2.9 Analysing Forces in Equilibrium

2.9Analysing Forces in Equilibrium

Chapter 2 Forces and Motion

The Effective Components of a Weight on an Inclined Plane

Consider a box resting on an inclined plane at an angle to the horizontal.

The weight of the box is

The weight can be resolved into two perpendicular components:

The component vertical / perpendicular to the plane

The component down / parallel to the plane

State out what are the both components?

The effective components of a weight on an inclined plane

To solve problems involving inclined planes, weight is replaced with its two perpendicular components.

Object in equilibrium on a rough inclined plane

When a box at rest on an inclined plane

Try to solve it in

(i) The net force perpendicular to the plane =0

(ii) The net force parallel to the plane =0

Acceleration of an object on a smooth inclined plane

When a box at rest on a smooth inclined plane

Try to solve it in

(i) The net force perpendicular to the plane =0

(ii) The net force parallel to the plane =0

ExerciseA carton of mass 5kg is at rest on an inclined plane making an angle of 15 with the horizontal. Find the frictional Force and the normal reaction force acting on the carton.

Figure shows a horizontal force, F acts on a wooden block of weight 8 N placed on a smooth plane inclined at 30 to the horizontal.

What must the magnitude of F be to prevent the block from sliding down?

Three Forces in Equilibrium

Problems involving three forces in equilibrium can be solved rather by:

(a) Method A: Resolution of forces

(b) Method B: Drawing a closed triangle of forces

Three Forces in Equilibrium

A 6 kg weight is suspended from a hook in the ceiling as shown in figure.

A horizontal string pulls the supporting string so that the latter makes an angle of 50 with the horizontal. Find the tensions in both strings.

Method AResolution of Forces

The slanting force, T1 is resolved as show.

Since the weight is in equilibrium, therefore;

Vertically,

Total force upwards = total force downwards

Method AResolution of Forces

horizontally,

Total force to the left = total force to the right

Method BDrawing a closed triangle of forces

Drawing a closed triangle forces

Method BDrawing a closed triangle of forces

After drawing the triangle, use simple trigonometry to solve the problem.

ExerciseJoan and her sister lift a pail of water of total mass 5.6 kg.

Each of them exerts a force of F at 25 to the vertical.

Find the magnitude of F.

ExerciseA lamp of weight 25 N is supported by two ropes as shown in figure.

Given that the tension in rope A is 20 N, find

The angle

The tension in rope B

ExerciseEach elephant in the diagram below is pulling a rope attached to a mass of 10 kg

The elephants pull with a force of 5000 N.

Find the angle between the ropes.

Can the rope be pulled to become horizontal?

ExerciseA mirror of weight 12 N is hung on the wall using a string as shown.

Draw a scale drawing of a triangle of forces to determine the tension, T in the string.

(use scale 1 cm = 2N)