The work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth plane inclined at an angle of 15° with the horizontal is

Options

A. 4.36 kJ
B. 5.17 kJ
C. 8.91 kJ
D. 9.82 kJ

Answer

To solve the problem of calculating the work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth inclined plane at an angle of 15° with the horizontal, we can follow these steps:

### Step 1: Identify the given values
- Weight of the block (W) = 2 kN = 2000 N (since 1 kN = 1000 N)
- Length of the incline (d) = 10 m
- Angle of inclination (θ) = 15°

### Step 2: Calculate the height (h) gained
The height gained (h) can be calculated using the sine function from the right triangle formed by the incline:
\[ h = d \cdot \sin(\theta) \]
\[ h = 10 \cdot \sin(15°) \]

Using a calculator, we find:
\[ \sin(15°) \approx 0.2588 \]
Thus,
\[ h = 10 \cdot 0.2588 \approx 2.588 \, \text{m} \]

### Step 3: Calculate the work done (W)
The work done against gravity when lifting the block is equal to the change in gravitational potential energy, which can be calculated using the formula:
\[ W = W \cdot h \]
Substituting the values we have:
\[ W = 2000 \, \text{N} \cdot 2.588 \, \text{m} \]
\[ W \approx 5176 \, \text{J} \]

### Step 4: Convert work done to kilojoules
Since 1 kJ = 1000 J, we can convert the work done into kilojoules:
\[ W \approx \frac{5176}{1000} \approx 5.176 \, \text{kJ} \]

### Final Answer
The work done in pulling up the block of wood is approximately **5.176 kJ**.

---