Question

Two identical cars with mass m = 1,325 kg are traveling in opposite directions at speeds of 54 m/s. They collide head on. After the collision, both cars recoil and move at 43 m/s, in opposite directions. According to the law of conservation of linear momentum, what type of collision occurred and how much kinetic energy was lost? A) The collision was inelastic and 1.4 × 106 joules of energy were lost. B) The collision was inelastic and 0.7 × 106 J joules of energy were lost. C) The collision was perfectly elastic and 1.4 × 106 joules of energy were lost. D) The collision was perfectly elastic and 0.7 × 106 joules of energy were lost.

Answer 1

The collision was completely inelastic and 1.4 × 10^6 joules of energy were lost.

Step-by-step explanation:

To determine the type of collision that occurred and the amount of kinetic energy lost, we can analyze the conservation of linear momentum.

In this case, the two cars have a head-on collision and stick together afterward. This means that the collision is completely inelastic.

The change in kinetic energy can be calculated by comparing the initial and final kinetic energy. The initial kinetic energy is the sum of the kinetic energies of both cars, and the final kinetic energy is the kinetic energy of the combined cars after the collision.

Using the equation for kinetic energy, we can calculate the change in kinetic energy:

Change in kinetic energy = Initial kinetic energy - Final kinetic energy

Given that the initial and final speeds of the combined cars are 54 m/s and 43 m/s respectively, we can calculate:

Change in kinetic energy = 0.5 * (2 * m * (54^2) + 2 * m * (43^2)) - 0.5 * (2 * m * (43^2))

By substituting the mass value of the cars to be 1325 kg, we find that the change in kinetic energy is 1.4 × 10^6 joules.

Answer 2

In a collision the kinetic energy is sometimes the same before the collision as it is afterwards - such a collision is called an elastic collision. Perfectly elastic collisions are rare - usually some of the kinetic energy is converted to sound or heat. Even a trampolinist colliding with a trampoline bed loses energy as the bed stretches and heats up. A perfectly inelastic collision is one where all the kinetic energy is converted into other forms - a piece of soft putty falling onto the floor is an almost perfectly inelastic collision, the kinetic energy of the moving putty is converted into heat and a little sound as the putty is deformed on impact. Most real collisions are usually somewhere between the two extremes.