A car moving with an initial speed v collides with a second stationary car that is 46.0 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 37.7 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v).

Question

A car moving with an initial speed v collides with a second stationary car that is 46.0 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 37.7 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v).

Is this collision elastic or inelastic?

Answer 1

A car is stationary at a stop sign when it is hit directly from behind by a truck of mass 3000kg which was travelling at a speed of 9 m/s immediately before the collision. The two vehicles lock together and move forward with an initial speed of 6 m/s.

a) what is the mass of the car?
b) If the car had been designed with a crumple zone, explain in correct physics term, why this might reduce the risk of injury to the driver.

Answer 2

To solve this problem, we can use the principles of conservation of momentum and kinetic energy.

Let's assume the mass of the first car is m1 and the mass of the second car is m2. We know that the second car is 46.0% as massive as the first car, so we can express m2 = 0.46m1.

Given:
Initial speed of the first car, v1 initial = v
Final speed of the first car, v1 final = 0.377v

Conservation of momentum states that the total momentum before the collision equals the total momentum after the collision. Mathematically, this can be expressed as:

m1 * v1 initial + m2 * v2 initial = m1 * v1 final + m2 * v2 final

Substituting the known values, we have:

m1 * v + 0.46m1 * 0 = m1 * 0.377v + 0.46m1 * v2 final

Simplifying the equation, we get:

v = 0.377v + 0.46 * v2 final

Now, we can solve for v2 final:

0.623v = 0.46 * v2 final

v2 final = (0.623v) / 0.46

v2 final ≈ 1.355v

Therefore, the final speed of the second car is approximately 1.355 times the initial speed (v).

Now, to determine whether this collision is elastic or inelastic, we need to compare the initial and final kinetic energy.

In an elastic collision, the total kinetic energy before and after the collision remains constant. In an inelastic collision, some kinetic energy is lost and converted into other forms of energy, such as heat or deformation.

In this case, since the final speed of the first car is less than its initial speed, we can conclude that some kinetic energy has been lost. Therefore, the collision is inelastic.