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?
Objectives
• After the lesson, you should be able to:
– State what is a force?
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
)
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.
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)
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
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
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
Scalars and Vectors
What are scalar and vector quantities?
• Scalar quantities are physical quantities that have magnitude only.
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
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
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
Scalars and Vectors
Addition of parallel vectors (Example 1)
Scalars and Vectors
Addition of Parallel Vectors (Example 2)
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.
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.
Parallelogram Method
Scalars and Vectors
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.
Scalars and Vectors
Tip-To-Tail Method
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,
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
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.
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
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
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
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
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.
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)
Newton’s First Law of Motion :
Balanced Force
Lift
Weight
20N 20N
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
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
Interest facts….
• When you throw an object vertically
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
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.
Unbalanced Force
• Vectors Addition in Straight Line
• Resultant Force
3N
5N
8N
3N 5N
2N
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).
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 objecta = acceleration of object
SI unit of force is N (newton)
• 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
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.
Force vs Weight
• Weight is an ever-present force exerted on every object
due to gravity. The acceleration of free fall ‘g’ 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
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,