A block of mass 5.0 kg slides down an incline of inclination `30^0` and length 10 m. find the work done by the force of gravity.

Explanation

To find the work done by the force of gravity on a block sliding down an incline, we can follow these steps:

### Step 1: Identify the parameters
- Mass of the block (m) = 5.0 kg
- Angle of inclination (θ) = 30 degrees
- Length of the incline (L) = 10 m

### Step 2: Calculate the height (h) of the incline
The height can be calculated using the sine function:
\[ h = L \cdot \sin(\theta) \]
Substituting the values:
\[ h = 10 \cdot \sin(30^\circ) \]
Since \(\sin(30^\circ) = 0.5\):
\[ h = 10 \cdot 0.5 = 5 \, \text{m} \]

### Step 3: Calculate the work done by gravity
The work done by the force of gravity can be calculated using the formula:
\[ W = mgh \]
Where:
- \( g \) (acceleration due to gravity) = 9.8 m/s² (approximately 10 m/s² for simplicity in some calculations)

Substituting the values:
\[ W = 5 \cdot 9.8 \cdot 5 \]
\[ W = 5 \cdot 49 = 245 \, \text{J} \]

### Final Answer
The work done by the force of gravity is approximately **245 Joules**.

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