Question

In Anchorage, collisions of a vehicle with a moose are so commonthat they are referred to with the abbreviation MVC. Suppose a1050 kg car slides into a stationary 520 kg moose on a very slippery road,with the moose being thrown through the windshield (a common MVCresult).

What percent of the original kinetic energyis lost in the collision to other forms of energy?
_____%

Answer 1

The original kinetic energy is lost in the collision to other forms of energy, such as heat, sound, and deformation of the car and moose is 50 %.

To determine the percentage of kinetic energy lost in the collision, we'll need to calculate the kinetic energy before and after the collision.

Before the collision:

The kinetic energy of an object is given by the formula:

KE = 1/2 * mv^2

where:

KE is the kinetic energy in joules (J)

m is the mass of the object in kilograms (kg)

v is the velocity of the object in meters per second (m/s)

In this case, the car has a mass of 1050 kg and is assumed to be traveling at a speed of v m/s. Therefore, the initial kinetic energy of the car is:

KE_initial = 1/2 * 1050 kg * v^2

After the collision:

Since the moose is initially stationary, it has no kinetic energy before the collision. After the collision, the car and moose are moving together, so their combined kinetic energy is:

KE_final = 1/2 * (1050 kg + 520 kg) * v^2

Calculating the percentage of kinetic energy lost:

The percentage of kinetic energy lost is given by:

KE_lost = (KE_initial - KE_final) / KE_initial * 100%

Substituting the expressions for KE_initial and KE_final, we get:

KE_lost = (1/2 * 1050 kg * v^2 - 1/2 * (1050 kg + 520 kg) * v^2) / (1/2 * 1050 kg * v^2) * 100%

Simplifying the expression, we get:

KE_lost = (530 kg / 1050 kg) * 100% = 50%

Therefore, 50% of the original kinetic energy is lost in the collision to other forms of energy, such as heat, sound, and deformation of the car and moose.