2.5 FORCE

Example:

Balanced Force

When the forces acting on an object are balanced, they cancel each other out. The net force is zero.

Effect :

the object at is at rest [ velocity = 0]

or moves at constant velocity [ a = 0]

Weight, W = Lift, U Thrust, F = drag, G

When the forces acting on an object are not balanced, there must be a net force acting on it.

The net force is known as the unbalanced force or the resultant force.

Unbalanced Force/

Resultant Force

Effect : Can cause a body to

- change it state at rest (an object will accelerate

- change it state of motion (a moving object will decelerate or change its direction)

Force, Mass & Acceleration

The acceleration produced by a force on an object is directly proportional to the magnitude of the net force applied and is inversely proportional to the mass of the object. The direction of the acceleration is the same as that of the net force.

Newton’s Second Law of Motion

When a net force, F, acts on a mass, m it causes an acceleration, a.

Force = Mass x Acceleration

Relationship between a & F

a α F

The acceleration, a, is directly proportional to the applied force, F.

Relationship between a and m ma1∝

The acceleration of an object is inversely proportional to the mass,

The acceleration produced by an object depends on the net force applied to it.

The acceleration produced by an object depends on the mass

Hypothesis

The acceleration of the object increases when the force applied increases

The acceleration of the object decreases when the mass of the object increases

An elastic cord is hooked over the trolley. The elastic cord is stretched until the end of the trolley. The trolley is pulled down the runway with the elastic cord being kept stretched by the same amount of force

An elastic cord is hooked over a trolley. The elastic cord is stretched until the end of the trolley. The trolley is pulled down the runway with the elastic cord being kept stretched by the same amount of force

Determine the acceleration by analyzing the ticker tape.

Acceleration tuva−=

Determine the acceleration by analyzing the ticker tape.

Acceleration tuva−=

Procedure :

- Controlling manipulated variables.

- Controlling responding variables.

- Repeating experiment.

1. What force is required to move a 2 kg object with an acceleration of 3 m s-2, if

(a) the object is on a smooth surface?

(b) The object is on a surface where the average force of friction acting on the object is 2 N?

2. Ali applies a force of 50 N to move a 10 kg table at a constant velocity. What is the frictional force acting on the table?

3. A car of mass 1200 kg traveling at 20 m/s is brought to rest over a distance of 30 m. Find

(a) the average deceleration,

(b) the average braking force.

4. Which of the following systems will produce maximum acceleration?

2.6 IMPULSE AND IMPULSIVE FORCE

Impulse

The change of momentum

mv - mu

Unit : kgms-1 or Ns

Impulsive Force

The rate of change of momentum in a collision or explosion

Unit = N

m = mass

u = initial velocity

v = final velocity

t = time

Longer period of time →Impulsive force decrease

Effect of time

Impulsive force is inversely proportional to time of contact

Shorter period of time →Impulsive force increase

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Situations for Reducing Impulsive Force in Sports

Situations

Explanation

Thick mattress with soft surfaces are used in events such as high jump so that the time interval of impact on landing is extended, thus reducing the impulsive force. This can prevent injuries to the participants.

Goal keepers will wear gloves to increase the collision time. This will reduce the impulsive force.

A high jumper will bend his legs upon landing. This is to increase the time of impact in order to reduce the impulsive force acting on his legs. This will reduce the chance of getting serious injury.

A baseball player must catch the ball in the direction of the motion of the ball. Moving his hand backwards when catching the ball prolongs the time for the momentum to change so as to reduce the impulsive force.

Situation of Increasing Impulsive Force

Situations

Explanation

A karate expert can break a thick wooden slab with his bare hand that moves at a very fast speed. The short impact time results in a large impulsive force on the wooden slab.

A massive hammer head moving at a fast speed is brought to rest upon hitting the nail. The large change in momentum within a short time interval produces a large impulsive force which drives the nail into the wood.

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A football must have enough air pressure in it so the contact time is short. The impulsive force acted on the ball will be bigger and the ball will move faster and further.

Pestle and mortar are made of stone. When a pestle is used to pound chilies the hard surfaces of both the pestle and mortar cause the pestle to be stopped in a very short time. A large impulsive force is resulted and thus causes these spices to be crushed easily.

Example 1

A 60 kg resident jumps from the first floor of a burning house. His velocity just before landing on the ground is 6 ms-1.

(a) Calculate the impulse when his legs hit the ground.

(b) What is the impulsive force on the resident’s legs if he bends upon landing and takes 0.5 s to stop?

(c) What is the impulsive force on the resident’s legs if he does not bend and stops in 0.05 s?

(d) What is the advantage of bending his legs upon landing?

Example 2

Rooney kicks a ball with a force of 1500 N. The time of contact of his boot with the ball is 0.01 s. What is the impulse delivered to the ball? If the mass of the ball is 0.5 kg, what is the velocity of the ball?

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2.7 SAFETY VEHICLE

Component

Function

Headrest

To reduce the inertia effect of the driver’s head.

