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)?
time = 100 * 3600 = 3.6 * 10^5 s
so
energy used= 120*3.6*10^5
= 432 * 10^5 Joules
= m g h = 65 * 9.81 * h
so
h = .677 * 10^5 = 67,700 meters
To determine the height the student could have been lifted, we need to calculate the total amount of heat energy lost during the 100 hours of reading and then convert that energy into potential energy to lift the student against gravity.
First, let's calculate the total heat energy lost in 100 hours:
Total Energy = Power x Time
Given:
Power = 120 W
Time = 100 hours
Total Energy = 120 W x 100 hours
Now, let's convert the heat energy into potential energy using the formula:
Potential Energy = Mass x Gravity x Height
Given:
Mass = 65 kg
Gravity = 9.8 m/s² (gravitational acceleration)
Potential Energy = Total Energy
Potential Energy = 65 kg x 9.8 m/s² x Height
Since the potential energy is equal to the total energy, we can set up the equation:
65 kg x 9.8 m/s² x Height = Total Energy
Plugging in the values:
65 kg x 9.8 m/s² x Height = 120 W x 100 hours
Note: We need to convert the time from hours to seconds since the power value is in watts (per second).
65 kg x 9.8 m/s² x Height = 120 W x 100 hours x (3600 seconds/1 hour)
Now we can solve for the height:
Height = (120 W x 100 hours x 3600 seconds/1 hour) / (65 kg x 9.8 m/s²)
To solve this problem, we'll use the formula for calculating work done. Work (W) is equal to the product of force (F) and displacement (d) in the direction of the force.
The force needed to lift the student against gravity can be calculated using the formula F = mg, where m represents the mass of the student and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the student weighs 65 kg, the force required to lift them against gravity is F = 65 kg * 9.8 m/s² = 637 N.
Now, we need to find out how much work is done over a period of 100 hours. The work done (W) can be calculated using the formula W = Power (P) * time (t). Power (P) is the rate at which work is done and is equal to the rate at which the body loses heat energy. In this case, the power is given as 120 W.
Using the formula, W = P * t, we have W = 120 W * 100 hours.
Before proceeding, we need to convert hours to seconds, as power is given in watts (Joules per second). Since there are 3600 seconds in one hour, multiplying the time by 3600 will convert hours to seconds:
W = 120 W * (100 hours * 3600 seconds/hour).
W = 120 W * 360,000 seconds.
Now, we can calculate the work done:
W = 43,200,000 J.
Finally, we can find the displacement (d) by rearranging the formula W = F * d:
d = W / F.
Substituting the values:
d = 43,200,000 J / 637 N.
d ≈ 68,000 meters.
Therefore, the student could have been lifted approximately 68,000 meters if all the heat energy lost was utilized to lift them against gravity.