Force and Momentum
Momentum That is, due to the effect of an external
force, the momentum of an object is
Multiplication between mass (m) of a changed. This change in momentum can be
moving object and the velocity (v) is called expressed by following formula.
the linear momentum of the object at that
moment. Also, linear momentum can be
= ‐
defined as the product of the mass and the
velocity of a particle.
∆𝑃 𝑃 𝑃
i.e., Momentum= mass x velocity
Change in momentum is a vector;
P=mv because of the momentum is a
vector. Therefore, we should
Momentum is a vector. consider both final and initial
SI units of momentum is kgms‐1 momentums in same directions.
Dimensions of momentum is MLT‐1
Ex: A 10kg object (called X) is moving with
the velocity 1ms‐1. Another 1kg object
(called Y) is moving with the velocity 10ms‐1.
Find the momentum of P and Q.
P=mv
PX=10kg x 1ms‐1=10kgms‐1
PY=1kg x 10ms‐1=10kgms‐1
NOTE: The momentum of the heavy object
with low velocity will be equal to the
momentum of the light object with high
velocity.
Change in momentum of an object
Magnitude or direction (or both) of the
moving object can be changed due to the
external force acts on that object. Then the
momentum will be changed accordingly.
Sanjaya Perera ~ 1 ~
B.Sc(Hons), Maths(Sp)
Force Inertia
Physical quantities such as velocity, Inertia is the resistance, of any
acceleration of a moving object is changing physical object, to any change in its velocity.
due to the external effect acts on it. Also, This includes changes to the object's speed,
when the external effect acts on a particular or direction of motion.
body, momentum is changed. That external
Depends on the mass of an object;
effect is called as a “Force”. Simply, we can
Objects with greater mass have
describe, “Force as a push or a pull acts on
greater inertia.
the body”.
Does not depend on the presence of
There are 03 laws introduced by Sir Isaac gravity
Newton regarding the force.
Examples:
Newton’s Laws
1. It is harder to stop a big vehicle, like
1. Newton's First Law (sometimes a bus, than a smaller vehicle, like a
referred to as the law of inertia) motorcycle. There is more inertia
states that an object will remain at with the bigger object.
rest or in uniform motion in a
straight line unless acted upon by an 2. When a car is abruptly accelerated,
unbalanced external force. drivers and passengers may feel as
though their bodies are moving
2. Newton's second law states that the backward. In reality, inertia is
rate of change of momentum of a making the body want to stay in
body is directly proportional to the place as the car moves forward.
force applied, and this change in
Problem: Explain why the coin falls into the
momentum takes place in the
glass when the cardboard is pulled?
direction of the applied force.
3. The third law states that all forces
between two objects exist in equal
magnitude and opposite direction.
If one object A exerts a force FA on a
second object B, then
B simultaneously exerts a
force FB on A, and the two forces are
equal in magnitude and opposite in
direction.
i.e: FA = −FB
Sanjaya Perera ~ 2 ~
B.Sc(Hons), Maths(Sp)
Mass Mathematical form of Newton’s 2nd law
In generally, the term "mass" is used to An object with mass m moves with uniform
refer to the amount of matter in any given velocity U. At that time, an external force F
object. In physics, mass is defined as a applies on that object in the same direction
quantitative measure of inertia. It is, in which it moves. Because of F, velocity of the
effect, the resistance that a body of matter object is changed in to V within time t.
offers to a change in its speed or position
upon the application of a force.
Mass of an object remains constant
regardless of its location.
SI unit of mass is kg.
Final momentum (to the direction) 𝑚𝑉
Reference frame Initial momentum (to the direction) 𝑚𝑈
Change in momentum () 𝑚𝑉 𝑚𝑈
A reference frame is a space in which we 𝑚 𝑉 𝑈
are making observations and measuring
physical quantities. According to the Newton’s second law,
There are two types of reference frames: 𝐹𝑜𝑟𝑐𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑐ℎ𝑎𝑛𝑔𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
1. Inertial reference frame;
𝑡𝑖𝑚𝑒
Reference frames in which Newton 𝑚 𝑉 𝑈
𝐹 1
first law of motion holds i.e. an 𝑡
object at rest and an object in
motion remains in motion unless Using equations of motion 𝑣 𝑢 𝑎𝑡,
𝑣 𝑢
acted by a net force. An inertial 𝑎
𝑡
reference frame is either at rest or Substitute 𝑎 in to the equation (1),
moves with a constant velocity.
Ex: A train moving with constant 𝑭 𝒎𝒂
velocity.
