A man weighing 60 kg climbs up a staircase carrying a load of 20 kg on his head. The stair case has 20 steps each of height 0.2 m. If he takes 10 s to climb find his power

Options

A. 313.6 W
B. 120.6 W
C. 510 W
D. 0

Explanation

To solve the problem step by step, we will calculate the total power exerted by the man while climbing the staircase.

### Step 1: Identify the given data
- Weight of the man (m1) = 60 kg
- Weight of the load (m2) = 20 kg
- Height of each step (h) = 0.2 m
- Number of steps = 20
- Time taken (t) = 10 s
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Calculate the total mass
The total mass (M) that the man is carrying is the sum of his weight and the load:
\[ M = m1 + m2 = 60 \, \text{kg} + 20 \, \text{kg} = 80 \, \text{kg} \]

### Step 3: Calculate the total height climbed
The total height (H) climbed is the product of the height of each step and the number of steps:
\[ H = \text{height of each step} \times \text{number of steps} = 0.2 \, \text{m} \times 20 = 4 \, \text{m} \]

### Step 4: Calculate the work done
The work done (W) against gravity is given by the formula:
\[ W = M \cdot g \cdot H \]
Substituting the values:
\[ W = 80 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 4 \, \text{m} \]
\[ W = 80 \times 9.8 \times 4 = 3136 \, \text{J} \]

### Step 5: Calculate the power
Power (P) is defined as the work done per unit time:
\[ P = \frac{W}{t} \]
Substituting the values:
\[ P = \frac{3136 \, \text{J}}{10 \, \text{s}} = 313.6 \, \text{W} \]

### Final Answer
The power exerted by the man while climbing the staircase is **313.6 Watts**.