GRAVITATION

Q According to Universal law of gravitation- every body on the earth attracts every other body with a gravitational force, why then this force does not cause any motion in the objects?Ans Though the various objects on this earth constantly attract each other, they do not cause any motion because-1) Each body experiences multiple forces from different directions and most of these forces get cancelled from each other.2) The gravitational force of attraction between them is very small due to their comparatively small masses.

Gravitation and Newton's laws of motion

According to Third law of motion every action has equal and opposite reaction. This means that if earth attracts a body towards it with a force, F then the body also attracts earth with same force but in opposite direction i.e. -F. But we know that earth does not move towards the object because according to second law of motion, F=maa=F/mAs we see that acceleration is inversely proportional to m, therefore a negligible acceleration is produced in earth due to its high mass.

Acceleration due to gravity

If we drop a body of mass 'm' from a distance 'R' from centre of earth of mass 'M', then earth will exert a force of gravitation on the body,FF=G M m/R*R - 1According to second law of motion, F=ma -2Equating 1 and 2GMm/R*R = maa= GM/R*RSince we know that in case of free fall, a= g (acceleration due to gravity),g= GM/R*RPutting values, we get g=9.8 m/s*s

Dependence of acceleration due to gravity

1) Since acceleration due to gravity is independent of mass of object i.e. 'm', therefore, both light and heavy objects are accelerated by same amount.

2) As 'g' depends on 'R', the value of 'g' varies at poles and equator. Since, 'R' is more at equator, 'g' is small at equator and 'R' is less at poles, therefore, 'g' is more at poles.

Weight on moon

Let We= weight on earth and Wm= weight on moonWm= GM*m/R*R where M is mass of moon, m is mass of object and R is radius of moonNow, mass of earth is 100 times mass of moon and radius of earth is 4 times radius of moonWe= G 100M*m/4R*4RWe= 100GmM/16R*RWm/We= 16/100or approximately, Wm/We=1/6Therefore, weight of an object on moon is 1/6th of weight of that object on earth.

Difference between mass and weight

Mass1) The mass of an object is the quantity of matter contained in it.2) The S.I. unit of mass is kilogram (kg).3) The mass of an object is constant.4) The mass of an object can never be zero.

Weight1) The weight of an object is the force with which it is attracted towards the centre of the earth.2) The S.I. unit of weight is Newton (N).3) The weight of an object is not constant. It changes with the change in acceleration due to gravity (g).4) The weight of an object can be zero. e.g. in the interplanetary space, where g=0, the weight of an object becomes zero.

Equations of motions for freely falling bodies1) v=u+gt2) h=ut+ 1/2gt*t3) v*v= u*u+ 2gh

IMPORTANT POINTS TO REMEMBER

1) The physical quantities having vertically upward motion are assigned +ve values whereas the physical quantities having downward motion are assigned -ve values.2) The acceleration due to gravity of earth is always taken -ve.3) When a body is dropped freely from a height, its initial velocity 'u' is zero.4) When a body is thrown vertically upwards, its final velocity 'v' becomes zero.5) The time taken by a body to rise to the highest point is equal to the time it takes to fall from the same height.

Numerical assignment- class IX Q What is the momentum of a man of mass 75kg when he walks with a uniform velocity of 2m/s?

Q What is change in momentum of a car weighing 1500 kg when its speed increases from 36km/h to 72km/h uniformly?

Q A man throws a ball weighing 500g vertically upwards with a speed of 10m/s.1) What will be its initial momentum?2) What would be its momentum at the highest point of his flight?

Q A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of 400m in 20s. Find the force acting on it if its mass is 7 metric tonnes. (1 metric ton= 1000kg)

Q A car of mass 2400kg moving with a velocity of 20m/s is stopped in 10s on applying brakes. Calculate the retardation and the retarding force.

Q For how long should a force of 100N acts on a body of 20kg so that it acquires a velocity of 100m/s?

Q A body of mass 2kg is at rest. What should be the magnitude of force which will make the body move with a speed of 30m/s at the end of 1s?

Q An unloaded truck weighing 2000kg has a maximum acceleration of 0.5 m/s*s. What is the maximum acceleration when it is carrying a load of 2000kg?

Q The car A of mass 1500kg, traveling at 25m/scollides with another car B of mass 1000kg traveling at 15m/s in the same direction. After

collision the velocity of car A becomes 20m/s. Calculate the velocity of car B after collision.

Q A bullet of mass 10g moving with a velocity of 400m/s gets embedded in a freely suspended wooden block of mass 900g. What is the velocity acquired by the block?

Q A 10g bullet traveling at 200m/s strikes and remains embedded in a 2kg target which is originally at rest but free to move. At what speed does the target move off?

Q A gun of mass 3kg fires a bullet of mass 30g. The bullet takes 0.003s to move through the barrel of the gun and acquires a velocity of 100m/s. calculate:a) the velocity with which the gun recoils.b) the force exerted on gunman due to recoil of the gun.

Q A ball X of mass 1kg traveling at 2m/s has a head on collision with an identical ball Y at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.

Q A boy of mass 50kg running at 5m/s jumps onto a 20kg trolley traveling in the same direction at 1.5m/s. What is their common velocity?

Q A girl of mass 50kg jumps out of a rowing boat of mass 300kg on to the bank, with a horizontal velocity of 3m/s. With what velocity does the boat begin to move backwards?

Q The velocity of a body of mass 10kg increases from 4m/s to 8m/s when a force acts on it for 2s.a) What is the momentum before the force acts?b) What is the momentum after the force acts?c) What is the gain in momentum per second?d) What is the value of the force?

Q Calculate the value of acceleration due to gravity on the surface of the moon?

Q The earth's gravitational force causes an acceleration of 5m/s*s in a 1kg mass somewhere in space. How much will the acceleration of a 3kg mass be at the same place?

Q To estimate the height of a bridge over a river, a stone is dropped freely in river from bridge. The stone takes 2s to touch the water surface. Calculate the height of bridge from the water level.

Q A cricket ball is dropped from a height of 20ma) Calculate the speed of the ball when it hits the ground.b) Calculate the time it takes to fall through this height.

Q A body has a weight of 10kg on the surface of the earth. What will be its weight when taken to the centre of the earth?

Q A stone resting on the ground has a gravitational force of 20N acting on it. What is the weight of the stone?

Chapter- Force and Laws of MotionAPPLICATIONS OF LAWS OF MOTION

Class-IX

First law of motionIntroduction: First law of motion states that- ‘A body at rest will

remain at rest and a body in uniform motion will continue in uniform motion with same velocity unless it is compelled by an external force

to change its state of rest or of uniform motion.’ The property of a body due to which it resists a change in its state of rest or of uniform motion is called Inertia. So, we can say that first law defines inertia.

Physical significance of inertia: Mass is the measure of inertia of a body. Heavier objects have more inertia than lighter objects.

Practical applications/ Related phenomenon: 1) When a hanging carpet is beaten with a stick, dust particles start coming out of it. This is because the force of stick makes the carpet move to and fro slightly but dust particles tend to remain at rest due

to their inertia and hence seperate from the carpet.2) When a tree (having flexible stem) is shaken vigorously, its fruits and leaves fall down. This is due to the fact that when branch of tree

is shaken, it starts moving to and fro but the fruits and leaves attached to it tend to remain at rest due to inertia and hence detach

from tree and fall down.3) When a car or bus stops suddenly, passengers are jerked forward

because due to force of brakes bus stops but passengers tend to remain in uniform motion. The seat belts are provided in cars so that if a fast running car stops suddenly due to some emergency, then the passengers are not thrown forward violently, and injury is prevented.

4) When a car or bus starts suddenly, passengers are thrown backward because the vehicle starts but passengers tend to remain at

rest.5) When a car or bus turns a corner sharply, we tend to fall sideways because of our inertia or tendency to continue moving in a straight

line.6) It is dangerous to jump out of a moving bus because the jumping person, who was moving with high speed of the bus, would tend to

remain in motion due to inertia even on falling to the ground and get hurt due to resistance offered by ground.

Definition of FORCE: Force is something which changes or tends to change the state of rest or of uniform motion of a body.

