Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an 80.0-kg astronaut in orbit moving at 27,500 km/h.
Solution:
The translational kinetic energy of an object of mass m moving at speed v is KE=\frac{1}{2}mv^{2}.
The Kinetic Energy of the Truck
For the truck, we are given the following:
\begin{align*}
m & = 20 000\ \text{kg} \\
v & = 110\ \frac{\text{km}}{\text{hr}} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{hr}}{3600\ \text{s}} = 30.5556\ \text{m}/\text{s}
\end{align*}Substitute these values to compute for the kinetic energy of the truck.
\begin{align*}
KE_{t} & = \frac{1}{2} mv^{2} \\
KE_{t} & = \frac{1}{2} \left( 20 000\ \text{kg} \right) \left( 30.5556\ \text{m}/\text{s} \right)^{2} \\
KE_{t} & = 9 336 446.9136\ \text{J} \\
KE_{t} & = 9.34 \times 10^{6} \ \text{J}
\end{align*}The Kinetic Energy of the Astronaut
For the astronaut, we have the following given values
\begin{align*}
m & = 80\ \text{kg} \\
v & = 27 500\ \frac{\text{km}}{\text{hr}} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{hr}}{3600\ \text{s}} = 7638.8889\ \text{m}/\text{s}
\end{align*}The kinetic energy of the astronaut is calculated as
\begin{align*}
KE_{a} & = \frac{1}{2} mv^{2} \\
KE_{a} & = \frac{1}{2} \left( 80\ \text{kg} \right) \left( 7638.8889\ \text{m}/\text{s} \right)^{2} \\
KE_{a} & = 2 334 104 945 .0617\ \text{J} \\
KE_{a} & = 2.33 \times 10^{9} \ \text{J}
\end{align*}Comparing the Kinetic Energies of the truck and the astronaut
\begin{align*}
\frac{KE_{a}}{KE_{t}} & = \frac{2 334 104 945 .0617\ \text{J}}{9 336 446.9136\ \text{J}} \\
\frac{KE_{a}}{KE_{t}} & = 250 \\
KE_{a} & = 250\ KE_{t} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}The kinetic energy of the astronaut is 250 times larger than the kinetic energy of the truck.
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