AP Physics 1 Exam Question:

A 500 kg car is traveling east with a velocity of 25 m/s. It collides head-on with a 300 kg car traveling west with a velocity of 20 m/s. The two cars stick together after the collision.

a) Calculate the final velocity of the two cars immediately after the collision.

b) Is linear momentum conserved in this collision? Explain your answer.

Answer:

a) To calculate the final velocity of the two cars after the collision, we will use the principle of conservation of linear momentum.

The principle of conservation of linear momentum states that the total momentum of a system of objects remains constant if no external forces are acting on the system. In this case, since the collision occurs only between the two cars and no external forces are mentioned, we can assume that momentum is conserved.

The initial momentum of the system is given by the sum of the individual momenta of the two cars before the collision, and the final momentum of the system is given by the sum of their momenta after the collision.

Since the cars are moving in opposite directions, we will consider one direction as positive and the other as negative. Let's take east as the positive direction.

The initial momentum of the system is calculated as:

Initial momentum = (mass of car 1 * velocity of car 1) + (mass of car 2 * velocity of car 2)
                 = (500 kg * 25 m/s) + (300 kg * -20 m/s)
                 = 12500 kgm/s - 6000 kgm/s
                 = 6500 kgm/s (in the positive direction)

Since the two cars stick together after the collision, their masses are combined, and we can consider them as a single object with a combined mass.

Combined mass = mass of car 1 + mass of car 2
              = 500 kg + 300 kg
              = 800 kg

To find the final velocity, we can use the equation:

Final momentum = Combined mass * Final velocity

Solving for final velocity:

Final velocity = Final momentum / Combined mass

Since momentum is conserved, the final momentum is equal to the initial momentum:

Final velocity = Initial momentum / Combined mass
               = 6500 kgm/s / 800 kg
               = 8.125 m/s

Therefore, the final velocity of the two cars immediately after the collision is 8.125 m/s in the positive (east) direction.

b) Yes, linear momentum is conserved in this collision. We can see this by comparing the initial momentum (6500 kgm/s) with the final momentum (6500 kgm/s). Since the momentum before the collision is equal to the momentum after the collision, we can conclude that momentum is conserved. This is in accordance with the principle of conservation of linear momentum.