Question

(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?

Short answer

In this collision,$3.68\times {10}^7\mathrm{J}$ thermal energy is produced.

Step-by-step solution

Given data

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$m=66000\mathrm{k}\mathrm{g}$.

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

$\begin{array}{rl}v& =85\frac{\mathrm{k}\mathrm{m}}{\mathrm{h}}\\ & =23.61\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

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

Calculation of thermal energy

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:

$\begin{array}{rl}\mathrm{\Delta }E& =2\times \frac{1}{2}m{v}^2\\ & =m{v}^2\\ & =\left(66000\mathrm{k}\mathrm{g}\right)\times \left(23.61\frac{\mathrm{m}}{\mathrm{s}}\right)\\ & =3.68\times {10}^7\mathrm{J}\end{array}$

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

Hence,$3.68\times {10}^7\mathrm{J}$ thermal energy is produced in this collision.