the angle of inclination of an inclined plane is 60 degree coefficient of friction between 10 kg body on oit and its surface is 0.2.find acceleration don the plane

To determine the acceleration of a 10 kg body on an inclined plane with a 60-degree angle and a coefficient of friction of 0.2, we need to analyze the forces acting on the body. This involves breaking down the gravitational force into components and accounting for friction. Let’s go through the calculations step by step.

Identifying the Forces

When a body is placed on an inclined plane, several forces act on it:

• Gravitational Force (Weight): This is the force due to gravity acting downwards, calculated as \( W = mg \), where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). For our 10 kg body, this is \( W = 10 \times 9.81 = 98.1 \, \text{N} \).
• Normal Force (N): This is the force exerted by the surface of the inclined plane perpendicular to the surface.
• Frictional Force (F_f): This opposes the motion of the body and is calculated as \( F_f = \mu N \), where \( \mu \) is the coefficient of friction.

Calculating the Components of Forces

Next, we need to resolve the weight into two components: one parallel to the incline and one perpendicular to it.

• The component of weight parallel to the incline is given by: F_{\text{parallel}} = W \sin(\theta) = 98.1 \sin(60^\circ) = 98.1 \times \frac{\sqrt{3}}{2} \approx 84.87 \, \text{N}.
• The component of weight perpendicular to the incline is: F_{\text{perpendicular}} = W \cos(\theta) = 98.1 \cos(60^\circ) = 98.1 \times \frac{1}{2} = 49.05 \, \text{N}.

Finding the Normal Force

The normal force (N) is equal to the perpendicular component of the weight since there are no vertical accelerations:

N = F_{\text{perpendicular}} = 49.05 \, \text{N}.

Calculating the Frictional Force

Now, we can calculate the frictional force:

F_f = \mu N = 0.2 \times 49.05 \approx 9.81 \, \text{N}.

Applying Newton's Second Law

According to Newton's second law, the net force acting on the body along the incline can be expressed as:

F_{\text{net}} = F_{\text{parallel}} - F_f.

Substituting the values we found:

F_{\text{net}} = 84.87 - 9.81 \approx 75.06 \, \text{N}.

Calculating Acceleration

Finally, we can find the acceleration (a) of the body using Newton's second law, which states that \( F = ma \):

a = \frac{F_{\text{net}}}{m} = \frac{75.06}{10} \approx 7.51 \, \text{m/s}^2.

Summary of Results

The acceleration of the 10 kg body down the inclined plane is approximately 7.51 m/s². This calculation illustrates how forces interact on an inclined plane and the role of friction in affecting motion.