Question

An 8000 kg car moving at a constant speed of 14m/s strikes a barrier. The two stick together and move for a while at a speed of 5m/s. What is the mass of the barrier?Show Your Solution

Answer 1

Conservation of momentum: the combined momentum of the car and the barrier before the collision must be the same of that after the barrier.

Let's first calculate the momentum before.

`momentum=mv`

m: mass in kg; v: velocity in m/s

Initially, the two objects are separate, so we must calculate the initial momentum of both separately.

`initialCarMomentum=mv=8000*14=112000kg(m)/(s)`
`initialBarrierMomentum=0`

(since v = 0)

Therefore, combined momentum is 112000 kgm/s.

After the collision, the momentum must be the same, but both objects are moving at the same speed since they are stuck together. Therefore, we can combine their masses.

`112000=(combinedMass)(combinedVelocity)`

combinedVelocity = 5 m/s, we can solve for combinedMass by simply dividing both sides by 5.

112000/5 = 22400 = combinedMass

The combined mass is equal to the car mass plus the barrier mass. We can therefore solve for the barrier mass.

`22400kg=8000kg+barrierMass`

barrierMass = 22400 - 8000 = 14400 kg

The barrier's mass is 14400 kg.