#### IIT (NTSE/Olympiad)

# Newton's Laws Of Motion & Friction

__9. Motion of a body on a smooth inclined plane__

__9. Motion of a body on a smooth inclined plane__

**9. Motion of a body on a smooth inclined plane**

A body is placed on a smooth inclined plane AB which makes an angle q with the horizontal. The forces acting on body are

**(i)**Weight of the body mg acting vertically down.

**(ii)**Normal reaction R acting perpendicular to the plane.

The weight mg of the body is resolved parallel and perpendicular to the plane as mg sin θ parallel to the plane and mg cos θ perpendicular to the plane.

Thus ma = mg sin θ ⇒ a = g sin θ ...(i)

R = mg cos θ ...(ii)

**Note:**

The same result can also be obtained by resolving the forces horizontally and vertically.

R sin θ = ma cos θ

mg – R cos θ = ma sin θ

solving we get,

a = g sin θ, R = mg cos θ

**Special case :**

When the smooth plane is moving horizontally with an acceleration (b) as shown in fig

In this case :

m (a + b cos θ) = mg sin θ

and mb sin θ = R – mg cos θ

solving we get a = g sin θ – b cos θ

R = m (g cos θ + b sin θ)

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#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION
- 1. First Law Of Motion
- 2. Second Law Of Motion
- 3. Third Law Of Motion
- 4. Reference Frames
- 5. Motion in a lift
- 6. Motion of a Block on a Horizontal Smooth Surface
- 7. Motion of bodies in contact
- 8. Motion of connected Bodies
- 9. Motion of a body on a smooth inclined plane
- 10. Motion of two bodies connected by a string
- 11. Friction and frictional force
- 12. Graphical representation of friction
- 13. Types of frictional force and their definition
- 14. Angle of Friction
- 15. Minimum force Required to move a block
- Points to Remember - Newton's Laws Of Motion & Friction

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION