F= μR .F= μ mg costheta .ma= 0.25 m 10 cos 60.cos 60= 1/2.a= 0.25 ×10 × 1/2 .a= 0.25 × 5.a= 1.25

Acceleration of a Block on an Inclined Plane

Given:
Angle of inclination, θ = 60 degrees
Coefficient of friction, μ = 0.25
Acceleration due to gravity, g = 10 m/s²

To find:
Acceleration of the block

We can start by analyzing the forces acting on the block.

1. Weight of the block (mg):
The weight of the block acts vertically downward and can be calculated using the formula: weight = mass × acceleration due to gravity.
In this case, the weight of the block is given by mg = m × g, where m is the mass of the block.

2. Normal force (N):
The normal force acts perpendicular to the inclined plane and is equal to the component of the weight of the block perpendicular to the plane. It can be calculated using the formula: normal force = weight × cos(θ).

3. Force of friction (f):
The force of friction acts parallel to the inclined plane and opposes the motion of the block. It can be calculated using the formula: force of friction = coefficient of friction × normal force.

4. Net force (F):
The net force acting on the block is the vector sum of the weight component parallel to the plane and the force of friction. It can be calculated using the formula: net force = mg × sin(θ) - force of friction.

5. Acceleration (a):
The acceleration of the block can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is: net force = mass × acceleration.

By equating the net force equations, we can solve for the acceleration of the block.

Steps to calculate the acceleration:

1. Calculate the weight of the block using the formula mg.
2. Calculate the normal force using the formula weight × cos(θ).
3. Calculate the force of friction using the formula coefficient of friction × normal force.
4. Calculate the net force using the formula mg × sin(θ) - force of friction.
5. Equate the net force with mass × acceleration and solve for acceleration.

The acceleration can be positive or negative, depending on the direction of the net force. If the net force is in the direction of the incline, the block will accelerate uphill and the acceleration will be positive. If the net force is in the opposite direction, the block will accelerate downhill and the acceleration will be negative.

Using the given values, follow the steps above to calculate the acceleration of the block on the inclined plane.