Heat, Work & Internal Energy

[dnl65078]

Homework Statement

Please help with this problem!
How many sprints from rest to a speed of 4.5 m/s would a 59 kg woman have to complete in order to burn off 5.0 x 102 Calories? (Assume 100% efficiency in converting food energy to mechanical energy.)

Homework Equations

The Attempt at a Solution

Speed (v) = 4.5 m /s
.
==> h = v2 / 2g = (4.5)2 / ( 2 * 9.8) = 1.033 m
.
Mass (m) = 59 kg
.
Energy (E) = 5.0 * 10-2 cal = 5.0 * 10-2 cal * (1000 * 4.186) J
.
= 209.3 J
.
number of sprints is :
.
n = E / 2 m g h
.
= (20.9.3 J) / ( 2 * 59 * 9.8 * 1.033 )
.
= 0.1752 sprints

 

[Legion81]

Have you tried calculating the kinetic energy the woman would have, converting it to calories, and finding the number of sprints? I'm not sure if that will get you the right answer, but I come up with about 3.5 sprints. You may want to check the back of the book to see if that is close.

 

[Redbelly98]

Is the energy to be burned off 5.0x10⁺² or 5.0x10^-2 ?

Legion81 is correct, you'll need to figure out the kinetic energy of the sprinter.