Question

derive an expression for perfectly inelastic collision in two dimensions​

Answer 1

Answer:

WHAT IS INELASTIC COLLISION?

Inelastic Collision: In the inelastic collision, the objects stick to each other or move in the same direction. The total kinetic energy in this form of collision is not conserved but the total momentum and energy are conserved. During this kind of collision, the energy is transformed into other energy forms like heat and light. Since during the phenomenon the two masses follow the law of conservation of momentum and move in the same direction with same the same speed v we have:

Step-by-step explanation:

DERIVATION

m1u1 + m2u2 = (m1+ m2)v

v= (m1u1 + m2u2)/(m1+ m2)

The kinetic energy of the masses before the collision is : K.E1 = 1/2  m1u21 + 1/2 m2u22

While kinetic energy after the collision is: K.E2 = 1/2 (m1+ m2) v2

But according to the law of conservation of energy: 1/2  m1u21 + 1/2 m2u22 = 1/2 (m1+ m2) v2 + Q

‘Q’ here is the change in energy that results in the production of heat or sound.

Answer 2

A collision is a transfer of momentum or kinetic energy from one object to another . Collisions are classified into elastic and inelastic collision.

Given:

Inelastic collision in two dimensions

To Find:

To get the equation for perfectly inelastic collision in two dimensions.

Solution:

The total linear momentum of system will remain conserved or constant

(i. e) Pf = Pi

m1v1 cosθ  + m2v2cosφ = m1u1 + m2u2 ............(1)

Also,

m1v1 sinθ -m2v2 sinφ = 0 ........(2)

Consider x and y axis,

Mass m1 makes an angle θ and Mass m2 makes an angle φ,

When the collision occurs the mass m1 and m2 gets added up ,

From, (1) and (2) ,

We get,

m1u1cosθ +m2u2 = (m1+m2)vcosφ

The above equation is the equation for inelastic collision in two dimensions.

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