**"Forces and Motion" - An Overview:**
1

**Kinematics**– the study of motion without considering the force acting on the object. Force F will not appear in any of the equations of motion. So, a convenient starting point in kinematics would be the study of linear motion and linear motion graphs.
1.1
In

**Linear Motion**, you will learn about:
1.1.1
Distance and Displacement

1.1.2
Speed and Velocity

1.1.3
Acceleration and deceleration

1.1.4
Ticker-Timer

1.1.5
Equations of Linear Motion

a) a = (v - u) / t

b) v = u + at

c) t = (v - u)/a

c) t = (v - u)/a

d) s = 1/2 (u + v)t (average velocity x time)

e) s = ut + 1/2(at^2) (i.e. the area under the Velocity-Time graph)

(or, s = 1/2(g)(t^2), free fall of a stationary object:

(or, s = 1/2(g)(t^2), free fall of a stationary object:

**2005 P1 Q4**,**pg 3**)
f) v^2 = u^2 + 2as

1.2
In

**Linear Motion Graphs**, you will learn about:
1.2.1
Displacement-Time (s-t) Graphs

(

(

**2007 P1 Q4 @ pg 92 /****2010 P1 Q5 @ pg 231**)
1.2.2
Velocity-Time (v-t) Graphs

(

(

**2005 P1 Q10 @ pg 5 /****2007 P1 Q5 @ pg 92 /****2008 P1 Q4 @ pg 140 /****2009 P1 Q4 @ pg 186 / 2009 P2 Q5 @ pg 251****2010 P1 Q3 @ pg 230 /****2011 P1 Q10 @ pg 282**)
1.2.3
The Use of Ticker-Tapes to Plot the Graphs

(

(

**2008 P3 Q 2 @ pg 180**/**2011 P2 Q1 @ pg 294)**
2

**Inertia**and**Newton’s 1st Law of Motion**(a.k.a. the**Law of Inertia**):
2.1

(

**Inertia**refers the**tendency**of an object**to resist change**in its state of motion:**If at rests**, it tends to**remain at rest**;**if in motion**, it tends to**move in straight line**at the**same speed****unless acted on by an external net force.**(

**2005 P1 Q6 & Q8 @ pg 4**)
Different words for the same thing -

**Inertia**may also be referred to as:**I**An object’s

**natural resistance to change**its current

**state of equilibrium –**if in

**static equilibrium**(at rest) or in

**dynamic equilibrium**(motion with uniform velocity)

**,**it tends to remain so

**.**

**II**An object’s

**natural resistance to change**its current

**velocity**, including zero velocity (at rest).

**III**An object’s

**natural resistance to change**its current

**momentum**including zero momentum – if at rest with zero momentum, it tends to remain at rest with zero momentum; if in motion in a straight line with a constant speed and therefore a constant momentum (= mass x velocity), it tends to continue to remain so with the same momentum.

2.2

**To overcome**an object’s**inertia**(i.e.**resistance to change**its current state of motion), an**external force -**i.e a**non-zero net force -**is needed
2.2.1
to make a

**stationary**object**moves and/or change position**;
2.2.2
to make a moving object

**moves**in the**same direction**with**greater or lower speed**(including stop with zero speed);
2.2.3
to make a moving object

**moves**with**changed direction**.
2.3

**Inertia**increases as:
2.3.1
the

**mass**of a**stationary object**(say, a trolley with different amount things loaded)**increases**and the converse is also true; or
2.3.2
the

**momentum**of**moving object****increases**and the converse is true too.
2.4

2.5 An object’s

2.6 Situations Involving Inertia:

**Inertia**- although related to mass and momentum - has**no unit of measurement**because it merely describes the natural tendency of all objects to resist change in their states of motion.2.5 An object’s

**inertia depends solely on its mass only if**the**object is stationary**; But if the**objects is moving**(say, a person sprinting as opposed to walking), its inertia (i.e. resistance to change its state of motion) does not depend on mass alone (since his mass is the same in both situations) –**inertia**of a**moving object**depends on**momentum**, i.e. on both its**mass and velocity**.2.6 Situations Involving Inertia:

