A man with a mass of 73 kg takes 4.0 seconds to run up the flight of stairs shown in the figure below at a constant speed. Assuming that the man has a 20% mechanical efficiency when climbing stairs, what is the average total power that the man generates to get to the top of the stairs? Air resistance may be neglected.


To solve this problem, we need to calculate the average total power generated by the man to climb the stairs. Here are the steps we’ll follow:

### Step 1: Identify the energy required to climb the stairs
The energy required to climb the stairs is the mechanical energy, which is related to the change in gravitational potential energy.

Gravitational potential energy is given by:
\[
E_p = mgh
\]
Where:
- \(m = 73 \, \text{kg}\) (mass of the man)
- \(g = 9.81 \, \text{m/s}^2\) (acceleration due to gravity)
- \(h = \text{height of the stairs (unknown, but required for solving)}\)

Without the height \(h\), we cannot compute the exact potential energy. Please confirm the height of the stairs or provide the dimensions.

### Step 2: Calculate the power output required to climb the stairs
The average power \(P_{\text{output}}\) required to climb the stairs is related to the mechanical energy and the time \(t = 4.0 \, \text{s}\):

\[
P_{\text{output}} = \frac{E_p}{t} = \frac{mgh}{t}
\]

### Step 3: Account for mechanical efficiency
Since the man has a 20% mechanical efficiency, only 20% of the total power he generates is used for mechanical work. Therefore, the total power \(P_{\text{total}}\) generated is:

\[
P_{\text{total}} = \frac{P_{\text{output}}}{\text{Efficiency}} = \frac{P_{\text{output}}}{0.20}
\]

Once we know the height \(h\), we can compute the total power using the formulas above.

Could you provide the height or any additional details on the flight of stairs?

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Would you like more details on any of the concepts or steps?

Here are five related questions that can expand on this topic:
1. How do you calculate power when dealing with variable forces?
2. What role does mechanical efficiency play in everyday activities like walking or running?
3. How would the calculation change if the man was running up a slope instead of stairs?
4. How does air resistance affect power output in different conditions?
5. How do different types of energy (kinetic, potential) relate to mechanical power?

**Tip:** Power is a rate of energy transfer, so even slight changes in time or height can significantly affect the total power generated.

A man with a mass of 73 kg takes 4.0 seconds to run up the flight of stairs at a constant speed. Assuming that the man has a 20% mechanical efficiency when climbing stairs, what is the average total power that the man generates to get to the top of the stairs?

Find out how to calculate the average total power generated by a 73 kg man climbing stairs in 4 seconds with 20% mechanical efficiency. This problem involves concepts of gravitational potential energy, power, and efficiency, suitable for high school physics students.

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