LAWS OF MOTION

SUBMITTED TO- MR.DC BHATT

Acknowledgement

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I made this project under the

guidance of my mathematics teacher

MR. D.C BHATT

CLASS X-A

1) Force :- Force is an external effort which may move a body at rest or stop a moving body or change the speed of a moving body or change the direction of a moving body or change the shape and size of a body. Effects of force :- i) Force can move a body at rest. ii) Force can stop a moving body.iii) Force can change the speed of a moving body.iv) Force can change the direction of a moving body.v) Force can change the shape and size of a body.

2) Balanced and unbalanced forces :- i) Balanced forces :- If two forces act on a body in opposite direction and if both the forces are equal, then the resultant force acting on the body is zero. Such forces are called balanced forces. Balanced forces cannot change the state of rest or motion of a body.

ii) Unbalanced forces :- If two forces act on a body in opposite direction and if one force is greater than the other, then the resultant force is not equal to zero. Such forces are called unbalanced forces. Unbalanced forces changes the state of rest or the motion of a body.

F1 F2

F1 = F2

F1F2

F1 > F2

3) Force of friction :- Force of friction is the force which opposes the motion of an object over a surface. Eg :- A ball rolling on ground gradually slows down and comes to a stop due to force of friction. If we stop pedalling a bicycle, it gradually slows down and comes to a stop due to force of friction.

An object with uniform motion will continue to move with uniform motion if the forces acting on it ( pushing force and frictional force ) are balanced. If an unbalanced force acts on the moving body, then its speed or direction of motion changes. If the unbalanced force is removed, then it will continue to move with the speed it had acquired till then.

4) Galileo’s experiment of motion of an object on an inclined plane :-

h h

When a marble rolls down an inclined plane, its velocity increases and when it goes up on the second inclined plane, its velocity decreases. If the inclinations of both the planes are equal, then the marble will reach the same height which it rolled down. If the inclination of the second plane is decreased, it will travel more distance to reach the original height. If the inclination of the second plane is made horizontal, the marble will travel forever trying to reach the same height. An unbalanced force is required to change the motion of the marble but no force is needed to sustain the uniform motion of the marble.

Newton’s Laws of MotionNewton’s Laws of Motion• 11stst Law Law – An object at rest will stay at

rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

• 22ndnd Law Law – Force equals mass times acceleration.

• 33rdrd Law Law – For every action there is an equal and opposite reaction.

5) Newton’s laws of motion :- Newton’s first law of motion states that :- ‘An object remains in a state of rest or in uniform motion in a straight line unless compelled to change that state by an applied force.’

Inertia :- The natural tendency of objects to remain in a state of rest or in uniform motion is called inertia. This is why the first law of motion is also known as the law of inertia.

11stst Law of Motion Law of Motion (Law of Inertia) (Law of Inertia)

An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

1st Law• Inertia is the

tendency of an object to resist changes in its velocity: whether in motion or motionless. These pumpkins will not move unless

acted on by an unbalanced force.

1st Law • Once airborne,

unless acted on by an unbalanced force (gravity and air – fluid friction), it would never stop!

1st Law

• Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever.

Examples of inertia :-i) If a striker hits a pile of coins on a carrom board, the lowest coin moves out and due to inertia of rest, the other coins fall down.ii) If a coin placed on a playing card over a tumbler is flicked with the finger, due to inertia of rest, the coin falls down into the tumbler.iii) When we travel in a car and the driver applies the brakes suddenly, we tend to fall forward due to inertia of motion.iv) When we are standing in a bus and the bus begins to move suddenly, we tend to fall backward because our feet in contact with the floor moves forward but the upper part of the body continues to remain at rest due to inertia of rest.

Don’t let this be you. Wear seat belts.Don’t let this be you. Wear seat belts.Because of inertia, objects (including you) Because of inertia, objects (including you) resist changes in their motion. When the resist changes in their motion. When the car going 80 km/hour is stopped by the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 brick wall, your body keeps moving at 80 m/hour.m/hour.

6) Inertia and Mass :- A body at rest continues to be at rest and a body in motion continues to be in motion. This property of a body is called its inertia. The inertia of a body is measured by the magnitude of force required to change the state of the body. The force required to change the state of a heavier body is more than the force required to change the state of the lighter body. This is because the mass of the heavier body is more than the mass of the lighter body. So ‘The mass of a body is a measure of its inertia.’

7) Momentum of a body :- The momentum of a body is the product of its mass and velocity. Momentum = mass x velocity p = mv where p is the momentum of a body m is the mass of the body v is the velocity of the body If a body is at rest its velocity is zero and so its momentum is also zero. The SI unit of momentum is kilogram metre per second or kg m/s or kg ms-1

Eg :- A truck moving at a very low speed can kill a person standing in its path because of the heavy mass of the truck. A bullet of small mass when fired from a gun can kill a person because of the large velocity of the bullet. So the impact of a body depends upon its mass and velocity.

2nd Law

2nd Law

The net force of an object is equal to the product of its mass and acceleration, or F=ma.

2nd Law

• When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N).

• One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.

2nd Law (F = m x a)

• How much force is needed to accelerate a 1400 kilogram car 2 meters per second/per second?