A.
Things Lurching

**Backward**When Carrier Starts to Move**Forward**;
B.
Things Lurching

**Forward**When Carrier Suddenly**Slows Down**or**Stops**;
C.
Person Lurch Forward When Skateboard Suddenly Stopped
by a Stone;

D.
Coin Drops Straight (into a glass) When Cardboard Is
Pulled Away Quickly;

E.
Book Pulled Out Quickly from Middle of a Pile Will Not
Cause Books Above It to be Pulled Along;

F.
Raw and Hard Boiled Eggs Spinning Experiment;

G.
Massive Objects Show Difficulty to Start Moving, Change
Direction or Stop Moving: Difficult for a massive charging bull to charge in zigzag manner or for a massive supertanker to change direction or stop.

H.
Fine Thread of Freely Hung Weight Snaps When Weight is
Raised and Released

I. Upper Thread of Freely Hung Weight Snaps Only When
Lower Thread is Gradually Pulled But When the Lower Thread is Yanked, It Is
Lower Thread Which Snaps

3

**Momentum**(a measure of a**moving object's inertia -**a**vector quantity**)**:**
3.1

**Momentum**=**Mass**x**Velocity**of an object.
3.2
The

**higher**the**momentum**of a moving object, the**higher**its**inertia**and**therefore the****higher**its**resistance to change**its speed and direction of motion.
3.3

**Newton’s Law of Inertia (1**, where it is applicable on a moving object, states that "unless an external net force acts on a moving object, the object would move in a straight line with constant speed (and therefore with the same momentum – herein^{st}Law of Motion)**lies**the**Principle of Conservation of Momentum**).
3.4

**Principle of Conservation of Momentum**states that “**the total momentum of a system is constant, if no external force acts on the system**”.
3.5
In a

(

**collision,**the total**momentum**of objects**before collision equals**to that**after collision.**The total**energy**is**conserved**too. However,**kinetic energy**is only**conserved in**an**elastic collision**where the colliding objects move apart after collision. In**inelastic collision**where the colliding objects stop moving or move together with a common velocity,**kinetic energy**is**not conserved**.(

**2011 P1 Q5 @ pg 280**)
3.6
In an

III Spring-triggered explosions

**explosion,**the**sum of momentum**remains**zero after**the**explosion.**Explosive situations include:
I.
Gun-powder triggered explosions

II.
Jet of Air Explosions

a.
Deflating balloon

b.
Jet engine

c.
Rocket

4
The

**Effects of a Force**(a Push or a Pull) on**Motion**and**Newton’s 2**:^{nd}Law of Motion
4.1
Evidence in nature and in science lab. shows that F = ma or a = F/m:

4.1.1
The

**acceleration**a of an object is**directly proportional**to the**force applied**F if the mass of the object m remains constant
4.1.2
The

**acceleration**a of an object is**inversely proportional**to the**mass**m of the body (say, a trolley with different amount of things loaded) if the force applied F remains constant.
4.2
Combining the 2 results, we have:

4.2.1

**Force**F**=****Mass,**m**x****Acceleration,**a (**F = ma**)
4.2.2

**Newton’s 2**states that “^{nd}Law of Motion**the acceleration of a body is directly proportional to the net force acting on it (and inversely proportional to the mass of the body)**”
4.3

4.3.1

When

4.3.2

"To every action there is an equal but opposite reaction."

