Physics FA-2

Project Work

FORCE & LAWS OF MOTION

BY: PRABHAT

GAURAV

CONTENTSFirst 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.

Deriving the Law of Conservation of Momentum.About Galileo Galilei.Numericals on Momentum.Numericals on Force.Numericals on Law of conservation of Momentum.

FIRST LAW OF MOTION“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.”

CONSEQUENCE OF FIRST LAW OF MOTION

(INERTIA)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.

TYPES OF INERTIAInertia 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 start leaving it tangentially.

MOMENTUMMomentum: it is derived as the product of Mass and Velocity.

p=mvWhere ‘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.

SECOND LAW OF MOTION“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=maWhere ‘F’ is force, ‘m’ is mass and ‘a’ is acceleration. S.I. unit of Force is kg-m/s ²

CONSEQUENCE OF SECOND LAW OF MOTION

(IMPULSE)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 TimeFor 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.

THIRD LAW OF MOTIONWhenever 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=F21Alternate 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).

CONSEQUENCE OF THIRD LAW OF MOTION (LAW OF CONSERVATION OF

MOMENTUM)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

DERIVING THE LAW OF CONSERVATION OF

MOMENTUMLet 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)

Substituting (ii) & (iii) for (i)m1v1 – m1u1 = - m2v2 – m2u2

t tm1v1 – m1u1 = - m2v2 + m2u2

m1v1 + m2v2 = m1u1 + m2u2

Hence Derived

ABOUT GALILEO GALILEIGalileo 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.

NUMERICALS ON MOMENTUMA 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 Velocityp= mvp= 1/ 10 X 20p= 2kg-m/s Ans.

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.

NUMERICALS ON FORCEA 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

= 25-0/ 5= 25/ 5= 5m/s²

So, Force= ma= 1000 X 5= 5000 N Ans.

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

1/2a= 25/251/2a= 1a= 1 X 2a= 2m/s²

Now, F= ma F= 1/2 X 2 F= 1 N Ans.

NUMERICALS ON LAW OF CONSERVATION OF

MOMENTUMA 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= ?

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.

THANK

YOUPrepared by: Prabhat GauravClass : 9-A