The cyclist power output to climb the same hill at the same speed.
Answer to Problem 71P
Solution:
Explanation of Solution
Given:
Angle made by hill with horizontal
Steady speed of cyclist in downward motion
Total mass of bicycle plus rider
Formula used:
W : Work
t : time
F: force
V: speed
θ : angle between force and velocity.
Newton’s second law
Calculation:
When cyclist moves down ward with steady speed.
N : normal reaction by hill on bicycle
Mg : weight of cyclist plus rider.
F : friction force acting upwards along the hill.
Considering x -axis along the inclined plane.
When cyclist moves up ward with steady speed
Friction force acts down ward, because cycle moves upward.
N : normal reaction by hill on bicycle
Mg : weight of cyclist plus rider
F : friction force
Normal, and contact surface is same so friction on the cyclist remain same only direction will be reversed. So
Friction force
Write Newton’s second law along the plane.
Calculation of power
Here θ =
Substitute the values and solve:
Conclusion: Power output of bicyclist
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