4.3.2.2 Action (Resultant Force)

4.3.2.2.2 Object moving with uniform velocity (

4.3.2.3 Action

4.3.2.3.1 Object moving with acceleration

4.3.3 Situations of

4.3.3.1 Book Resting on a Horizontal Table Surface

4.3.3.2 Box Resting on an Inclined Plane

4.3.3.3 Object Hung by Two Ropes Fixed to Two Points in the Ceiling/Wall

4.3.3.4 Object in Stationary Lift

4.3.4 Situations of

4.3.4.1 Object (Parachutist, etc) Falling at Terminal Velocity

4.3.4.2 Object Rolling Down Friction-Compensated Incline at Constant Velocity

4.3.4.3 Plane Cruising Horizontally at Constant Velocity

4.3.4.4 Car Moving Horizontally at Constant Velocity

4.3.4.5 Object in Lift Moving (Upwards or Downwards) at Constant Velocity

**Balanced Forces - Static Equilibrium**(at rest)**and****Dynamic Equilibrium**(constant velocity):4.3.1

**General Principle**of Balanced Forces:When

**2 or more forces**act on an object and**balance**each other, the net or**resultant force**acting on the object is**zero**- the object, if**at rest**, will**remain at rest**(i.e. remain in**static equilibrium**)**;**or, if**in motion,**will**continue to move****with**the**same velocity (**i.e.**in a straight line**with the**same speed**with no acceleration) and thus**with**the**same momentum**(i.e remain in**dynamic equilibrium**).4.3.2

**Newton's Third Law of Motion:****4.3.2.1**

**Newton's Third Law of Motion**states that:"To every action there is an equal but opposite reaction."

4.3.2.2 Action (Resultant Force)

**=**Opposite Reaction means**Balanced Forces**Resulting in**4.3.2.2.1 Object at rest (****static equilibrium**)4.3.2.2.2 Object moving with uniform velocity (

**dynamic equilibrium**)4.3.2.3 Action

**Not Equal**to Opposite Reaction means**Unbalanced Forces**Resulting in4.3.2.3.1 Object moving with acceleration

4.3.3 Situations of

**Balanced Forces with Static Equilibrium**4.3.3.1 Book Resting on a Horizontal Table Surface

4.3.3.2 Box Resting on an Inclined Plane

4.3.3.3 Object Hung by Two Ropes Fixed to Two Points in the Ceiling/Wall

4.3.3.4 Object in Stationary Lift

4.3.4 Situations of

**Balanced Forces with Dynamic Equilibrium**4.3.4.1 Object (Parachutist, etc) Falling at Terminal Velocity

4.3.4.2 Object Rolling Down Friction-Compensated Incline at Constant Velocity

4.3.4.3 Plane Cruising Horizontally at Constant Velocity

4.3.4.4 Car Moving Horizontally at Constant Velocity

4.3.4.5 Object in Lift Moving (Upwards or Downwards) at Constant Velocity

4.4

4.4.1

When

4.4.2 Situations of

4.3.2.1

A) Lift Moving (Upwards or Downwards) with Acceleration

B) Rocket Lifting Off Vertically with Acceleration (Force > Its Weight + Friction)

C) Car Moving Horizontally with Acceleration (Force > Static Friction + Drag)

D) Plane Moving Horizontally with Acceleration (Force > Drag)

4.3.2.2

A) Object Sliding Down Inclined Slope with Acceleration

B) Mowing Machine Moving with Horizontal Acceleration When Pushed

C) Object Moving with Horizontal Acceleration When Towed

**Unbalanced Forces - Object Moving with Acceleration**:4.4.1

**General Principle**of Unbalanced Forces:When

**2 or more forces**act on a object of**mass m**with a**net resultant force F**, then the object will experience an**acceleration a**(**= F/m**) and a change in momentum or**impulse**(=**mv – mu**=**Ft,**where**v**= final velocity;**u**= initial velocity and t = time during which the force F acts) in the direction of the net force. (**2005 P1 Q9 @ pg 4**/**2011 P1 Q6 @ pg 281**)4.4.2 Situations of

**Unb****alanced Forces**:4.3.2.1

**Unbalanced Parallel Forces**A) Lift Moving (Upwards or Downwards) with Acceleration

B) Rocket Lifting Off Vertically with Acceleration (Force > Its Weight + Friction)

C) Car Moving Horizontally with Acceleration (Force > Static Friction + Drag)

D) Plane Moving Horizontally with Acceleration (Force > Drag)

4.3.2.2

**Unbalanced Non-Parallel Forces**A) Object Sliding Down Inclined Slope with Acceleration

B) Mowing Machine Moving with Horizontal Acceleration When Pushed

C) Object Moving with Horizontal Acceleration When Towed

5.

