21. Graphs can be useful in studying motion. They show the changes in
the motion of an object with the time.
There are 2 main types of linear motion graphs:
the displacement-time graph
the velocity-time graph
Analyzing Motion Graphs
22. A displacement-time graph (s-t graph) is a graph that shows how the
displacement of an object varies with time.
23. Try to draw how the cyclist
travel.
Gradient of the graph =
velocity
24.
25. A velocity-time graph (v-t graph) is a graph that shows the variance in
the velocity of an object against time.
26. Gradient of the graph
= accelaration (positive
/ negative)
Area under graph =
distance travelled
Importa
nt!
32. You could see the distance time graph above. The body
starts moving from point A moves towards point B very fast.
At point C its in steady speed then in a stationary mode
reaches the point D. Finally returns point E.
If the graph is steeper, it shows that the motion of
the object would be faster.
If the graph is horizontal, it means that the object is
at rest.
Distance vs time graph
33. In case of the speed time graph or the velocity time graphs,
speed or velocity of the object is generally plotted on the y
direction and the time is plotted in the x direction.
Remember that the speed is a scalar quantity and it only
has the magnitude associated with it. On the other hand,
velocity and displacement are the vector quantities and
they also have direction associated with them.
Steepness on the graph is showing that the object is
having more acceleration.
If the graph is horizontal, it means that the object is
moving with constant speed and acceleration is zero.
When the graph is coming down, it shows that the
moving object is slowing down.
Velocity vs time graph
34. In case of the acceleration time graph, acceleration of
the object is generally plotted on the y direction and the
time is plotted in the x direction.
In the figure, it is explained that how the acceleration
time graph can be obtained from the Velocity time
graph. At any point in the velocity time graph
acceleration at that point can be defined as the slope at
that point.
Positive value of the acceleration in the acceleration
time graph shows that velocity in increasing and it is
increasing in the positive direction.
Negative value of the acceleration shows that the
velocity is decreasing and it is decreasing in the negative
direction. Acceleration goes zero when the slope in the
velocity time graph becomes zero. The slope in the
velocity time graph becomes zero when the velocity
becomes maximum and reaches at its peak point.
Acceleration vs time graph
40. All objects tend to continue with what they are doing.
Newton’s first law of motion = Law of Inertia states that:
Every object continue in its state of rest or uniform speed in
a straight line unless acted upon by an eternal force.
The tendency of an object to maintain its state of rest or uniform motion
in a straight line is called inertia.
The tendency of an object to maintain its state of rest or uniform motion
in a straight line is called inertia.
Only an external force (or a non-zero net force) can cause a change to
the state of motion of an object (either rest or moving at the same
speed in a straight line).
The external force is a non-zero net force, if more than one external
force act on the object.
55. Momentum = mass x velocity = mv
SI unit: kg ms^-1
Principle of Conservation of Momentum:
In the absence of an external force, the total momentum of a system remains
unchanged.
Momentum is a vector quantity with the same direction as velocity.
If the direction to the right is denoted as positive, an object moving to the
right possess a positive momentum while an object moving to the left will
have a negative momentum.
56. If a loaded lorry and a car are moving at the same speed, it is more
difficult for the lorry to stop.
This is because the lorry possesses a physical quantity, momentum,
more than the car.
It is harder to stop a massive object moving at a high velocity.
All moving objects possess momentum.
57.
58.
59. The term conservation is used if the total amount of matter or quantity
remains the same before and after the occurrence of an event.
Principle of Conservation of Momentum:
The total momentum of a system is constant, if no external force acts on the
system.
An example of an external force is friction.
The Principle of conservation of momentum is true for a closed system.
A closed system is one where the sum of external forces acting on the system
is zero.
60. Principle of Conservation of Momentum shall be discussed in two situations
as shown below:
A collision
The total momentum of
the objects before a
collision equals that
after the collision.
An explosion
The sum of the
momentums remains
as zero after an
explosion.
79. What is force?
A force is a push or a pull.
When you push or pull on an object, you need to know
(a) the strength or magnitude of your force, and
(b) the direction in which you are pushing or pulling
Therefore, force is a vector quantity since it has both magnitude and
direction.
82. a∝F / m
∴ F = kma , k is a constant
The unit of force is Newton, N.
In order to make the formula a simple as possible, we make k = 1 by
defining a force of 1 N as:
83.
84.
85. The net force on an object is proportional to the rate of change
of momentum.
89. Balanced Force
In general, there may be several forces acting on the mass, whether parallel or
anti-parallel, or in different directions.
