The illustrations show two ways of providing impulse to change the momentum of a vehicle. In the top illustration, the vehicle collides with a massive concrete barrier. In the bottom illustration, the vehicle collides with water-filled barrels.
*two illustrations are shown one above the other. The top illustration shows a car with a crash test dummy behind the wheel being driven into a cement barrier. The bottom illustration shows a car with a crash test dummy behind the wheel being driven into barrels containing water.*
Explain which type of crash barrier would likely produce less damage to the vehicle and less injury to the occupants.
let us start by writing the second law of physics:
`F = m*a`
and recall that the average acceleration is defines as the change in speed per time unit
`a = (Delta(v))/(Delta(t))`
If one combines the two of them, one gets
`F = (m*Delta(v))/(Delta(t)) = (Delta(m*v))/(Delta(t)) = (Delta(P))/(Delta(t))`
which is named the law of momentum change: The average change of linear momentum (particle impulse) per unit time is equal to the applied force.
Now back to our figures. The variation of momentum is the same in both cases since the car is approaching to the obstacle with the same speed `v` and it comes to a stop (`v_(f) =0` and `V_(i) =v` ).
`Delta(P_1)=Delta(P_2) = 0 - m*v =-m*v`
What is different in the two figures is the time of contact. For the first case (car crushing into the concrete barrier) the time of collision is very small. In contrast, for the second case (car crushing into water barrels) the time of contact is longer than in the first case.
`Delta(t1) < Delta(t2) rArr F_1 > F_2`
Therefore, as explained above, in the first case the impact force is greater than in the second case and the damage to the car (and injury to the occupants) will be greater.