Temperature rise after collision

[savaphysics]

Homework Statement

Determine the fractional decrease in total kinetic energy of each set of asteroids when they collide. If the average specific heat of the material composing the asteroids is assumed to be that of ice (2.05 kJ/kg·˚C), by how much does the temperature of the asteroids rise as a result of the collision in each case?

Homework Equations

Before the collision, asteroid A (mass 1,000 kg) moved at 100 m/s, and asteroid B (mass 2,000 kg) moved at 80 m/s. (asteroid b is going i an opposite direction.)

The Attempt at a Solution

After the collision I have
(1,000 kg)(100m/s) + (2,000 kg)(-80m/s)= -60,000/3,000 =20m/s

We haven't been taught temperature after collision so this is where i am stuck

 

[haruspex]

How much KE was lost? Where has that energy gone?

 

[savaphysics]

There is no KE lost right? Since they collided and there is no external forces.

 

[haruspex]

There is no KE lost right?

In an inelastic collision you should expect work energy to be lost.
You can calculate the KE before and after.

 

[HalfLostAndSearching]

.

I understand that collisions between objects can result in changes in temperature. In this case, the collision between the two asteroids will result in a decrease in total kinetic energy, as some of the energy is converted into other forms such as heat and sound. To determine the fractional decrease in total kinetic energy, we can use the equation:

Fractional decrease in total kinetic energy = (initial total kinetic energy - final total kinetic energy) / initial total kinetic energy

Plugging in the values given in the problem, we get:

Fractional decrease in total kinetic energy = (2,000,000 J - 1,600,000 J) / 2,000,000 J = 0.2 or 20%

Next, we can calculate the change in temperature of the asteroids using the specific heat equation:

Change in temperature = (change in energy) / (mass x specific heat)

For asteroid A, the change in energy is equal to the decrease in kinetic energy (400,000 J). Plugging in the values, we get:

Change in temperature = (400,000 J) / (1,000 kg x 2.05 kJ/kg·˚C) = 0.195 ˚C

Similarly, for asteroid B, the change in temperature is also 0.195 ˚C.

Therefore, the temperature of both asteroids will rise by approximately 0.195 ˚C as a result of the collision. This is a small change and may not significantly affect the overall temperature of the asteroids. However, it is important to consider that this calculation assumes that all of the kinetic energy is converted into heat, which may not be the case in a real-world scenario. Other factors, such as the composition and structure of the asteroids, may also affect the change in temperature. Further analysis and experimentation would be needed to accurately determine the temperature rise after the collision.