Inclined Planes

According to question, a small block is slide down from top of inclined plane as shown in figure,

Step 1: Understanding Forces Acting on the Body
- The forces acting on the body on an inclined plane of angle are:
- Gravity acts downward.
- Normal reaction acts perpendicular to the plane.
- Friction force acts opposite to motion along the plane.
Step 2: Resolving Forces Along the Inclined Plane
- The gravitational force along the inclined plane: - The normal force perpendicular to the plane: - The frictional force opposing the motion: Step 3: Applying Newton’s Second Law
- The net force along the inclined plane:
- The acceleration is given by: Step 4: Conclusion
Thus, the acceleration of the body is:

Step 1: Understanding the Given Data
- Mass of the body:
- Acceleration while sliding down:
- Inclination angle:
- Acceleration due to gravity:
Step 2: Finding the Net Force while Sliding Down
The equation of motion along the incline while sliding down is: Step 3: Finding the Required Force to Move Up
For moving up with the same acceleration: Step 4: Conclusion
Thus, the external force required to take the body up with the same acceleration is: