Find the components of weight along and perpendicular to a plane if a mass of 4 kg is laying on the plane making an angle making an angle of `60^(@)` with the horizontal .

Answer

To find the components of weight along and perpendicular to a plane for a mass of 4 kg resting on an inclined plane at an angle of 60 degrees with the horizontal, we can follow these steps:

### Step 1: Calculate the Weight of the Mass
The weight (W) of the mass can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 4 \, \text{kg} \) (mass)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 40 \, \text{N} \]

### Step 2: Identify the Angle of Incline
The angle of the incline with the horizontal is given as \( \theta = 60^\circ \).

### Step 3: Calculate the Component of Weight Perpendicular to the Plane
The component of the weight perpendicular to the incline (W_perpendicular) can be calculated using the cosine of the angle:
\[ W_{\perpendicular} = W \cdot \cos(\theta) \]
Substituting the values:
\[ W_{\perpendicular} = 40 \, \text{N} \cdot \cos(60^\circ) \]

Since \( \cos(60^\circ) = \frac{1}{2} \):
\[ W_{\perpendicular} = 40 \, \text{N} \cdot \frac{1}{2} = 20 \, \text{N} \]

### Step 4: Calculate the Component of Weight Along the Plane
The component of the weight along the incline (W_parallel) can be calculated using the sine of the angle:
\[ W_{\parallel} = W \cdot \sin(\theta) \]
Substituting the values:
\[ W_{\parallel} = 40 \, \text{N} \cdot \sin(60^\circ) \]

Since \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \):
\[ W_{\parallel} = 40 \, \text{N} \cdot \frac{\sqrt{3}}{2} = 20\sqrt{3} \, \text{N} \]

### Final Results
- The component of weight perpendicular to the plane is \( W_{\perpendicular} = 20 \, \text{N} \).
- The component of weight along the plane is \( W_{\parallel} = 20\sqrt{3} \, \text{N} \).