Air bag

Absorbing impact by increasing the amount of time the driver’s head to come to the steering. So that the impulsive force can be reduce

Windscreen

The protect the driver

Crumple zone

Can be compressed during accident. So it can increase the amount of time the car takes to come to a complete stop. So it can reduce the impulsive force.

Front bumper

Absorb the shock from the accident. Made from steel, aluminium, plastic or rubber.

ABS

Enables drivers to quickly stop the car without causing the brakes to lock.

Side impact bar

Can be compressed during accident. So it can increase the amount of time the car takes to come to a complete stop. So it can reduce the impulsive force.

Seat belt

To reduce the inertia effect by avoiding the driver from thrown forward.

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2.8 GRAVITY

Gravitational Force

Objects fall because they are pulled towards the Earth by the force of gravity.

This force is known as the pull of gravity or the earth’s gravitational force.

The earth’s gravitational force tends to pull everything towards its centre.

Free fall

�� An object is falling freely when it is falling under the force of gravity only.

�� A piece of paper does not fall freely because its fall is affected by air resistance.

�� An object falls freely only in vacuum. The absence of air means there is no air resistance to oppose the motion of the object.

�� In vacuum, both light and heavy objects fall freely. They fall with the same acceleration ie. The acceleration due to gravity, g.

Acceleration due to gravity, g

�� Objects dropped under the influence of the pull of gravity with constant acceleration.

�� This acceleration is known as the gravitational acceleration, g.

�� The standard value of the gravitational acceleration, g is 9.81 m s-2. The value of g is often taken to be 10 m s-2 for simplicity.

�� The magnitude of the acceleration due to gravity depends on the strength of the gravitational field.

Gravitational field

The gravitational field is the region around the earth in which an object experiences a force towards the centre of the earth. This force is the gravitational attraction between the object and the earth.

The gravitational field strength is defined as the gravitational force which acts on a mass of 1 kilogram. mFg= Its unit is N kg-1.

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Gravitational field strength, g = 10 N kg-1

Acceleration due to gravity, g = 10 m s-2

The approximate value of g can therefore be written either as 10 m s-2 or as 10 N kg-1.

Weight

The gravitational force acting on the object.

Weight = mass x gravitational acceleration

W = mg SI unit : Newton, N and it is a vector quantity

Comparison between weight & mass

Mass

Weight

The mass of an object is the amount of matter in the object

The weight of an object is the force of gravity acting on the object.

Constant everywhere

Varies with the magnitude of gravitational field strength, g of the location

A scalar quantity

A vector quantity

A base quantity

A derived quantity

SI unit: kg

SI unit : Newton, N

The difference between a fall in air and a free fall in a vacuum of a coin and a feather.

Both the coin and the feather are released simulta-neously from the same height.

At vacuum state:

There is no air resistance.

The coin and the feather will fall freely.

Only gravitational force acted on the objects.

Both will fall at the same time.

At normal state:

Both coin and feather will fall because of gravitational force.

Air resistance effected by the surface area of a fallen object.

The feather that has large area will have more air resistance.

The coin will fall at first.

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Two steel spheres are falling under gravity. The two spheres are dropped at the same time from the same height.

(a) The two sphere are falling with an acceleration.

The distance between two successive images of the sphere increases showing that the two spheres are falling with increasing velocity; falling with an acceleration.

(b) The two spheres are falling down with the same acceleration

The two spheres are at the same level at all times. Thus, a heavy object and a light object fall with the same gravitational acceleration.

Gravitational acceleration is independent of mass.

Motion graph for free fall object

Free fall object

Object thrown upward

Object thrown upward and fall

Example 1

A coconut takes 2.0 s to fall to the ground. What is

(a) its speed when it strikes the ground

(b) the height of the coconut tree.

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2.9 FORCES IN EQUILIBRIUM

Forces in Equilibrium

When an object is in equilibrium, the resultant force acting on it is zero.

The object will either be

1. at rest

2. move with constant velocity.

Newton’s 3rd Law

Examples( Label the forces acted on the objects)

Resultant Force

A single force that represents the combined effect of two of more forces in magnitude and direction.

Addition of Forces

Resultant force, F = ____ + ____

Resultant force, F = ____ + ____

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Two forces acting at a point at an angle [Parallelogram method]

STEP 1 : Using ruler and protractor, draw the two forces F1 and F2 from a point.

STEP 2

Complete the parallelogram

STEP 3

Draw the diagonal of the parallelogram. The diagonal represent the resultant force, F in magnitude and direction.

scale: 1 cm = ……

Resolution of Forces

A force F can be resolved into components which are perpendicular to each other:

(a) horizontal component , FX

(b) vertical component, FY

Fx = F cos θ

Fy = F sin θ

Inclined Plane

Component of weight parallel to the plane

= mg sin θ

Component of weight normal to the plane

= mg cos θ 27

find the resultant force

(d)

(e)

Lift

Stationary Lift

Lift accelerate upward

Lift accelerate downward

Resultant Force =

Resultant Force =

Resultant Force =

The reading of weighing scale =

The reading of weighing scale =

The reading of weighing scale =

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Pulley

1. Find the resultant force, F

2. Find the moving mass,m

3. Find the acceleration,a

4. Find string tension, T

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