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Mechanics

Collisions

One dimensional collisions between two objects can be studied using a linear air track (shown below). The mobiles "float" on a cushion of air to eliminate the force of friction. The mass of a mobile can be changed by adding an extra piece of metal.

Elastic collisions

An elastic collision is a collision in which kinetic energy is conserved. The springs on the mobiles ensure that the collisions are (very nearly) elastic.

Different collisions were observed but in each case mobile B was initially stationary.

i) Mass of A = mass of B
After collision:

A stops
B moves with the speed which A had before the collision

ii) Mass of A > mass of B
After collision: A slows down but continues to move in the same sense
B moves to the right faster than A was moving before the collision
iii) Mass of A < mass of B
After collision: A moves to the left
B moves slowly to the right

These observations confirm Newton’s third law of motion.

It can easily be shown that for an elastic collision, the relative velocity of approach is equal to the relative velocity of separation.

Non-elastic collisions

During a non-elastic collision, some K.E. is converted to other forms of energy.

A totally non-elastic collision is one in which the relative velocity of separation is zero. In other words, the two bodies remain in contact (stick together) after the collision.

Detailed study of totally non-elastic collisions is quite easy because there is only one speed to measure after the collision.

The speed of A was measured before the collision. B was initially stationary. The mass of A was varied. The speed of A and B together was measured after the collision.

Results

Mass of A

Speed of A before collision

Mass of A + mass of B

Speed of A and B after collision

m

 

m

 

2m

 

m

 

m

 

2m

 

The results suggest that the quantity mass multiplied by speed is the same before and after the collision. Experiments involving interactions between bodies moving in two (or three) dimensions show that it is mass multiplied by velocity which is the useful quantity.

The product of mass and velocity is called the linear momentum of the body.

The Principle of Conservation of Linear Momentum
During any interaction in which no external forces act, the total linear momentum is conserved.

Linear Momentum
The linear momentum of a body of mass m, moving with velocity , is given by

The units of momentum are kgms-1

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