Question

It’s early fall and you are driving along a two-lane highway in a rented moving van. It’s full of all of your possessions so you and the loaded truck weigh 8000 lb. You have just slowed down to 15 mph because you’re in a school zone. It’s a good thing you thought to do that because a group of first graders are just starting to cross the road. Just as you pass the children you see a 2000-lb sports car in the other lane heading straight for the children at about 80 mph. A desperate thought crosses your mind. You just have time to swing into the other lane and speed up a bit before making a head-on collision with the sports car. You want your truck and the sports car to crumple into a heap that sticks together and doesn’t move. Can you save the children or is this just a suicidal act?

A. Prediction: How fast would you have to be going to completely stop the sports car? Explain the reasons for your prediction. (doesn't have to be an exact answer)

B. : What happens when the less massive car is moving much faster than the more massive car? Much slower? At an intermediate speed?

C. Based on your prediction and your observations, what mathematical definition might you use to describe the momentum you would need to stop an oncoming vehicle traveling with a known mass and velocity? Should it depend on the mass, the velocity, or both? Explain your choice.

Answer 1

Let u be the velocity of truck just before collision .

Hence initial momentum of truck = mass Velocity = 8000 u lb-mph

Inital momentum of sports car with respect to the direction of truck = 2000 (-80) = -16000 lb-mph

After collsion if both the vehicles comes to rest, then we have

8000 u - 160000 = 0

from above equation we get u = 20 mph . Hence it is possible for the truck to stop the speedy sports car by moving with speed 20 mph and collide with sports car.

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When less massive car is moving much faster than more massive car and collide, it will transfer momentum of small magnitude and will rebound in opposite direction with reduced momentum and hence with less speed. Momentum of massive car is slightly reduced, hence it will continue to move in same direction but with slightly less speed.

When less massive car is moving much slower than more massive car and collide, massive car will transfer appreciable momentum to small car and small car will rebound in opposite direction with increased momentum and hence with increased speed. Momentum of massive car is reduced, hence it will continue to move in same direction with less speed.

When less massive car is moving with intermediate speed , by controlling the speed of more massive car it is possible to stop the less massive car .

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Mathematical definition :- Conservation of Momentum

Ability to stop the vehicle depends on momentum , hence depends of mass and speed both