A body of mass 2kg is placed on a rough inclined plane whose angle of inclination is 30°. Fine the resultant force acting down the slope and the acceleration if frictional force of 5N acts between the body and the inclined surface.

The resultant farce acting down the slope is 4.8 N

The acceleration is 2.4 m/s²

Explanation:

A body of mass 2kg is placed on a rough inclined plane whose angle of

inclination is 30°

The weight of the body acting vertically down word, then we must to

find the two components of the weight which parallel and perpendicular

to the surface

→ The mass of the body is 2 kg

→ weight = mg, m is the mass and g is the acceleration of gravity

→ m = 2 kg, g = 9.8 m/s²

→ The weight of the body = 2 * 9.8 = 19.6 N

We must to distribute the weight of the body into two component

one perpendicular to the plane and the other is parallel to it by

using Ф the angle of inclination

→ The perpendicular component of the weight to the plane is w cosФ

→ The parallel component of the weight to the plane is w sinФ

→ w = 19.6 N, Ф = 30°

→ The perpendicular component = 19.6 cos (30) 16.97 N

→ The parallel component = 19.6 sin (30) = 9.8 N

The plane is rough, then there is a friction force acting parallel to the

plane and in opposite direction of motion

There are two forces acting parallel to the slope, the component of the

weight down and the frictional force up

The resultant force acting down the slope is the difference between them

→ The component of the weight = 9.8 N and friction force = 5 N

→ Resultant force down the slope = 9.8 - 5 = 4.8 N

The resultant farce acting down the slope is 4.8 N

Due to Newton's Law

∑ Force in direction of motion = mass * acceleration

→ The resultant force in direction of motion = 4.8 N, mass = 2 kg

→ 4.8 = 2 * acceleration

Divide both sides by 2

→ Acceleration = 2.4 m/s²

The acceleration is 2.4 m/s²