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A Love Story…….

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Introduction

• Motion of objects can be described precisely in terms of their distance travelled, displacement, speed, velocity and acceleration.

• However what actually makes a body move?

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Objectives

• After the lesson, you should be able to:

– State what is a force?

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What is a Force?

• A force is a

PUSH

or a

PULL

• Lifting, bending, stretching, twisting,

compressing etc involves push or pull

Exert

a force.

• SI unit of force is

newton

(

N

)

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Nature of Forces

Simple definition of a Force

A force is a push or a pull that one object

exerts on another which produces, or tends to produce motion, stops or tends to stop motion.

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2 Types of Forces

Contact Forces

– Forces that acts when objects touch.

– Pushing trolley, lifting bicycle, wind on sails and open a door

– Eg: Frictional force

Non-Contact Forces

– Forces that acts at a distance.

– Magnet, diver, or object falling (gravity)

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Common Types of Forces

• Weight: Force of gravity acts on a mass

• Friction: Force that resists the motion of an object

• Magnetic force: The push (repulsion) or pull (attraction) exerted between magnetic poles.

• Electric force: The push (repulsion) or pull (attraction) between electric charges

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Effects of Forces on Motion

A force can:

• Cause a stationary body to move and a moving body to stop moving.

• Change the speed of a moving body (accelerate or decelerate the body).

• Cause a moving body to change its direction

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Scalars and Vectors

Learning Outcomes

At the end of this section, you’ll be able to:

• understand and distinguish between scalar and vector quantities

• add two vectors using a graphical method

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Scalars and Vectors

What are scalar and vector quantities?

• Scalar quantities are physical quantities that have magnitude only.

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Scalars and Vectors

When referring to a scalar quantity, we only need to

consider its magnitude.

Example:

– The mass of an object is 2.0 kg

– The volume of the box is 5 m3

– The distance traveled by the car is 800 m

Scalar quantities are added by summing the magnitude

Example:

A mass of 100 g added to 200 g gives a total of

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Scalars and Vectors

When referring to a vector quantity, we must consider

both its magnitude and direction.

Example:

The car travels with a velocity of 20 ms-1 in the direction of

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How do we add vectors?

• When adding vectors, both the magnitude and direction of the vectors must be considered.

• Addition of two or more vectors together gives a

single vector called the RESULTANT VECTOR

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Scalars and Vectors

Addition of parallel vectors (Example 1)

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Scalars and Vectors

Addition of Parallel Vectors (Example 2)

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Addition of Parallel Vectors

(Example 3)

N 0 N 3 N) (-3 Force Resultant = + =

The object is in a state of equilibrium i.e. it remains stationary or continues moving in a straight line.

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Scalars and Vectors

Addition of non-parallel vectors using the parallelogram method

In most cases, vectors such as forces act at an angle to

each other, such as in the diagram below.

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Parallelogram Method

Scalars and Vectors

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Scalars and Vectors

Another method of adding non-parallel vectors is the tip-to-tail method. We can use the tip-to-tail method to find the resultant of the diagram below.

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Scalars and Vectors

Tip-To-Tail Method

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Scalars and Vectors

Worked Example 3.1

A weight W (6.0 N) hangs on the end of a string, which is pulled sideways by a force F. The string makes an angle of 30 with the vertical, as show in the diagram. The string supports the weight by exerting a pull known as tension T

of 7.0 N.

Determine the force F by using the

(a) parallelogram method,

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Scalars and Vectors

Solution to Worked Example 3.1(a)

(a) Parallelogram Method: For the weight to be stationary, the resultant force must be zero. Therefore, force F must balance out the resultant of

weight W and tension T. Hence, we will first find the resultant of W and T, then determine F.

From the force parallelogram (as shown in the diagram), drawn with a scale of 1 cm:2 N, the diagonal, which is the resultant of T and W, has a length of 1.75 cm. In order to balance this

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Scalars and Vectors

Solution to Worked Example 3.1(b)

(b) Tip-to-tail Method: Using an

appropriate scale, e.g. 1 cm:2 N, let W

be the first force vector drawn, followed by T as the second vector. Force F is found by joining the end point of T to the start point of W to form a closed triangle.

In doing so, the resultant force will be zero, and the system is in equilibrium (i.e. stationary in this case). By measuring the vector, F has a length of 1.75 cm.

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Scalars and Vectors

Key Ideas

A scalar quantity has magnitude only.

A vector quantity has magnitude and direction.

When there are two or more forces acting on an object, the resultant can be found by adding the forces together.

> For parallel forces, the resultant force is found by

taking one direction as positive and the opposite as negative, and then adding up the forces.