• Write the formula• F = m x a• Fill in given numbers and units• F = 1400 kg x 2 meters per second/second• Solve for the unknown• 2800 kg-meters/second/second or 2800 N

8) Newton’s second law of motion :- Newton’s second law of motion states that :- ‘ The rate of change of momentum of an object is proportional to the applied force in the direction of force.’ Mathematical formulation of Second law of motion :- If an object of mass m is moving along a straight line with initial velocity u and is accelerated to velocity v in time t by applying a force F, then Initial momemtum p1 = mu Final momentum p2 = mv Change in momentum p2 – p1 = mv – mu = m (v – u ) Rate of change of momentum = m (v – u ) tOr the applied force F α m (v – u ) or F = k m (v – u ) but (v – u ) = a t t t So F = kma where k is a constant of proportionality Or F = ma The SI unit of mass is kg and acceleration is m/s2 or ms-2 so the unit of Force is kg ms-2 or newton . It’s symbol is N

Newton’s 2nd Law proves that different masses accelerate to the earth at the same rate, but with different forces.

• We know that objects with different masses accelerate to the ground at the same rate.

• However, because of the 2nd Law we know that they don’t hit the ground with the same force. F = maF = ma

98 N = 10 kg x 9.8 m/s/s98 N = 10 kg x 9.8 m/s/s

F = maF = ma

9.8 N = 1 kg x 9.8 9.8 N = 1 kg x 9.8 m/s/sm/s/s

3rd Law

• For every action, there is an equal and opposite reaction.

3rd LawAccording to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.

3rd Law

There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces.

Newton’s 3rd Law in Nature• Consider the propulsion of a

fish through the water. A fish uses its fins to push water backwards. In turn, the water reacts by pushing the fish forwards, propelling the fish through the water.

• The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards).

3rd Law

Flying gracefully through the air, birds depend on Newton’s third law of motion. As the birds push down on the air with their wings, the air pushes their wings up and gives them lift.

• Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards.

• The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards).

• Action-reaction force pairs make it possible for birds to fly.

10) Newton’s third law of motion :- Newton’s third law of motion states that :- ‘To every action there is an equal and opposite reaction and they act on two different bodies.’

To prove that action and reaction are equal and opposite :- Take two spring balances A and B connected together. Fix the spring balance B to a rigid support. When a force is applied by pulling the free end of the spring balance A, both the spring balances show the same readings. This shows that the force exerted by the spring balance A on B is equal but opposite in direction to the force exerted by spring balance B on A . The force exerted by the spring balance A on B is action and the force exerted by the spring balance B on A is reaction.

AB

Examples of action and reaction :-i) When a bullet is fired from a gun, it exerts a forward force (action) on the bullet and the bullet exerts an equal and opposite force on the gun (reaction) and the gun recoils.

ii) When a sailor jumps out of a boat, he exerts a backward force of the boat (action) and the boat exerts an equal and opposite force on the sailor (reaction) and the sailor jumps forward.

Recoil forceon the gun

Accelerating forceon the bullet

Action

Reaction

iii) When an air filled balloon is released, the force of the air coming out of the balloon (action) exerts an equal and opposite force on the balloon (reaction) and it moves upward.

iv) When a rocket is fired, the force of the burning gases coming out (action) exerts an equal and opposite force on the rocket (reaction) and it moves upward.

Other examples of Newton’s Third Law

• The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction).

3rd Law• Consider the motion of

a car on the way to school. A car is equipped with wheels which spin backwards. As the wheels spin backwards, they grip the road and push the road backwards.

3rd LawThe reaction of a rocket is an application of the third law of motion. Various fuels are burned in the engine, producing hot gases.

The hot gases push against the inside tube of the rocket and escape out the bottom of the tube. As the gases move downward, the rocket moves in the opposite direction.

11) Conservation of momentum :- The Law of conservation of momemtum states that :-

‘The sum of momenta of two objects before collision is equal to the sum of momenta after collision provided there is no unbalanced forces acting on them.’ This means that the total momentum of the two objects is unchanged or conserved by collision.

uA uB vA vB

FBA FAB

If two balls A and B of masses mA and mB are travelling in a straight line with initial velocities uA and uB and if uA > uB, the two balls will collide with each other. During collision at a time t, ball A exerts a force FAB on ball B and ball B exerts a force FBA on ball A. If vA and vB are the velocities of balls A and B after collision,

The momenta of ball A before and after collision are mAuA and mAvA and the momenta of ball B before and after collision are mBuB and mBvB.

A B A B BA

mA mAmB mB

Change in momentum of ball A during collision = mAvA – mAuA

(vA - uA) Rate of change of momentum of ball A (FAB) = mA

t Change in momentum of ball B during collision = mBvB – mBuB (vB - uB) Rate of change of momentum of ball B (FBA ) = mB

t According to Newton’s third law of motion the force FAB exerted by ball A on ball B is equal and opposite to the force FBA exerted by ball B on ball A. Therefore FAB = - FBA (vA - uA) (vB - uB) or mA = = - mB t t or mAvA - mAuA = - mBvB + mBuB

or - mAuA - mAuA = - mAvA - mBvB or mAuA + mBuB = mAvA + mBvB Momentum of the two balls before collision is equal to the momentum of the two balls after collision.

05/03/23

05/03/23