Question

A van of mass 1500 kg travelling at a speed of 54 km h⁻¹ is stopped in 10 s. Assuming that all the mechanical energy lost appears as thermal energy in the brake mechanism, find the average rate of production of thermal energy is cal s⁻¹.

Answer 1

Given:
Mass of van, m = 1500 kg
Speed of van, v = 54 km/h
$=54\times \left(\frac{5}{18}\right)=15\mathrm{m}/\mathrm{s}$

Total kinetic energy of the van is given by
$K=\frac{1}{2}m{v}^2$
$$\begin{gathered} K=\frac{1}{2}\times 1500\times {\left(15\right)}^2 \\ K=750\times 225 \\ K=168750\mathrm{J} \\ K=\frac{168750}{4.2} \\ K=40178.57\mathrm{cal} \end{gathered}$$

Loss in total energy of the van = 40178 cal
Loss in energy per second $=\frac{40178}{10}=4017.8$
$\approx$ 4000 cal./sec

∴ Average rate of production of thermal energy ≈ 4000 cal/sec