Question

When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that F ∝ v^2 exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s.

Answer 1

The answers are

95. 10 kJ

96. 10W

97. 40 kJ

98. 40W

99. 50W

How to solve for the energy

95. Energy for 1 km = (Drag force × distance)

= (10 N × 1000 m)

= 10 kJ (Answer: B)

96. Power = Energy / time

= (10 kJ / 1000 s)

= 10 W (Answer: A)

97. Doubling speed quadruples the drag force.

Energy for 1 km = (10 N × 4 × 1000 m)

= 40 kJ (Answer: B)

98. At 10 m/s, with quadrupled drag force,

Power = (40 kJ / 1000 s)

= 40 W (Answer: C)

99. Against a headwind matching her speed, total apparent speed becomes 0 m/s. Energy consumption is now solely due to maintaining motion, hence Power

= Drag force × (speed + headwind)

= (10 N × 5 m/s)

= 50 W (Answer: C)