetic energy of 30 J when the cyclist stops pedaling, how many rotations will it make before coming to rest?

(d) During a second workout, the cyclist reduces the force on the friction pads by 50%, then pedals for two times the previous distance in 1/2 the previous time. How does the amount of energy dissipated by the pads in the second workout compare with energy dissipated in the first workout?

(e) What is the ratio of the distance moved by a pedal to the distance moved by a point on the wheel located at a radius of 0.3 m in the same amount of time?

(f) A cyclist's average metabolic rate during a workout is 500 W. If the cyclist wishes to expend at least 300 kcal (1 kcal = 4186 J) of energy, how long must the cyclist exercise at this rate?

Explanation / Answer

power =mg sin theta *v

=100*10 *sin30 *3

=1500

avg power = 20% (535 -85)

=90

speed,

v= 4800/20 *60/1 =4

p = fk*v

=20*4 =80

diff in power =90-80

=10w

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.