   Chapter 11, Problem 3P

Chapter
Section
Textbook Problem

A 75-kg sprinter accelerates from rest to a speed of 11.0 m/s in 5.0 s. (a) Calculate the mechanical work done by the sprinter during this time. (b) Calculate the average power the sprinter must generate. (c) If the sprinter converts food energy to mechanical energy with an efficiency of 25%, at what average rate is he burning Calories? (d) What happens to the other 75% of the food energy being used?

(a)

To determine
The mechanical work done by the sprinter.

Explanation

Given Info: mass of the sprinter is 75 kg, speed of the sprinter is 11.0 m/s and time is 5.0 s.

Mechanical work done is equal to the change in kinetic energy of the sprinter.

W=ΔKE

• W is the mechanical work done,
• ΔKE is the change in kinetic energy,

Formula for the change in kinetic energy is,

ΔKE=12m(vf2vi2)

• m is the mass of the sprinter,
• vi is the initial velocity of the sprinter,
• vf is the final velocity of the sprinter,

Use 12m(vf2vi2) for ΔKE to rewrite W

(b)

To determine
The average power the sprinter must generate.

(c)

To determine
The average rate of burning of Calories.

(d)

To determine
What happens to the other 75% of the food energy.

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