**Impulse and Impulsive Force**:
5.1

**Impulse**is defined as the**product**of a**force**F acting on an object of mass m for**time**t:**Impulse**=**Ft**=**mv-mu**=**change in momentum**
Impulse = Ft (in N s)

=

**mat**(since F = ma)
= mt (v – u)/t

= m(v – u)

= mv – mu (change in momentum) (in kg
m s^-1)

5.2

**Impulsive Force**is defined as the**rate of****change in momentum**:**Impulsive Force F**=

**Change in Momentum**/

**Time Taken**

**F = (mv – mu)/t**

(

(

**Effects of time on impulsive force**F if the change in momentum is constant as in collision or explosion:**If**time**t**is**small**, then impulsive**F**is**large**)(

**2005 P1 Q7 @ pg 4**/**2011 P1 Q4 @ pg 280**)
6.

**Safety Features in Vehicles That Seek to Reduce Impulsive Force on Collision**
6.1
Padded Dashboard

6.2
Automatic Airbag

6.3
Headrest

6.4
Safety Seat Belt

6.5
Shatter-Proof Wind Screen

6.6
Rubber Bumper

6.7
Strong Steel Struts

7.

**Gravity**
7.1

**Gravity**refers to the**force****that attracts**a body**towards the centre of the earth**or towards the centre of any object that has matter/mass.
7.2
A

**gravitational field**is the**space****around**a**mass**in which**another****mass**would experience a**force of attraction towards**the**centre**of the object with**mass.**The more matter/mass that an object has, the stronger the gravitational field in the space around it.
7.3

**Gravitational field strength g**at a point in the gravitational field is a measure of the gravitational force F acting on per unit mass of a body (say, of mass m):**g = F / m**(g is the ratio of Weight / Mass)

**F = mg**(Gravitational F = Weight of the body of mass m)

7.4
Thus, at the

**same point**in the gravitational field, a body of**higher mass**will experience a**higher gravitational force**on it (F = mg); and a**higher weight**(because gravitational force = its weight) (**F = mg = Weight**).
7.5
If a body of mass m is allowed to

**free-fall****at**a point with**gravitational field strength g**, it would experience a**gravitational force F = mg**; and its**acceleration**a due to gravitation force F would be the**same as g**(because F = mg = ma; therefore a = g)
7.6
The

**closer to**the**centre**of earth, the**stronger**the**gravitational field strength g**and therefore the**higher**the**gravitational acceleration**. Thus, with the earth being somewhat flattened at the polar regions,**g at the polar regions**(of maximum latitude 90`N / 90`S) is**higher**at 9.832 m s^-2 as they are nearer to the centre of the earth as compared to locations of lower latitudes.
7.7
Thus,

**at**the**equator**(of lowest latitude of 0`),**g is lower**at 9.780 m s^-2.
7.8
Since the gravitational field force acting on a
body of mass m is a measure of the weight of the body (Weight = mg),

**at polar region**, a body would**weigh more**(since g is higher) and lower latitude such as**at equator**, the same body would**weigh less**(g is lower at equator). We**weigh less****on**the surface of the**Moon**because**g is lower**at the surface of the Moon as compared to that on Earth because Moon has less mass than our earth.
8.

**Forces in Equilibrium**
8.1
When

**forces**acting**on an object are in****equilibrium**, the net force or**resultant force**on the object is**zero**.**The object**will either be:
8.1.1

**at rest**(**static equilibrium**); or
8.1.2

**in motion with constant velocity**(**dynamic equilibrium**).
8.2
When

**2 forces**acting on an object are**in equilibrium**, they must be**acting**in**opposite direction**with**equal magnitude**. For examples:
8.2.1
A book resting on a table exerts a downward
force which equals to its weight (F = mg) and the table reacts with an equal
but opposite reaction force in accordance with Newton’s 3

^{rd}Law of Motion: The 2 opposite forces of equal magnitude balance each other out;
8.2.2
A skydiver descending at constant velocity
exerts a downward force equals to his weight (F = mg) and the air reacts with
an equal but opposite air resistance force.

