A man of mass 50kg ascends a flight of stains 5m high in 5 seconds. If acceleration due to gravity is 10ms$^{-2}$ the power expended is

Analysis

To solve this problem, we need to calculate the power expended by the man. Power is defined as the rate at which work is done or the rate at which energy is transferred.

Concept

The formula for Power ($P$) is:

Since the man is ascending a height, the work done is equal to the gravitational potential energy gained, which is given by:

Where:

• $m$ = mass of the man (kg)
• $g$ = acceleration due to gravity (ms$^{-2}$)
• $h$ = height (m)

Combining these, the formula for power becomes:

Step-by-Step Solution

1. Identify the given values: • Mass ($m$) = 50 kg • Height ($h$) = 5 m • Time ($t$) = 5 s • Acceleration due to gravity ($g$) = 10 ms$^{-2}$

2. Calculate the Work Done: $$\text{Work} = m \times g \times h$$ $$\text{Work} = 50 \times 10 \times 5$$ $$\text{Work} = 2500 \text{ Joules}$$

3. Calculate the Power: $$P = \frac{\text{Work}}{t}$$ $$P = \frac{2500}{5}$$ $$P = 500 \text{ Watts}$$

Conclusion

Comparing our result to the given options, the power expended is 500W.

Exam Tip: Always check your units before calculating. If the mass were in grams, you would need to convert it to kilograms first. Also, remember that $1 \text{ Watt} = 1 \text{ Joule/second}$. Keeping your units consistent is the best way to avoid silly mistakes in JAMB Physics!