Thus, the force, F, must be replaced with the net or resultant force when there
are several forces acting on the mass.
However, for simplicity, F = ma is always used, bearing in mind that F is the net
force acting on the object (whether a single force or several forces are acting
on it).
90.
91. Balanced Force
When the forces acting on an object are
balanced, they cancel each other out (that is,
net force = 0).
The object then behaves as if there is no force
acting on it.
Since F net = 0, the acceleration of the object, a = 0. Thus, the object remains
at rest or moves at constant velocity when there is no net force acting on it.
This is Newton’s first law of motion.
108. An object might rebound from a wall, or stick to it without rebounding
after striking it.
In which situation will the wall exert a greater impulse?
Thus, a greater impulse is exerted on an object if it rebounds after a
collision.
115. The impulsive force is inversely
proportional to the time of impact. The
athlete bends his legs upon landing to
lengthen the time of impact; reducing
the impulsive force.
Answer: B
120. All objects are pulled towards the centre of the Earth
by the force of gravity.
The objects will fall with an acceleration of 9.8 ms^-2
due to the pull of this gravitational force.
Since this acceleration is due to the force of gravity, it is
called the gravitational acceleration.
It’s denoted by the symbol, g.
Gravitational force is always
acting towards the centre of
the Earth.
121. The value of g depends on:
(a) Latitude
Generally, the value of g increases
with latitude.
(b) Height above sea level
The greater the height above the sea
level is, the smaller is the value of g.
138. A frictionless pulley serves to change the
direction of a force.
The tension, T that results from pulling at
the ends of the string or rope has the same
magnitude along its entire length.
139. A force pulling a mass over a pulley:
In this situation, the tension T, is equal to the pulling force F, even if the rope is
slanting.
140. A pulley with 2 masses:
The heavier mass will accelerate downwards while the lighter one will
accelerate upwards with the same magnitude.
The tension is not equal to the weight of either mass.
143. Forces in Equilibrium or balanced forces have been discussed previously.
When the forces are in equilibrium, the net force, Fnet, or resultant force,
FR is zero.
The object will either be:
(a) at rest
(b) in motion with constant velocity
144. A tilted surface is called an inclined plane.
To understand better how three forces work in equilibrium, we need to
understand
a) the resultant force of two forces
b) the resolution of a force
145. Addition of Forces and Resultant Force
When 2 forces of 3N and 4N, pushing a wooden block
of mass 2kg on a smooth surface in the same
direction, it causes the block to accelerate at 3.5ms^-
2.
If the 2 forces are replaced with a single force of 7N, it
will still accelerate at 3.5ms^-2.
Thus the effect of both cases is the same. The block
have a = 3.5ms^-2.
7N is the resultant force of the combined forces of 3N
and 4N.
The resultant force is defined as a single force
that will produce the same effect as the two
or more combined forces that it replaces.
146. To find the Resultant Force
Addition Subtraction
Note: For Parallel Forces only!!!
147. To find the Resultant Force
Simple arithmetic cannot be applied to find the resultant force of
two non-parallel forces.
Instead, we can determine the resultant
force by drawing scaled diagrams using
the two methods:
a) The Triangle Method
b) The Parallelogram Rule
148. Method 1: The Triangle Method (Tail-to-Tip Method)
Measure the length of the completed triangle.
149. Method 2: The Parallelogram Rule (Parallellogram of Forces)
166. Three Forces in Equilibrium
Problems involving three forces in equilibrium can be solved either by:
(a)Method A: Resolution of forces
(b)Method B: Drawing a closed triangle of forces
172. Work is done when a force causes an object to move in the direction of the
force.
The work done, W is defined as the product of the force, F and the
displacement, s in the direction of the force.
The SI unit of work is the
joule, J. Work is a scalar
quantity.
173. One joule is the work done when a force of one
newton moves an object over a distance of one
metre, in the direction of the force.
190. The Principle of Conservation of Energy:
Energy cannot be created or destroyed. It can be
transformed from one form to another, but the total
energy in a system is constant.
199. Power, P is the rate at which work is done, or the rate at which energy is
transformed.
The SI unit of power is the watt (W).
1W = 1J/1s = 1Js^-1
The larger units are the kilowatt (kW) and the megawatt (MW).
Power is a scalar quantity as both the work done and energy are scalar
quantities.
Another unit of power is the horsepower (hp), which is commonly used in
electrical appliances such as air conditioners.
1hp = 746 W
≃3/4 kW
