Mike is cutting the grass using a lawn mower. He pushes the mower with a force of 45 N directed at an angle of `41^(@)` below the horizontal direction. Calculate the work that Mike does on the mower in pushing it 9.1 m across the yard.

Options

A. 510J
B. 410J
C. 310J
D. 360J

Answer

To calculate the work done by Mike in pushing the lawn mower, we can use the formula for work done, which is given by:

\[ W = F \cdot d \cdot \cos(\theta) \]

Where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the direction of displacement.

### Step 1: Identify the given values
- Force \( F = 45 \, \text{N} \)
- Displacement \( d = 9.1 \, \text{m} \)
- Angle \( \theta = 41^\circ \) (below the horizontal)

### Step 2: Calculate the work done
Using the formula for work done:

\[ W = F \cdot d \cdot \cos(\theta) \]

Substituting the known values into the formula:

\[ W = 45 \, \text{N} \cdot 9.1 \, \text{m} \cdot \cos(41^\circ) \]

### Step 3: Calculate \( \cos(41^\circ) \)
Using a calculator, we find:

\[ \cos(41^\circ) \approx 0.7547 \]

### Step 4: Substitute \( \cos(41^\circ) \) back into the equation
Now substituting the value of \( \cos(41^\circ) \):

\[ W = 45 \, \text{N} \cdot 9.1 \, \text{m} \cdot 0.7547 \]

### Step 5: Perform the multiplication
Calculating the work done:

\[ W = 45 \cdot 9.1 \cdot 0.7547 \approx 310.0 \, \text{J} \]

### Conclusion
The work done by Mike in pushing the lawn mower is approximately:

\[ W \approx 310 \, \text{J} \]