> For non-parallel forces, the resultant force is found by

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Test Yourself 3.2

1. A man can row a boat in still water at a speed of 1.0 m s-1. The

man sets out to row the boat in a river from A to B. The water in the river flows at 0.5 m s-1 in the direction B to A. Find the velocity

of the boat through the water.

Answer: Since the velocity of water is acting opposite to that of the boat, the velocity of the boat through water, Vbw, is

Vbw = Vb - Vw = 1.0 - 0.5 = 0.5 m s-1

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Test Yourself 3.2

2. A lorry, which has been stuck in muddy ground, is being pulled by two jeeps. Each jeep exerts a

force of 3000 N at an angle of 20o to the horizontal in the direction shown. Find, using a scale diagram, the resultant force pulling the lorry forward.

Answer: Using an appropriate scale diagram, the resultant force F = 5600 N

3000 N

3000 N

5600 N 20o

20o

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Test Yourself 3.2

3. A mass of weight W is supported by two strings as shown in the diagram. The tension in each string is 10 N. Using a scale diagram, find the value of W.

Answer: Since the weight is in equilibrium, then the weight W is equal to 17.3 N but opposite to the resultant of the two tensions.

Scalars and Vectors

10 N 10 N

30o

30o

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Newton’s First Law of Motion :

Balanced Force

Newton’s first law of motion states that an

object at rest will remain at rest, or uniform

motion in a straight line when the net force

acting on it is zero.

• When an object is at rest, the net force acting on it is

zero.

• When an object is moving with constant speed in a straight line, the net force acting on it is zero.

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Newton’s First Law of Motion :

Balanced Force

• When an object is at rest, the net force acting on it is zero.

Contact Force (reaction)

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Newton’s First Law of Motion :

Balanced Force

Lift

Weight

20N 20N

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Newton’s First Law of Motion :

Balanced Force

• When an object is moving with constant speed

in a straight line, the net force acting on it is

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Newton’s First Law of Motion:

Balanced Force

Remember!!

No net force

does not

mean that there

are

no forces acting on the body

. It is just

that all the forces are

balanced

.

5N 5N

3N 4N

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Interest facts….

• When you throw an object vertically

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Terminal Velocity (esp for

parachute)

• Resistance increases as the velocity of a body increases. • Ball bearing’s acceleration decreases as it falls faster.

• Resistance of the oil acting upwards on the ball bearing will equal to the force of gravity (weight of ball bearing) downwards.

No resultant force

• Falls at constant velocity

Terminal velocity.

Upward force

(resistance of oil on ball)

Downward force (weight of ball)

F = mg

time velocity

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Recall: Representing a Force

• Force is a vector quantity

– It has direction and magnitude

• SI unit of force is the newton (N)

– Not Newton unless you are talking about the person.

• It can be represented by an arrow.

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Unbalanced Force

• Vectors Addition in Straight Line

• Resultant Force

3N

5N

8N

3N 5N

2N

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Unbalanced Force

A force can:

• Cause a stationary body to move and a moving body

to stop moving.

• Change the speed of a moving body (accelerate or

decelerate the body).

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Newton’s Second Law of Motion:

Unbalanced Force

• The net force 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.

F = ma

where F = resultant force m = mass of the object

a = acceleration of object

SI unit of force is N (newton)

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• A trolley of mass 2 kg is pulled along a smooth surface (no friction) with a constant force F

– If acceleration of trolley is 1.5ms-2, what is the

magnitude of F?

F = ma = 2kg x 1.5ms-2 = 3.0N

– If the applied force is double, what will the acceleration produced?

• F = 2 x 3.0N = 6.0N

• a = F/m = 6N/2kg = 3ms-2

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Summary

Newton’s first law of motion

– An object will continue its state of rest or uniform motion in a straight line when the net force acting on it is

zero.

Newton’s second law of motion

– When a resultant force acts on an object of constant mass, an

acceleration will result with product of its mass and acceleration equal to the resultant force.

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Force vs Weight

Weight is an ever-present force exerted on every object

due to gravity. The acceleration of free fallg’ due to

Earth’s gravity is 10 m s-2

mg W mg F ma F F W Force Weight = = = = =

Note: SI unit for

Weight and Force is

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Newton’s Third Law (optional)

Newton’s Third Law of Motion

states that:

Newton’s Third Law of Motion tells us four

characteristics:

– Forces always occur in pairs.

– Action and reaction forces are equal in magnitude. – Action and reaction forces act in opposite directions. – Action and reaction forces act on different bodies.

For every action, there is an equal and opposite reaction,

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Newton’s Third Law (optional)

References

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