Question

What type of impact will cause the metal in the car to “splash” (eliminating all hope of a simple conservation of momentum calculation) should the New Horizons interplanetary space probe hit your car?

Answer 1

To solve this problem one must be aware of the law of conservation of momentum. The law of conservation of momentum states that for an isolated system its momentum is always conserved unless an external force is applied on the system. So the law of conservation of momentum does not hold good if an external force comes into action.

Complete answer:
Let us first understand what the question is all about. Let us assume that your car is parked somewhere and the New Horizons interplanetary space probe somehow hits the car, which causes the car body to burst into small pieces. Now we have to explain what kind of impact will cause such an effect on your car.

As discussed earlier the law of conservation of momentum does not hold good if an external force acts on the body. As assumed earlier that our car is parked which means it is at rest. The space probe hits the car and there is no other force acting on them, in such a condition the momentum will be conserved. So when the probe hits the car it transfers all of its momenta to the car and comes to a rest breaking the car into pieces.

Now if m is the mass of the probe and v is the velocity with which it struck the car then, the initial momentum (or momentum before the collision) will be mv. As we know that there is no external force acting on the system so the total momentum will be conserved. Therefore, the combined momentum of all the pieces of the car (momentum after the collision) will also have a value equal to mv. However, the kinetic energy of the probe $m{v^2}/2$ will not be conserved.

Note: The law of conservation of momentum was a work of Issac Newton. The basis of the law of conservation of momentum is Newton’s third law of motion which states that for every action there is an equal and opposite reaction. For example, while jumping your legs exert a certain amount of force on the ground and the ground also exerts an equal amount of force on your legs, propelling you into the air.