Final answer:
To determine how fast a person would need to run to have a certain amount of energy, we can use the formula E = mgh, where E is the energy, m is the mass, g is the acceleration due to gravity, and h is the height. By calculating the potential energy gained or the external mechanical energy delivered, we can determine the speed required.
Step-by-step explanation:
In order to calculate how fast a person would need to run to have a certain amount of energy, we need to consider the relationship between energy and work done. Energy can be calculated using the formula E = mgh, where E is the energy, m is the mass, g is the acceleration due to gravity, and h is the height.
Now, let's look at the given examples:
Example 1: If a 70 kg person climbs 10 flights of stairs, each flight 3 m high, the potential energy gained can be calculated as follows:
E = mgh = 70 kg * 10 * 3 m = 2100 J
Example 2: If a 80 kg person is capable of delivering external mechanical energy at a rate of 200 W sustained over several minutes, we can calculate how high they would be able to climb in two minutes:
E = Pt, where P is the power and t is the time. Thus, 200 W * 2 min = 400 J
By using these formulas, you can calculate the energy and determine how fast a person would need to run to have a certain amount of energy.