NOTE
2. A non‐inertial reference frame; According to the above equation, Newton’s
Reference frames, that is second law can be expressed as below.
accelerating, either in linear motion “An external force acts on an object equals
or rotating around some axis. to the product of mass of the object and its
Ex: A rotating merry‐go‐round acceleration”
𝐹𝑜𝑟𝑐𝑒 𝑚𝑎𝑠𝑠 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
Sanjaya Perera ~ 3 ~
B.Sc(Hons), Maths(Sp)
When the mass is constant, force acts Equilibrium
on the object is proportional to its
If the size and direction of the forces acting
acceleration.
on an object are exactly balanced, then
𝐹 ∝𝑎
there is no net force acting on the object
and the object is said to be in equilibrium.
The acceleration of a moving object
Because there is no net force acting on an
under the constant force is inversely
object in equilibrium, then from
proportional to its mass.
1 Newton's first law of motion, an object at
𝑎∝ rest will stay at rest, and an object in
𝑚
motion will stay in motion.
SI units: kgms‐2, N
Definition: One newton is the force needed to
accelerate one kilogram of mass at the rate of Action and Reaction principle
one meter per second squared in the direction of
the applied force. This phenomena is based on the Newton’s
Dimensions: MLT‐2 3rd law of motion.
Force is a vector quantity.
In every interaction, there is a pair of forces
acting on the two interacting objects. The
Weight size of the force on the first
object equals the size of the force on the
The weight of an object is related to the
second object. The direction of the force on
amount of force acting on the object, either
the first object is opposite to the direction
due to gravity that holds it in place. All
of the force on the second object.
objects upon earth experience a force of
Forces always come in pairs ‐ equal and
gravity that is directed "downward"
opposite action‐reaction force pairs.
towards the center of the earth.
𝑊 𝑚𝑔;
𝑚 𝑚𝑎𝑠𝑠,
𝑔 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦
For example, an object with a mass of one
kilogram has a weight of about 9.8N on the
surface of the Earth, and about one‐sixth as
much on the Moon.
Sanjaya Perera ~ 4 ~
B.Sc(Hons), Maths(Sp)
Types of forces with another stable object. For example, if a
book is resting upon a surface, then the
Mainly, there are two types of forces;
surface is exerting an upward force upon
1. Contact forces‐ interactions the book in order to support the weight of
between objects that touch the book.
(Applied forces (push/pull), Normal
force, frictional force, drag force)
2. Non‐ contact forces‐ attract or repel,
even from distance
(Magnetic force, electric force,
gravitational force)
Tension (T):
The tension force is the force that is Spring force:
transmitted through a string, rope, cable or
The spring force is the force exerted by a
wire when it is pulled tight by forces acting
compressed or stretched spring upon any
from opposite ends. The tension force is
object that is attached to it. An object that
directed along the length of the wire and
compresses or stretches a spring is always
pulls equally on the objects on the opposite
acted upon by a force that restores the
ends of the wire.
object to its rest or equilibrium position.
For most springs (specifically, for those that
are said to obey "Hooke's Law"), the
magnitude of the force is directly
T T proportional to the amount of stretch or
compression of the spring.
T
Normal Reaction (R):
The normal force is the support force
exerted upon an object that is in contact
Sanjaya Perera ~ 5 ~
B.Sc(Hons), Maths(Sp)
Frictional force: (c) If the elevator accelerates downward at
a rate of 2 ms‐2
Frictional force refers to the
force generated by two surfaces that (90kg, 75kg, 60kg)
contacts and slide against each other.
These forces are mainly affected by the
surface texture and amount
of force impelling them together.
W=mg
Air resistance force:
The air resistance is a special type of 2) A 500kg motor car is on the frictionless
frictional force that acts upon objects as road. After switch on the engine, the car
they travel through the air. The force of air moves on straight forward under the
resistance is often observed to oppose the 100N constant force generated by the
motion of an object. engine. Find the acceleration of the car
and the displacement and final velocity
after 60 second. (0.2ms‐2, 360m, 12ms‐1)
Problem:
3) A 500g hammer is on a stage. Height of
1) A following figure shows, 75.0kg man is the stage from the sand floor is 5m.
standing on a bathroom scale in an Incidentally, the hammer falls freely on
elevator. Calculate the scale reading: the sand floor and it travels 25cm into
the floor. Find the resistance force
(a) if the elevator accelerates upward at
applied by the floor on the hammer.
a rate of 2 ms‐2
(105N)
(b) If the elevator moves upward at a
constant speed of 1 ms‐1 4) Two masses 1kg and 3kg are attached to
the both ends of a massless, non‐tensile
string going through a frictionless
Sanjaya Perera ~ 6 ~
B.Sc(Hons), Maths(Sp)
pulley. When the system released at
rest, find the acceleration of the system
and the tension of the string. Also, find
the applied force on the pulley.
(5ms‐2, 15N, 30N)
5) Two masses m1 and m2 (>m1) are
attached to the both ends of a massless,
non‐tensile string going through a
frictionless pulley. When the system
released at rest,
a. Show that the acceleration of the
system is 𝑔.
b. Show that the tension of the string is
.
6)
Sanjaya Perera ~ 7 ~
B.Sc(Hons), Maths(Sp)
