# Homework Help: Heat, Work & Internal Energy

1. Jan 9, 2010

### dnl65078

1. The problem statement, all variables and given/known data

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.)

2. Relevant equations

3. 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

2. Jan 9, 2010

### 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.

3. Jan 10, 2010

### Redbelly98

Staff Emeritus
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.