(I) Two railroad cars, each of mass 66,000 kg, are traveling 85 km/h toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

The generated thermal energy in a system is equal to the loss of mechanical energy from the system.

Given data:

The mass of each railroad car is\(m = 66000\;{\rm{kg}}\).

The initial speed of each railroad car is calculated as follows:

\(\begin{aligned}v &= 85\;\frac{{{\rm{km}}}}{{\rm{h}}}\\ &= 23.61\;\frac{{\rm{m}}}{{\rm{s}}}\end{aligned}\)

The final velocity of each railroad is zero as it comes to rest.

The initial kinetic energy of each railroad car is \(\frac{1}{2}m{v^2}\), and final kinetic energy of each railroad car is zero as it comes to rest.

The loss of kinetic energy of the system is calculated as follows:

\(\begin{aligned}\Delta E &= 2 \times \frac{1}{2}m{v^2}\\ &= m{v^2}\\ &= \left( {66000\;{\rm{kg}}} \right) \times \left( {23.61\;\frac{{\rm{m}}}{{\rm{s}}}} \right)\\ &= 3.68 \times {10^7}\;{\rm{J}}\end{aligned}\)

The loss in kinetic energy is equal to the thermal energy produced in the collision.

Hence,\(3.68 \times {10^7}\;{\rm{J}}\) thermal energy is produced in this collision.