Chapter 2 Forces and Motion

2.9 Force in equilibrium

2.9 Forces in equilibriumEquilibrium state exists when all

the forces acting on an object are canceled out.

• No net force = no acceleration = constant velocity

2.9 Forces in equilibrium

Newton’s 3rd law of motion states that for every action, there is an equal and opposite reaction

So, forces always come on pairs.

2.9 Forces in equilibriumApplies to object at rest• An object stands on

the floor, pulled down by the force of Earth’s gravity.

• However, the object does not move in that direction because the floor stops it.

• The floor is exerting on the object an equal and opposite force.

2.9 Forces in equilibriumApplies to object in motion• The oars move in a

backward motion.• The boat moves

forward.• The movement of oars

is the “action”.• The movement of the

boat is “reaction”.• The movements are

opposite in direction but equal in force.

2.9 Forces in equilibriumThe diagram shows a weight hanger attached to a string and which is in a stationary state.The forces acting on the weight hanger are(i) the weight, W, which

acts downwards.(ii) the tension, T, which

acts upwards. The weight, W, is balanced by the tension, T of the string.Hence the hanger is in a state of equilibrium.

2.9 Forces in equilibrium

The cat resting on an inclined plane is also in equilibrium.The three forces acting on the cat cancel out each other so that the resultant force is zero.

2.9 Forces in equilibrium

(a) Two forces that act along the same directionAddition of forces

21 force,Resultant FFF

2.9 Forces in equilibrium

(b) Two forces that act in opposite directionAddition of forces

21 force,Resultant FFF

2.9 Forces in equilibrium

(c) Two forces acting at a point at an angle to each other• The resultant force can be determined by using the

parallelogram of forces.

Addition of forces

2.9 Forces in equilibrium

(c) Two forces acting at a point at an angle to each other

Addition of forces

Step 1: Draw the forces from a point with an angle with each other

2.9 Forces in equilibrium

(c) Two forces acting at a point at an angle to each other

Addition of forces

Step 2: Draw another two lines to complete the parallelogram

2.9 Forces in equilibrium

(c) Two forces acting at a point at an angle to each other

Addition of forces

Step 3: Draw the diagonal of the parallelogram. The diagonal represents the resultant force, F and its direction, α can be determined by measuring the angle between the diagonal with either one side of the parallelogram.

2.9 Forces in equilibrium(c) If the two forces are perpendicular to each other, the resultant force can be determined by using Pythagoras theorem and trigonometry to solve the problem.

Addition of forces

2.9 Forces in equilibriumAddition of forces

2.9 Forces in equilibriumResolution force

A single force can be resolved into two components,a) horizontal component, Fx = F cos Θb) vertical component, Fx = F sin Θ

cosFFx

sinFFy

2.9 Forces in equilibriumResolution force

cosFFx

sinFFy

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibriumResolution force

2.9 Forces in equilibrium

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2.9 Forces in equilibrium

2.9 Forces in equilibrium

2.9 Forces in equilibriumThree forces in equilibrium

2.9 Forces in equilibriumThree forces in equilibrium

2.9 Forces in equilibriumThree forces in equilibrium