   Chapter 5, Problem 51P

Chapter
Section
Textbook Problem

What average mechanical power must a 70.0-kg mountain climber generate to climb to the summit of a hill of height 325 m in 45.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fraction of the power that must be produced by the climber’s body.

To determine
The average mechanical power the mountain climber generate to climb the summit of a hill.

Explanation

Given Info:

The mass of the climber is 70.0kg .

Height of the hill is 325m .

The time taken by the climber to climb the hill is 45.0min .

Assume that the climber starts from the rest hi is zero to hf to 325m .

Using the Work-Energy theorem, the work required to climb the hill is,

W=mghf

• hf is the height of the hill
• m is the mass of the climber
• g is acceleration due to gravity

Thus,

Formula to calculate the average mechanical power is,

P¯=WΔt=mghfΔt

• W is the work required to climb the hill
• Δt is the time taken by the climber to climb the hill

Substitute 70

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