Question

2. A 1250 kg car is moving down the highway with a velocity of 32.0 m/s when it bumps into the car ahead of it which has a mass of 875 kg and a velocity of 25.0 m/s. After the collision, the two cars stick together. What will be the resulting velocity of the two cars together? How much energy will be lost in this collision?

Answer 1

Energy lost in the collision = approximately 6.14 x 10^6 Joules.

Step-by-step explanation:

The resulting velocity of the two cars together can be found using the principle of conservation of momentum. The total momentum before the collision is the momentum of the first car plus the momentum of the second car, and this total momentum will be equal to the total momentum after the collision.

Momentum = mass x velocity

Total momentum before collision = (1250 kg x 32.0 m/s) + (875 kg x 25.0 m/s) = 40,000 kg m/s

Total momentum after collision = (1250 kg + 875 kg) x velocity = 2125 kg x velocity = 40,000 kg m/s

Velocity = 40,000 kg m/s / 2125 kg = 18.84 m/s

To find the energy lost in the collision, we can use the equation for the change in kinetic energy (1/2 * m * (vf^2 - vi^2))

Change in kinetic energy = 1/2 * (1250 kg + 875 kg) * (18.84 m/s - (32.0 m/s + 25.0 m/s))^2 = 1/2 * 2125 kg * (-33.16 m/s)^2

= 1/2 * 2125 kg * 1103.69 m^2/s^2

Energy lost in the collision = approximately 6.14 x 10^6 Joules.

Answer 2

The resulting velocity of the two cars together can be calculated using the law of conservation of momentum, which states that the total momentum of the system before the collision is equal to the total momentum after the collision. The momentum of the first car before the collision is 1250 kg * 32 m/s = 40,000 kg m/s and the momentum of the second car before the collision is 875 kg * 25 m/s = 21,875 kg m/s. The total momentum before the collision is 61,875 kg m/s.

After the collision, the two cars stick together, so the final velocity of the two cars together is the same. Therefore, the momentum of the two cars together after the collision is (1250 kg + 875 kg) * v = 2125 kg * v = 61,875 kg m/s. Solving for v, the final velocity of the two cars together is v = 61,875 kg m/s / 2125 kg = 29.2 m/s.

The energy lost in the collision can be calculated using the equation E = 1/2 * m * v^2, where m is the mass of the system and v is the change in velocity. The mass of the system is 2125 kg and the change in velocity is 32 m/s - 29.2 m/s = 2.8 m/s. Therefore, the energy lost in the collision is E = 1/2 * 2125 kg * (2.8 m/s)^2 = 1/2 * 2125 kg * 7.84 m^2/s^2 = 6614.4 J (Joules).