8.3 When

**3 forces**are**in equilibrium**, it means either:
8.3.1
that the

**resultant force of 2**of the forces is**equal but opposite**to the**third force**; or
8.3.2
that if

**1**of the 3 forces is resolved into**2 forces**in the direction parallel to the other 2 forces, the**2 resolved forces balance out the other 2 forces**; or
8.3.3
that if all

**3 forces are resolved**into 2 perpendicular axis such as x and y axis, the**resultant forces**along the 2 axis**are zero**.
8.4
The

**resultant force**is the single force that will produce the**same effect as the 2 or more combined forces that it replaces**– the**resultant force**can be**determined by graphical method**by way of geometric construction of:
8.4.1

**parallelogram**; or
8.4.2

**triangle**; or
8.4.3

**rectangle or square**if the forces are perpendicular
8.5

**Resolution of Force**: A**force**can be**resolved**into any number of component forces in any direction provided the combined effect of these component forces is the original force. Normally, a force is resolved into 2 component forces that are perpendicular to each other.
9.

**Work, Energy, Power and Efficiency**
9.1

**Work**:
a) In lower secondary, you have learnt about
work done W as the product of the force, F and the distance, s in the direction
of the force:

**W = F x s**

a)
In upper secondary: If the

**distance moved**, s is not in the direction of the force but**at an acute angle A` to the direction of the force**, then work done W is the product of the component of force in the direction of displacement, FcosA` and s:**W = FcosA` x s**

b)
If

**displacement s is perpendicular**to the direction of the force F, then work done**W is zero**:
W = F x 0 (since displacement in
direction of force = 0)

W = 0

c)

**Work done**, Wg**, against gravity**: The displacement s is always the vertical height h because gravitational force, mg (mass x gravitational acceleration), always acts vertically downwards and work done against gravity is always in the opposite direction. Thus:**Wg = mg x h**(even if the object is lifted upwards along an inclined slope)

9.2

**Energy**– The**Capacity to Do Work**(Energy, E = Work Done, W)
a)

**Energy**can exist in**different forms**:
1)
mechanical energy (kinetic energy + potential
energy)

2)
heat energy

3)
electrical energy

4)
chemical energy

5)
sound energy

6)
light energy

7)
nuclear energy

b)
When

**work**is**done**,**energy**is**transferred**from one object to another. For examples:
1)
When a weightlifter lifts a weight, chemical
energy (stored in food) of the weightlifter is transferred to the weight as
gravitational potential energy;

2)
When a pitcher throws a ball, chemical energy
(stored in food) of the pitcher is transferred to the ball as kinetic energy.

(

(

**2011 P1 Q9**@**pg 282**)
c)

(

**Potential energy, Ep**, of an object is defined as the energy stored in the object because of its position (gravitational potential energy = mgh) or its state (elastic potential energy = ½ kx^2).(

**2005 P1 Q5 @ pg3**)
d)

**Kinetic energy, Ek**, is the energy possessed by an object due to its motion (Ek = ½ m(v^2 – u^2) (or, = ½ mv^2, if u = 0)
e)

(

**Principle of Conservation of Energy**states that: “energy cannot be created or destroyed. It can however be transformed from one form to another – the total energy in a system is constant”(

**2011 P1 Q8**@**pg 281)**
9.3

**Power**is defined as:
a)
The rate at which work is done:

Power = Work Done / Time taken;

(

**2011 P1 Q7 @ pg 281**)

b)
The rate at which energy is transformed:

Power
= Energy Transformed / Time Taken

c)
The product of force, F and velocity v (in the direction of the force):

Power = Work Done / Time

= Force x Displacement / Time

= Force x Velocity (since Velocity =
Displacement / Time)

**P = F x v**

9.4

**Efficiency**:
a)
Efficiency = Useful Energy Output, Eo / Energy
Input, Ei x 100%; or,

b)
Efficiency = Useful Power Output, Po / Power Input, Pi x 100%.

c)
An engine is a device which converts one form of
energy (say, heat or lectricity) into another (usually mechanical) to do work for
us.

d)
No engine is 100% efficient because there will
be energy loss as noise, heat, etc.

