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Force and laws of motion by Prabhat Gaurav IX
1.
2.
3. First Law of Motion.
Consequence of First Law of Motion.
Types of Inertia.
Momentum.
Second Law of Motion.
Consequence of Second Law of Motion.
Third Law of Motion.
Consequence of Third Law of Motion.
4. Deriving the Law of Conservation of
Momentum.
About Galileo Galilei.
Numericals on Momentum.
Numericals on Force.
Numericals on Law of conservation of
Momentum.
5. “Every body retains its state of rest or state of
motion , until an external force is applied on it.”
This law is also known as law of Inertia.
Or,
“Every body continues to be in its state of rest
or of uniform motion unless & until an external
agent, called the force acts on it, to change its
state.”
6. Inertia: It is the virtue of the body due to which it tries to retain
its state.
Or,
The inability of a body to change its state is called Inertia.
The mass of a body is the measure of Inertia.
For example:
A truck has more Inertia than a car.
A car has more Inertia than a scooter.
7. Inertia of Rest.
For example:
Dust is removed from a hanging carpet by beating it with
a stick. As the carpet is beaten, it suddenly moves forward
while the dust particles tend to remain at rest due to
Inertia.
Inertia of Motion.
For example:
If a Horse running fast suddenly stops, the rider is
thrown forward if he/she is not seated properly.
Inertia of Direction.
For example:
As a bicycle moves, the water drops sticking to its wheel
8. Momentum: it is derived as the product of Mass and Velocity.
p=mv
Where ‘p’ is Momentum, ‘m’ is Mass of the body and ‘v’ is
Velocity.
It is a vector physical quantity. It has the same direction as
that of velocity. S.I. unit of momentum is kg-m/s.
9. “The Force applied on a body is equal to the product of
Mass of the body and the acceleration produced in it.”
Or,
“The Force acting on a body is directly proportional to
the rate of change in momentum and acts in the
direction of acceleration.
F=ma
Where ‘F’ is force, ‘m’ is mass and ‘a’ is acceleration.
S.I. unit of Force is kg-m/s ²
10. Impulse: When a large Force acts on a body for a short
period of time then the product of Force and Time is
called Impulse.
Impulse = Force X Time
For example:
A cricketer moves his hands backward while
catching a ball to increase the time of contact and
reduce the force of Impulse.
Vehicles like car, buses and bikes are provided
with shockers.
11. Whenever any two bodies interact with each other, the Force
exerted by (1) on (2) is equal in magnitude but of opposite in
direction to the Force exerted by (2) on (1).
F12=F21
Alternate Statement:
For every action there is an equal and opposite reaction
provided that the action & reaction doesn’t act on the same
body.
For example:
In a rocket, gases are ejected with a great speed
from the rocket backwards (action) and rocket is
pushed forward(reaction).
12. Whenever any two bodies interact, the total momentum before their
interaction is equal to the total momentum after their interaction.
m1 u1 m2 u2 = m1 v1 m2 v2
Before collision After collision
m1u1 + m2u2 = m1v1 + m2v2
13. Let F12 be the force on (1) due to (2) and F21 be the force o (2) due to (1).
According to III law of motion
F12 = -F21 (i)
According to II law of motion
F12 = Rate of change in momentum of body (1)
F12 = m1v1 – m1u1
t (ii)
F21 = Rate of change in momentum of body (2)
F21 = m2v2 – m2u2
t (iii)
14. Substituting (ii) & (iii) for (i)
m1v1 – m1u1 = - m2v2 – m2u2
t t
m1v1 – m1u1 = - m2v2 + m2u2
m1v1 + m2v2 = m1u1 + m2u2
Hence Derived
15. Galileo Galilei was born on 15 February 1564 in Pisa, Italy.
Galileo, right from his childhood, had interest in mathematics
and natural philosophy.
In 1586, he wrote his first scientific book ‘the Little Balance
(la Balancitta)’
In 1592, he was appointed professor of mathematics at the
university of Padua in the Republic of Venice.
Around 1640, he designed the first pendulum clock.
In his book ‘Starry Messenger’ on his astronomical
discoveries, Galileo claimed to have seen mountains on the
moon, the Milky Way made up of tiny stars, and four small
bodies orbiting Jupiter.
16. A body of mass 100g is moving with a velocity of
20m/s. Calculate the momentum of the body.
• Mass= 100/ 1000
= 1/10 kg
Velocity= 20m/s
Now,
Momentum= Mass X Velocity
p= mv
p= 1/ 10 X 20
p= 2kg-m/s Ans.
17. A car of mass 1000kg moving at a speed of 72km/h is
brought to rest by applying brakes. Calculate the
change in momentum.
• Mass (m)= 1000kg
Initial velocity (u)= 72 X 5/ 18
= 4 X 5
= 20m/s
Final velocity (v)= 0
Now,
Change in momentum= m(v-u)
=1000 (0-20)
= 1000 (-20)
= -20000 kg-m/s Ans.
18. A car of mass 1000kg starting from rest, picks up
speed of 90km/h in 5 sec. Calculate the force acting
on the car.
• Initial velocity= 0
Final velocity= 90 X 5/ 18
= 5 X 5
= 25m/s
Time= 5sec
Mass= 1000kg
Acceleration= v-u
t
19. = 25-0/ 5
= 25/ 5
= 5m/s²
So, Force= ma
= 1000 X 5
= 5000 N Ans.
20. Starting from rest, a body covers a distance of 25m in
5 sec. Calculate the force exerted on the body if the
mass of the body is 500gm.
• Mass= 500/1000
= 1/2 kg
Time= 5sec
Initial velocity= 0
Now,
s=ut+1/2 at²
25= 0+1/2 a X 5²
25= 0+1/2 a X 25
25= 1/2 a X 25
22. A bullet of mass 20gm is horizontally fired with a
velocity of 150m/s from a pistol of mass 2kg. What is
the recoil velocity of the pistol?
• m1= 2kg
u1= 0
m2= 20 gm
= 20/1000
=0.02 kg
u2= 0
v1= ?
23. v2= 150m/s
Now,
m1u1 + m2u2 = m1v1 + m2v2
0= 2 X v1 + (0.02 X 150)
0= 2v1 + 3
- 2v1 =3
-v1= 3/2
v1= -3/2
= -1.5 m/s Ans.
Negative sign indicates the opposite direction of
force i.e. recoiling of the gun.