Second Law of Motion

Introduction: Second law of motion states that-‘The rate of change of momentum of a body is directly proportional to the applied force, and

takes place in the direction in which the force acts.’Force α Change in momentum / time taken

Formula: F=ma where, m=mass of body,

a= acceleration produced on applying force F

NOTE: first law is special case of second law (explained in class)

Practical applications/ Related phenomenon:

1) A cricket player moves his hands backward on catching a fast cricket ball. This is because a fast moving cricket ball has a

large momentum. In stooping such a ball its momentum has to be reduced to zero. Now, when a cricket player moves his hands

back, the time taken to reduce momentum of ball to zero is increased which reduces the rate of change of momentum( rate of change of momentum α change in momentum/ time taken; if

denominator is increased, whole value decreases, so force decreases). Hence, a small force is exerted on the hands of

player and he does not get hurt.2) During athletics meet, a high jumping athlete is provided

either a cushion or a heap of sand on the ground to fall upon. When the high jumper falls on a soft landing site, then the jumper takes a longer time to come to a stop. Thus rate of

change of momentum is less due to which small stopping force acts on athlete’s body and the athlete does not get hurt.

Third Law of MotionIntroduction: Whenever one body exerts a force on another body, the second body exerts equal and opposite force on the first body

i.e. to every action there is an equal and opposite reaction.

NOTE: Both the forces are opposite, so if one is positive, other will be negative.

Physical significance: Forces always exists in pairs.

Practical applications/ Related phenomenon:

1) When we walk on the ground, then our foot pushes the ground backward and in return ground pushes our foot forward. The forward reaction exerted by the ground on our foot makes us walk forward.

2) When a bullet is fired from a gun, the force sending the bullet forward is equal to the force sending the gun backward. But due to

the high mass of the gun, it moves only a little distance backward and gives a backward jerk or kick to the shoulder of the gunman. The gun

is said to have recoiled.3) In jet airplanes and rockets, the hot gases obtained by rapid

burning of fuel rush out of a jet (nozzle) at the rear (back) end of aircraft at a great speed. The equal and opposite reaction of the

backward going gases pushes the aircraft forward at a great speed.4) Moving of a boat is also similar to those of aircrafts with the

difference that backward force is provided by oars (chapu).5) When a man jumps out of a boat to the bank of the river, the boat

moves backwards, away from him. This is because while stepping out of the boat, man pushes the boat in backward direction with his leg

(action). In return of this boat exerts an equal force on man in forward direction which makes the man move forward.

6) When firemen are directing a powerful stream of water on fire from a hose pipe, they have to hold the hose pipe strongly due to its

tendency to go backward. The backward movement of hose pipe is due to the backward reaction of water rushing through it in the

forward direction at a great speed.7) To make the cart move, the horse bends forward and pushes the

ground with its feet. In return to this ground exerts a forward push on horse. When the forward reaction to the backward push of the horse is greater than the opposing frictional forces of the wheels, the cart

moves.

Law of Conservation of momentumIntroduction: The law of conservation of momentum states that ‘When two or more bodies act upon one another, their total momentum remains constant provided no external forces are acting.’

Total momentum before collision= total momentum after collision

Practical application/ Related phenomenon: The chemicals inside the rocket burn and produce high velocity blast of hot gases. These gases pass out through the tail nozzle of the rocket in the downward direction with tremendous seed or velocity, and the rocket moves up to balance the momentum of the gases. Although the mass of gases

emitted is comparatively small, but they have a very high velocity and hence a very large momentum. An equal momentum is imparted to the rocket in the opposite direction, so that, inspite of its large mass, the

rocket goes up with a high velocity.

Q Why more force is required to move a heavier body?A A greater force is required to move a body with more mass. This

can be explained as follows-a) First law of motion- According to first law of motion, a body with

more mass has more inertia and more the inertia of a body, more is its tendency to resist change in its state of rest. So, a greater force is

required to overcome this high inertia.b) Second law of motion- According to second law of motion, F=ma i.e. Fα m when ‘a’ is constant. So, greater the mass of a body, more

force it requires to produce a particular amount of acceleration.

Q How does a rocket move?A A rocket moves due to gases produced from its nozzle. This can be

explained as-a) Third law of motion- see explanation above

b) Law of conservation of momentum- see explanation above

Q Why are seat belts used in cars?A Seat belts are used in cars to save the passengers from injuries.

This is because

a) First law of motion- see explanation aboveb) Second law of motion- In a fast moving car when brakes are

applied, car stops suddenly. Due to this car’s large momentum is reduced to zero in a very short time. The stretchable seat belts worn

by the passengers of the car increase the time taken by the passengers to fall forward. Due to longer time, the rate of change of momentum of passengers decreases and hence less stopping force is

applied on passengers. This prevents the passengers from getting hurt seriously.

NOTE: Similarly, there are many other phenomena which cannot be explained simply by one law of motion.