A person of mas 50 kg carryign a load of 20 kg walks up a staircase. If the width and heigh of each step are 0.25 mand 0.2 m respectively, the work done by the man in walking up 20 steps is `(g=10ms^(-2))`

Options

A. `1400 J`
B. 800 J
C. 2000 J
D. 2800 J

Answer

To solve the problem step by step, we will calculate the work done by a person carrying a load while walking up a staircase.

### Step 1: Identify the total mass
The total mass that the person is carrying includes their own mass and the mass of the load.

- Mass of the person = 50 kg
- Mass of the load = 20 kg

**Total mass (m)** = Mass of the person + Mass of the load
**Total mass (m)** = 50 kg + 20 kg = 70 kg

### Step 2: Determine the height of one step
The height of each step is given as 0.2 meters.

### Step 3: Calculate the total height for 20 steps
To find the total height the person climbs, multiply the height of one step by the number of steps.

**Total height (H)** = Height of one step × Number of steps
**Total height (H)** = 0.2 m × 20 = 4 m

### Step 4: Calculate the work done against gravity
The work done (W) against gravity can be calculated using the formula:
\[ W = F \times d \]
where:
- \( F \) is the force (weight of the person and the load),
- \( d \) is the displacement (total height climbed).

The force due to gravity (weight) is given by:
\[ F = m \times g \]
where:
- \( g \) is the acceleration due to gravity (10 m/s²).

Substituting the values:
\[ F = 70 \, \text{kg} \times 10 \, \text{m/s}^2 = 700 \, \text{N} \]

### Step 5: Calculate the work done
Now, substitute the values of force and height into the work done formula:
\[ W = F \times H \]
\[ W = 700 \, \text{N} \times 4 \, \text{m} = 2800 \, \text{J} \]

### Final Answer
The work done by the man in walking up 20 steps is **2800 Joules**.

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