forces

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T H E M E T W O : N E W T O N I A N M E C H A N I C S

C h a p t e r 3Learning outcomes• Describe how balanced and unbalanced

forces affect body• Describe how a force may change motion of a

body• Identify and draw free body diagrams of

forces acting on object • Solve problems using a graphical method for

a static point mass being acted on by 3 forces for 2-D cases

• Use resultant force = mass × acceleration• Explain effects of friction on motion of a body

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C h a p t e r 33.1 Balanced and Unbalanced ForcesForces• Newton’s first law of motion states that

an object at rest will remain at rest and an object in motion will continue in motion at constant speed in a straight line in the absence of a resultant force acting on it

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C h a p t e r 33.1 Balanced and Unbalanced ForcesBalanced Forces• Newton’s first law of motion implies that

when no resultant force acts on a body, the body will continue with whatever motion it has

• If it is at rest, it will remain at rest• If it is moving, it will continue moving at

constant speed in a straight line

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• Rock at rest, net force acting

on it must be zero.• Weight of rock acting

downwards.• So there must be a

second force pushing it upwards.

• This second force is the reaction of the table and it balances the weight of the rock.

3.1 Balanced and Unbalanced ForcesBalanced Forces

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• The weight of the aircraft is balanced by the lift from the wings, so the aircraft flies at constant height.

• Air resistance encountered on moving forward is balanced by the thrust of the engines, so the velocity of the aircraft is constant.


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• A falling object will reach a point when air resistance = weight.

• Object falls with terminal velocity.• Resultant force acting on it is zero.• No resultant force does not mean that no forces act on body.

• It means all forces are balanced.


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Balanced Forces• When the forces acting on an object are

balanced, the object is either at rest or moving with uniform velocity.

3.1 Balanced and Unbalanced Forces

Rest Constant velocityor

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Unbalanced Forces• If the forces on an object are unbalanced, there will be a resultant force acting

on it and changing its velocity.


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• A resultant force will cause(i) a stationary object to move(ii) a moving object to

– stop– move faster– slow down– change direction


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C h a p t e r 33.1 Balanced and Unbalanced Forces

• Newton’s second law of motion states that the resultant forces acting upon an object is equal to the product of the mass and the acceleration of the object.

• The direction of the force is the same as that of the object’s acceleration.

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• Force = mass × acceleration• F = ma• SI unit for force is the newton (N)• One newton (N) is defined as the force

which produces an acceleration of 1 m s−2 when it is applied to a mass of 1 kg.

• 1 N = 1 kg m s−2


1 N1 kg

a = 1 m s–2

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C h a p t e r 33.1 Balanced and Unbalanced Forces

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Resultant Forces • When several forces act on an object, these

forces can be replaced with a single resultant force.


Resultant force

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Resultant Forces (Cases of Parallel Forces)• For cases of parallel forces, the magnitude of

the resultant force can be calculated by simple addition or subtraction


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1. When forces acting on an object are balanced(or no resultant forces are acting on an object):

(a) If it is at rest, it will remain at rest. (b) If it is moving, it will continue moving at constant speed in a straight line.2. When the forces on an object are

unbalanced, a resultant force acts on the object and it accelerates (or decelerates).

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Action and Reaction• Newton’s third law of motion

states that for every action there is an equal and opposite reaction

3.2 Free-body Diagram

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Action and Reaction• If object A exerts a force on object B, then B exerts an equal but opposite force on A• Action and reaction act on different objects.


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Free-body Force Diagrams• According to Newton’s 3rd law, forces always

occur in pairs with one force acting on a body, and an equal and opposite force acting on another body.

• If both forces and bodies are drawn in the same diagram, it can cause confusion about which force acts on which body.

• A free-body force diagram shows forces acting on a single body only.


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Example

Free-Body Diagram


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Mass under Action of 3 forces in 2 dimensions

(a) Unbalanced forces

–When we apply 3 forces to a point object, the resultant force acting on the object can be obtained by adding the force vectors


A

B C

AB

C

R

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• Vector A is drawn according to scale.• Vector B is drawn according to scale

with its starting point touching the ending point vector A.

• Vector C is drawn according to scale with its starting point touching the ending point of B.

• Draw an arrow from the starting point of A to the ending point of C to obtained the resultant R.

• The same R can also be obtained by starting with vector B or C.

Procedure for Adding Vectors

A

B

C

R


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(b) Balanced forces• When 3 forces acting on

an object are balanced, the

object will not accelerate.

• When we draw the vector diagram the 3 vectors form a closed triangle.

• Resultant is zero.


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C h a p t e r 33.2 Free-body Diagram

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1. For every action there is an equal and opposite reaction

2. Action and reaction forces act on different objects

3. A free-body force diagram shows the forces that act on a single body

4. The resultant of 3 or more forces that act on an object can be determined using vector addition

5. When the 3 forces that act on an object are balanced the object will not accelerate. The 3 forces will form a closed triangle.

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C h a p t e r 33.3 FrictionFriction as a Useful Force• Friction is needed for walking and rolling• No friction will cause slip

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Friction as a Nuisance• Friction causes surfaces to heat up, results

in wear and tear.• In machinery, friction reduces efficiency as

large amount of energy wasted as heat.• Much research carried out in industries on

ways to reduce friction.

3.3 Friction

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Ways to reduce friction:• Moving parts made as smooth as

possible• Materials with very low frictional

resistance is used• Ball and roller bearings are placed

between moving parts• Surfaces separated by lubricant• Surfaces separated by air cushion

3.3 Friction

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Frictional force between two surfaces on a horizontal plane:

• Depends on material in contact• Depends on roughness of surfaces• Is proportional to the force pressing the

surfaces together• Is independent of the area of contact

3.3 Friction

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C h a p t e r 33.3 Friction

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1. Friction is a force that opposes sliding motion between two surfaces in contact.

2. For a body on a horizontal plane, the frictional force depends

(a) the nature of the contact surfaces(b) the weight of the body

3. Friction does not depend on the area of contact of the surfaces.

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• What happens when there is no resultant force on a body?

• How are force and acceleration related?• How can an object move if action equals

reaction?• Is friction a useful force or a nuisance?

Questions

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forces

Education

unbalanced forces newtons

free body diagrams of

opposite force

resultant force acts

point object

force vectors

freebody force diagrams

single resultant force