Power, Collisions and its Types | Physics Grade XI

Detail Introduciton of Power and Collisions

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Power, Collisions and its Types | Physics Grade XI

Power, Collisions and its Types

Power

Power is defined as the rate of which the work is done.

Mathematically, Power = Work Done/ time

Thus, power of an agent measures how fast it can do the work.

For constant force,

Power, p = W/t = F.s / t = F. v

Where v = s/t, is linear velocity

If θ be the angle between F and V, then

P = F. v cosθ

Collisions

Collison is the mutual interaction between two particles for a short interval of time so that their momentum and kinetic energy may change. In general, collision is an isolated event in which the colliding bodies exert relatively strong forces to one another for relatively short time.

There are two types of collisions.

i. Elastic collision

Elastic collision is the mutual interaction between two bodies where their momentum and kinetic energy is conserved. It occurs when conservative force is applied to a body.

Characteristics of an Elastic collision;

  1. The momentum is conserved
  2. Kinetic energy is conserved
  3. Total energy is conserved
  4. Forces involved during the interaction is conservative in nature.
  5. Mechanical energy is not transformed into any other form of energy.

Elastic collision in one dimension

If the colliding bodies move in the same path even after collision then it is said to be collision in one direction.

Let us consider two bodies A and B with masses m1 and m2 moving in a straight line with velocity u1 and u2 such that u1>u­2. After some time, they collide with each other.

Let v1 and vbe the velocities of the bodies A and B respectively after collision such that v1<v2.

Elastic Collision

From the principle of conservation of momentum,

       m1u1 + m2u2 = m1v1 + m2v2   …………. (i)

       m1(u1­-v1) = m2(v2-u2)   ………………. (ii)

In elastic collision,

       K.E before collision = K.E. after collision

       ½ m1u12 + ½ m2u22 = ½ m1v12 + ½ m2v22

       Or, m1(u1 – v1)(u1+v1) = m2(u2 – v2)(u2+v2) ……(iii)

Dividing (iii) by (ii), we get

       u1 -u2=v2 -v1 ………. (iv)

This shows that in an elastic collision between two particles, the relative velocity of separation after collision is equal to the relative velocity of an approach before the collision.

ii. Inelastic collision

The collision in which the momentum is conserved but kinetic energy is not conserved is called Inelastic collision.

Characteristics of inelastic collision

  1. The momentum is conserved
  2. Total energy is conserved.
  3. Kinetic energy is not conserved.
  4. Forces involved during the interaction re non-conservative forces.
  5. Mechanical energy is transformed into any other form of energy.

Inelastic collision in one dimension

Let us consider two perfectly inelastic bodies of mass m1 and m2. Body A is moving with velocity u1 and B is at rest. After some time, they collide and move together with same velocity v. So, initial momentum before collision = m1u1.

Final momentum before collision = m11

Final momentum after collision = (m1 + m­2) v

Since momentum is conserved, i.e. (m1 + m­2) v =m11

     V = m1u­1/(m1 + m­2) ……. (i)

     (K.E before collision) / (K.E. after collision) = (½ m1u12) / ½ (m1 + m­2) v2

     = m1u12 / (m1 + m­2) [m11/ (m1 + m­2)]2

     = (m1+m2)/m1> 1

Therefore, K.E. before collision = K.E. after collision

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