Types of Impact - Free MCQ Practice Test with solutions, GATE Civil Engineering

• Momentum is conserved in all collisions.
• In elastic collision, kinetic energy is also conserved.
• In inelastic collision, kinetic energy is not conserved. In a perfectly inelastic collision, objects stick together after the collision.

Perfectly elastic collision:
If the law of conservation of momentum and that of kinetic energy hold good during the collision.

Inelastic collision:
Law of conservation of momentum holds good during a collision while that of kinetic energy is not conserved.
Coefficient of restitution (e)

• For perfectly elastic collision, e = 1
• For inelastic collision, e < 1
• For perfectly inelastic collision, e = 0

Coefficient of restitution (e):  The coefficient of restitution is the ratio of relative velocity after impact to the relative velocity before impact. 

EXPLANATION:

• Perfectly elastic collision: A perfectly elastic collision is defined as one in which there is no loss of kinetic energy and the momentum of the system is conserved in the collision.
• Inelastic or plastic collision: A inelastic collision is defined as one in which there is a loss of kinetic energy and the momentum of the system is conserved in the collision.
  • In the plastic collision, the velocity of separation is always less than the velocity of approach

⇒ 0 < e < 1

• Perfectly inelastic collision or plastic collision: A collision between two bodies in which two bodies stick together after collision and then move as one body, is called a perfectly inelastic collision or plastic collision. In this type of interaction, the momentum of the system remains conserved and the loss of kinetic energy is maximum.
  • So, for perfectly plastic collisions,

⇒ e = 0

• For perfectly elastic collision, energy is conserved, so the height rebounds by an object are some as the initial height 

So, options 1, 3, and 4 are correct.

Concept:
In perfectly elastic collision, both the balls will interchange their velocity after impact, i.e. velocity of ball A after impact = 0

Important Point
Coefficient of restitution, 
1 = before impact, 2 = after impact
For perfectly elastic body, e = 1
​​​​​​​For perfectly plastic body, e = 0

Consider a body having an indirect impact on a fixed plane as shown in the figure.
where, u = Initial velocity of the body, v = Final velocity of the body, α = Angle, which the initial velocity of the body makes with the line of impact, β = Angle which the final velocity of the body makes with the line of impact, and e = Coefficient of restitution.
The component of u, along the line of impact, will cause the direct ‘impact’ of the body with the fixed plane.
The other component of u along the perpendicular to the line of impact will not affect the phenomenon of impact and will be equal to the other component of v (i.e., along the perpendicular to the line of impact).
We know that velocity of approach = u cos α and velocity of separation = v cos β 
And the coefficient of restitution is,


v cos β = eu cos α

• Momentum is conserved in all collisions.
• In elastic collision, kinetic energy is also conserved.
• In inelastic collision, kinetic energy is not conserved. In perfectly inelastic collision, objects stick together after collision.

Perfectly elastic collision:
If law of conservation of momentum and that of kinetic energy hold good during the collision.
Inelastic collision:
If law of conservation of momentum holds good during collision while that of kinetic energy is not.
Coefficient of restitution (e)

• For perfectly elastic collision, e = 1
• For inelastic collision, e < 1
• For perfectly inelastic collision, e = 0

Coefficient of restitution (e):
The coefficient of restitution or coefficient of the resilience of a collision is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of an approach before the collision.


Properties of different types of collision are given in the table below:

Given Data:
Length of bar(l)= 2 m
Cross-sectional Area of bar(A)= 1500 mm²
Weight of fall on collar of bar(P)= 2 kN= 2000 N
Height from which weigh falls(h)= 100 mm
Modulus of Elasticity(E)= 120 GPa = 120 x 1000 N/mm²
Explanation:
Stress-induced due to the load is applied with impact:

Additional Information
Stress-induced due to the load is applied with impact:

where Length of the bar(l), Cross-sectional Area of the bar(A), Weight of fall on the collar of the bar(P)'
Height from which weight falls(h), Modulus of Elasticity(E)
Case- When Deformation is very small as compared to h, Then

• Momentum is conserved in all collisions.
• In elastic collision, kinetic energy is also conserved.
• In inelastic collision, kinetic energy is not conserved. In a perfectly inelastic collision, objects stick together after the collision.

Perfectly elastic collision:
If the law of conservation of momentum and that of kinetic energy hold good during the collision.

Inelastic collision:
Law of conservation of momentum holds good during a collision while that of kinetic energy is not conserved.
Coefficient of restitution (e)

• For perfectly elastic collision, e = 1
• For inelastic collision, e < 1
• For perfectly inelastic collision, e = 0