Basics of Inelastic Collision

What is inelastic collision?

An inelastic collision is a type of collision which occurs between two objects when some amount of energy is lost. The momentum of the object under inelastic collision is conserved while the kinetic energy is not.

What is the formula used in inelastic collision?

Following is the formula used in inelastic collision:

Total momentum before = Total momentum after

mTvT + mCvC = (mT + mC) vFinal

Examples of inelastic collision

Following are the two everyday examples of inelastic collision:

• Ball bouncing back when hit to a wall or on the ground
• Any vehicle hitting the tree

What is the difference between elastic and inelastic collision?

The difference between elastic and inelastic collision is the loss or conservation of kinetic energy. Following is a table explaining the difference between elastic collision and inelastic collision:

 Elastic collision Inelastic collision When both the momentum as well as the kinetic energy of the system are conserved, it is known as an elastic collision When the momentum of the system is conserved but not the kinetic energy, it is known as an inelastic collision All the forces that are involved during the interaction are of conservative nature All the forces that are involved during the interaction are of non-conservative nature The mechanical energy is not converted into other forms of energy The mechanical energy is converted into other forms of energy either partially or entire energy.

Problem on inelastic collision

Q1. What will be the final velocity of the two vehicles, if a 3000 kg truck moving with 50 km.hr-1 velocity strike a stationary car of 1000 kg? Also, calculate the initial kinetic energy that is lost in the collision.

Ans: The final velocity is calculated using the below formula:

Total momentum before = Total momentum after

mTvT + mCvC = (mT + mC) vFinal

mT = mass of the truck = 3000 kg

mC = mass of the car = 1000 kg

vT = velocity of the truck = 50 km.hr-1

vC = velocity of the car = 0 km.hr-1

vFinal = final velocity of the truck or the car = ?

Substituting all the values in the formula, we get:

[(3000 kg)(50 km.hr-1)] + [(1000 kg)(0 km.hr-1)] = [(3000 kg) + (1000 kg)] vFinal

vFinal = 37.5 km.hr-1

Therefore, the final velocity of both the vehicles is 37.5 km.hr-1

Below is the formula used for calculating the initial kinetic energy that is lost in the collision:

KE before = ½ mTvT2 + ½ mCvC2

= ½ (3000 kg)(50 km.hr-1)2 + ½ (1000 kg)(0 km.hr-1)2

= ½ (3000 kg)(50 km.hr-1)2

KE after = ½ (mT+mC)vFinal2

= ½ (4000 kg)(37.5 km.hr-1)2

By dividing KE after and KE before, we get ¾

Therefore, ¾th of the total kinetic energy of the system remains while ¼th of the energy is lost during the collision.

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