10.

**Maximising Efficiency**– Means:
10.1
Minimising Energy Wastage

10.2
Prolonging the Availability of Existing
Non-Renewable Energy Resources (Fossil Fuels, etc.)

10.3
Minimising Sound and Other Environmental
Pollutions

11.

**Elasticity, Hooke’s Law and Elastic Potential Energy**
11.1

**Elasticity**is the**ability to return to the original 1) shape and 2) size**after being deformed - stretched (extended), squashed (compressed) or bent - by a force:- Materials
that can do so are
**elastic materials**. - Materials
that cannot do so are
**inelastic**.

11.2 A

**spring**is**elastic**.
a.
At its

**natural length**, there is no net force stretching or squashing it.
b.
When subjected to

**a force**to**stretch**it, a spring will**lengthen**and the amount of lengthening is known as the**extension.**
c.
Conversely, when subjected to

**a force**to**squash**it, a spring will**shorten**and the amount of shortening is known as the**compression.**
11.3 There
is a

**relationship**between the**force applied**and the amount of**extension**or**compression**of a spring; and**this relationship is summed up by****Hooke’s Law**which states that:
“The

**force, F**, applied to a spring is**directly proportional**to the spring’s**extension or compression, x**.”**F = kx**, where

**:**

**k**is the spring’s constant which indicates the

**stiffness of the spring**.

(

**2011 P1 Q15 @ pg 283**)

**F-x graph**is a linear graph which passes through the origin;

**k**is the

**gradient**of the linear F-x graph.

(

**2005 P1 Q3 @ pg 3**- on unit of measurement for k constant;

**2005 P1 Q11 @ pg 5**/

**2011 P1 Q17 @ pg 284**- comparison on extension of identical springs in different arrangements)

11.4
If the

**force F**applied is progressively**increased**, there will**come a point**(**1st point**) when the spring's extension or compression x is no longer directly proportional to the force applied F but will still return to its original shape and size if the force applied is removed - that point is call**limit of proportionality**. Shortly after this point, there will come**another point**(**2nd point**) when further force is applied, the spring becomes**permanently lengthened**or**shortened**and will not return to its original shape and size:
a.
the

**2nd. point**is known as the**elastic limit**of the spring;
b.
the

**1st point**is the point beyond which the**F-x graph deviates**from being a linear graph.
c.
a spring that

**obeys Hooke’s Law**is known as an**ideal spring**- it only behaves so**up to**the 1st point,**the limit of proportionality**.
11.5
When a

**force**is applied from**zero to F**to**lengthen or shorten**a spring**by x**(metres):
a.
the average amount of force moves over the
distance of x is:

**F / 2**(newtons, N)
b.
thus, the

**work done W**by the force to bring about extension or compression**x**is:**W = (F/2) (x)**(which is the

**triangular area under**the

**F-x linear graph**)

c

**.**the**work done W**is**converted**into**elastic potential energy Ep**. Thus,**W = Ep = (1/2) F x**; or

Ep = (1/2) (Kx) x (since F = kx,
from Hooke’s Law)

**Ep = (1/2) k x^2**

11.6

**Nitinol**is a**special elastic material**: When deformed, Nitinol has the**ability to return to its original shape through heating**– it has shape memory! Its possible uses include: springs in car suspension systems, frames and panels of car body.**Nitinol**is an alloy that contains**ni**ckel and**ti**tanium metal.
11.7

**Applications of Spring:**
a.
As shock absorber and vibration damper in
vehicles when moving over uneven surface;

b.
As automatic door-closing device: After the
force that opens the door is released, the elastic potential energy built-up in
the spring will push and close the door.

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