Newton’s Law Of Motion SS2 Physics Lesson Note

NEWTON’S LAWS OF MOTION

Newton’s first law of motion states that everybody continues in its state of rest or of uniform motion in a straight line unless it is acted upon by a force. The tendency of a body to remain at rest or, if moving, to continue its motion in a straight line is called inertia. That is why Newton’s first law is otherwise referred to as the law of inertia.

 Newton’s 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 of the force. 

F α mv –mu

t

F α m (v –u)

           t

F α ma

F = kma

Where k =1

F =ma

MOMENTUM

The momentum of a body is the product of the mass and velocity of the body. The S.I. unit of momentum is kgm/s. 

IMPULSE

Impulse is the product of force and time. It is also defined as the change in momentum. Thus both momentum and impulse have ‘Ns’ as a unit

F = m (v-u)/t

Ft = mv – mu (where ‘mv-mu’ is the change of momentum)

F x t = I (Ns)

Newton’s third law of motion states that to every action, there is an equal but opposite reaction. A practical demonstration of this law can be observed when a bullet is fired from a gun, the person holding it experiences the backward recoil force of the gun (reaction) which is equal to the propulsive force (action) acting on the bullet.

According to Newton’s second law of motion, force is proportional to change in momentum

Therefore the momentum of the bullet is equal and opposite to the momentum of the gun i.e. 

Mass of bullet x muzzle velocity = mass of gun x recoil velocity

Hence, if: m= mass of the bullet, v= velocity of the bullet, M=mass of the gun, V= velocity of the recoil of the gun.

Then, the velocity, V, of the recoil of the gun is given by:

MV = mv

V = mv/M

CONSERVATION OF LINEAR MOMENTUM

The principle of conservation of linear momentum states that when two or more bodies collide, their momentum remains constant provided there is no external force acting on the system. This implies that in a closed or isolated system where there is no external force, the total momentum after collision remains constant. The principle is true for both elastic and inelastic collisions.

COLLISION

There are two types of collision- elastic and inelastic.

In elastic collision, the two bodies collide and then move at different velocities. Both momentum and kinetic energy are conserved e.g. collision between gaseous particles, a ball which rebounds to its original height etc.

If the two colliding bodies have masses m1 and m2 initial velocities u1 and u2 and final velocities v1 and v2. The conservation principle can be mathematically expressed as:

 m1u1 + m2u2 = m1v1 + m2v2 

In an inelastic collision, the two bodies joined together after the collision and with the same velocity. Here, momentum is conserved but kinetic energy is not conserved because part of it has been converted to heat or sound energy, leading to deformation.

Thus, the conversation principle can be re-written as:

m1u1 + m2u2 = v (m1 +m2)

Since momentum is a vector quantity, all the velocities must be measured in the same direction, assigning positive signs to the forward velocities and negative signs to the backward or opposite velocities

EXAMPLE

Two moving toys of masses 50 kg and 30 kg are travelling on the same plane with speeds of 5 m/s and 3 m/s respectively in the same direction. If they collide and stick together, calculate their common velocity.

MAVA + MBVB = V (MA + MB)

V= MAVA + MBVB

       (MA + MB)

V = (50 x 5) + (30 x 3)

             50 + 30 

V = 250 + 90

            80

V = 340

        80 

V = 4.05 m/s

TWO BODIES TRAVELING IN OPPOSITE DIRECTION 

>>>O    O<<<             >>>OO             

MA     MB     MA MB

= MAVA – MBVB = V (MA + MB) 

V= MAVA + MBVB

         MA + MB

ASSIGNMENT

1. Derive from Newton’s law the relationship between Force, mass and acceleration
2. State Newton’s laws of  motion and explain the consequences of each law
3. State the principle of conservation of linear momentum.
4. A 15 kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 200N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (g=10m/s2)?