Inelastic Collision Example Problem – Physics Homework Help

A collision is considered an inelastic collision when kinetic energy is lost during the collision. This inelastic collision example problem will show how to find the final velocity of a system and the amount of energy lost from the collision.

Inelastic Collision Example Problem

Question: A 3000 kg truck travelling at 50 km/hr strikes a stationary 1000 kg car, locking the two vehicles together.
A) What is the final velocity of the two vehicles?
B) How much of the initial kinetic energy is lost to the collision?

Inelastic Collision Example Problem Illustration

Before and after of an inelastic collision.


Part A: To find the final velocity, remember momentum is conserved before and after the collision.

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
vC = velocity of the car = 0 km/hr
vFinal = final velocity of the combined truck and car = ?

Plug these values into the equation

(3000 kg)(50 km/hr) + (1000 kg)(0 km/hr) = (3000 kg + 1000 kg)vFinal

Solve for vFinal

150,000 kg⋅km/hr + 0 kg⋅km/hr = (4000 kg)vFinal

150,000 kg⋅km/hr = (4000 kg)vFinal

vFinal = 150,000 kg⋅km/hr/(4000 kg)

vFinal = 37.5 km/hr

The final velocity of the combined truck-car mass continues on at 37.5 km/hr.

Part B: To find the amount of kinetic energy lost in the collision, we need to find the kinetic energy just before the collision and after the collision.

Kinetic energy before = ½mTvT2 + ½mCvC2

KE before = ½(3000 kg)(50 km/hr)2 + ½(1000 kg)(0 km/hr)2

KE before = ½(3000 kg)(50 km/hr)2

Let’s leave it at that for right now. Next, we need to find the final kinetic energy.

Kinetic energy after = ½(mT + mC)vFinal2

KE after = ½(4000 kg)(37.5 km/hr)2

Divide KE after by KE before to find the ratio between the values.

Ratio between kinetic energy before and after an inelastic collision

Working this out, we get

KEafter/KE before = 3/4

3/4 of the total kinetic energy of the system remains after the collision. This means 1/4 of the energy is lost to the collision.

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