Question

Two 1.0 metric ton cars crash into each other. Both collide head-on, and each was travelling 27 mi/hr when the collision occurred. The wreckage is at rest after the collision. How much thermal energy was gained by the cars and road in the collision? (in case you are worried, these were driverless vehicles with no passengers inside!

Recall that a 100 W lightbulb uses up 100 Joules of energy in 1 second. If there was a way that the thermal energy from the accident described above could be completely captured and used to power such a bulb, how long would it stay lit?

Answer 1

In the situation above, each car has kinetic energy K.E directly before the collision. At the end of the collision, both cars are at rest, and the total kinetic energy of the system is 0.

Since these are inelastic collisions, the kinetic energy is not conserved, but total energy is always conserved, so the kinetic energy "lost" in the collision has to convert into some other form, such as heat, sound, etc.

In case of  two cars moving in head on collision, so the total energy released during the collision is 2K.E

Therefore K.E=(1/2)mv²

Here m=1metric ton=1000kg, v=27mi/hr=12m/s

Therefore thermal energy release during collision is

H=2×(1/2)×1000×(12)²=144000J=144kJ

Now in second problem light bulb is of power p= 100w, consuming 100j of energy for 1 sec can glow by the above thermal enegy upto

As we know E=p×t................(1)

So the energy by above accident is 144kJ, power of bulb 100w we calculate time by placing all these in( 1)

Si 144000=100×t

t=1440sec=24min

So the bulb can glow upto 1440 sec or 24min.