College Physics by Openstax Chapter 7 Problem 10

(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.

Solution:

The translational kinetic energy of an object of mass mm moving at speed vv is KE=12mv2KE=\frac{1}{2}mv^{2}.

Part A. The Velocity of the Elephant to have the same Kinetic Energy as the Sprinter

First, we need to solve for the kinetic energy of the sprinter.

KEsprinter=12(65.0 kg)(10.0 m/s)2KEsprinter=3250 J\begin{align*} KE_{\text{sprinter}} & = \frac{1}{2} \left( 65.0\ \text{kg} \right)\left( 10.0\ \text{m}/\text{s} \right)^{2} \\ KE_{\text{sprinter}} & = 3250\ \text{J} \end{align*}

Then, we need to equate this to the kinetic energy of the elephant with the velocity as the unknown.

KEelephant=KEsprinter12(3000 kg)v2=3250 J1500v2=3250v2=32501500v=32501500v=1.4720 m/sv=1.47 m/s  (Answer)\begin{align*} KE_{\text{elephant}} & = KE_{\text{sprinter}} \\ \frac{1}{2}\left( 3000\ \text{kg} \right) v^{2} & = 3250\ \text{J} \\ 1500 v^{2} & = 3250 \\ v^{2} & = \frac{3250}{1500} \\ v & = \sqrt[]{\frac{3250}{1500}} \\ v & = 1.4720\ \text{m}/\text{s} \\ v & = 1.47\ \text{m}/\text{s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

Part B. How Larger Energies Needed for the Movement of Larger Animals would Relate to Metabolic Rates

If the elephant and the sprinter accelerate to a final velocity of 10.0 m/s, then
the elephant would have a much larger kinetic energy than the sprinter.
Therefore, the elephant clearly has burned more energy and requires a faster
metabolic output to sustain that speed.   (Answer)\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)