NEWTONS LAW OF MOTION.

• Objects on earth do not move by themselves, they are said to be conservative.
• An external influence is required to make a body move or stop moving and this is called a force.
• A force is that which alters the existing state of a body in motion or at rest.
• The effects of force on motion of a body are based on the laws known as newtons law of motion.

1. Newton’s 1^st law of motion.

• It states that a body remains in its state of rest or uniform motion in a straight line unless acted upon by an external force.
• The law suggests that matter has an inbuilt reluctance to change its state of motion or rest.
• This property of a body to resist change is called inertia.
• The mass of a body is a measure of its inertia and the first law is referred to as the law of inertia.
• A large mass requires a large force to produce a given acceleration or deceleration on it than a small mass.

                                    Momentum.

• To succeed in changing the state of motion or rest, there is need for motion of the force and the mass of the material used to apply force. This quantity of motion is known as momentum. It depends on two other factors;

1. The mass of the body.
2. The rate of change of motion or displacement(velocity)

• Momentum is therefore the product of the mass and velocity.

                        P = mass   x   velocity

                        SI units of momentum = kgm/s

• It is a vector quantity whose direction is that of velocity. This implies that an object of small mass moving very fast may be just as difficult to stop or as dangerous as a large mass moving slowly.

                        Example.

1. An oil tanker of mass 500,000 tones moving at 18km/h. Calculate its momentum.

            P = Mass x velocity

            P = 500,000,000 x 5

            P = 2,500,000,000 kgm/s

            P = 2.5 x 10¹⁹  kgm/s

2. A van of 3 metric tones is travelling at 72km/h. Calculate the momentum of the van.

            P = Mass x velocity

            P = 3000 x 20

            P = 60,000 kgm/s

3. A car is travelling at 90km/h. At what velocity will its momentum be doubled.

            P = mass x velocity

            MV = 2MV1

            V = 2MV1/M

            V = 2V1

            V = 2 x 25 m/s

            V = 50 m/s

1. Newton’s 2^nd law of motion.

• Rate of change of momentum of a body is directly proportional to the resultant external force applied and takes place in the direction in which the force acts.

            Impulse.

• Impulse force is a force that act on a body for a very short time. The result produced is called impulse of the force.
• The impulsive force occurs when two moving bodies collide head on e.g. when a force F acts on a body of mass M for time T, then the impulse of the force is given by force x 

Impulse of force = f  x  t      or         ft, impulse force Mv– Mu

                                                                                     T

ft = Mv-Mu

• Mv-Mu is change in momentum on time t then the impulse of a force acting on a body during a given time interval is equal to the change in momentum produced in the body at that time.

Example.

1. A ball of mass 35g travelling horizontally at 20m/s strikes thewall at right angles and rebounds with a speed of 16m/s. Find the impulse exerted by the ball.

            Momentum before Mu = 35 x 10^-3 x20 = 700 x10^-3kgm/s

            Momentum after Mv = 36 x 10^-3 x 16 = 560 x 10^-3kgm/s

            Change in momentum = Mv – Mu

                                                = (700 – 560) x 10^-3

                                                = 1260 x 10^-3 m/s

                                                = 1.26 m/s

1. Newton’s 3^rd law of motion.

• States that for every action there is an equal and opposite reaction, that is, if a body exerts force on another body, the 2^nd body exerts an equal and opposite force on the 1^st
• This implies that a body does not occur in single but in pairs. E.g. magnetism, electrostatics, gravitational effect etc.

                        Example.

1. A lorry of mass 500 kg collides into a stationary car of mass 1000 kg together with the occupants. If the velocity of the lorry before collision was 10m/s and the collision is perfectly inelastic, find
2. The common velocity.

Momentum before = Momentum after

M₁U₁ + M₂U₂ = (M₁ + M₂)V

M₁U₁=(M₁ + M₂)V

V =       V =   v = 8.33 m/s

1. The average force on a 60kg passenger in the car if the impact lasts 0.5 seconds.

F = 1666.67 n/kg

                        Application of the law of momentum.

1. Rockets and jet propulsion. Mostly uses 3^rd law of motion action- reaction. Rockets use liquid hydrogen as their fuel and liquid oxygen for combustion. When the hydrogen is burnt, the rocket propels itself forward by forcing the exhaust gases out at high velocity hence gain momentum in one direction. The rocket gain and equal momentum is opposite. The rate at which its momentum changes i.e. force provides the forward upthrust on the rocket as it moves faster in the outer space where there is no air resistance than in the earth’s atmosphere.
2. A jet engine uses air which provides oxygen to push out its exhaust gas through the nozzle corner so as to provide greater force.

                        Conservation of linear momentum.

• The principle of conservation of momentum states that for a system of moving bodies which is not acted upon by any external forces, the total momentum of the system remains constant, that is both constant in magnitude and direction. The particles of the body collide.
• There are two types of collisions.

1. Elatic collision.
2. Inelastic collision.
3. Elastic collision.

• Is a collision where bodies collide and separate either move in the same or opposite direction. They may collide head on.
• During collision, bodies undergo slight distortion as a result of the action of impulsive force, that is, they are temporarily fused together.
• If the time of impact is very short, the collision is said to be perfect elastic collision. In this collision

1. The momentum is conserved. That is, momentum before is equal to momentum after collision.
2. The kinetic energy is conserved. That is, kinetic energy before is equal to kinetic energy after collision.

• The velocity of approach is equal to velocity of separation when the masses of colliding bodies is the same.

1. Inelastic collision.

• It is a collision where bodies collide, fuse and move in the same direction or remain stationary. If they do not separate at all, the collision is said to be perfect inelastic collision. In this collision

1. The momentum is conserved.
2. The kinetic energy is not conserved.

• The total mass is the sum of the individual masses M = M1 + M2
• The two bodies move with a common velocity V in the same direction.