The human body loses heat at a rate of 120W when sitting quietly at rest. If a 65 kg student takes 100 hours to read War and Peace by Leo Tolstoy, how high could they have been lifted if all the heat energy lost was utilised to lift them against gravity (assuming that the force of gravity on the student remains constant)?
watts = energy/time
so, use this to find the energy (watch the units!)
PE = mgh
To find out how high the student could have been lifted, we need to calculate the total energy lost in 100 hours and then convert it to potential energy.
First, let's calculate the total energy lost by the student in 100 hours. We know that the student loses heat at a rate of 120W (Watts). One watt is equal to one joule per second. Therefore, in one hour, the energy lost would be:
Energy Lost in 1 hour = Power x Time = 120W x 1 hour
Since we are working with time in hours, we need to convert it to seconds:
Energy Lost in 1 hour = 120W x 3600 seconds
Now, let's calculate the total energy lost in 100 hours:
Total Energy Lost = Energy Lost in 1 hour x 100 hours
= (120W x 3600 seconds) x 100 hours
Next, we can convert the energy to potential energy using the formula:
Potential Energy (PE) = mass x gravity x height
In this case, the potential energy will be the total energy lost, the mass is 65 kg (given in the question), and gravity is approximately 9.8 m/s².
Total Energy Lost = 65 kg x 9.8 m/s² x height
Now we can rearrange the formula to solve for height:
height = Total Energy Lost / (mass x gravity)
Finally, substitute the values into the equation:
height = ( (120W x 3600 seconds) x 100 hours ) / (65 kg x 9.8 m/s²)
Simplify and calculate to find the result.