Elon Musk goes cycling on the moon, where there is no air resistance. He
finds a hill which has a nice smooth slope on one side, and a cliff on the
other. If he jumps off the cliff his speed is greater that when he rides to the
bottom of the slope, even though the starting height, and therefore potential
energy is the same. His cycle has no friction. What is the explanation?
The conversion of potential energy is more efficient if the resulting
kinetic energy is along the same vector as the force due to gravity.
The distance travelled down the slope is greater, so it takes longer, so
the final speed is slower.
The gas in his space suit applies friction even though the cycle has
none.
The wheels of the bicycle acquire kinetic energy when he rides
down the cliff.
Elon Musk achieves greater speed jumping off the cliff because the bicycle’s wheels gain rotational kinetic energy when rolling down the slope, reducing translational speed at the bottom. In free fall off the cliff, all potential energy converts directly to the cyclist’s translational kinetic energy without wheel rotation. This classic physics scenario highlights energy partitioning in rolling versus sliding motion on the airless moon.
Correct Explanation
When riding down the smooth slope, gravitational potential energy \( mgh \) converts to both translational kinetic energy \( \frac{1}{2}mv^2 \) of the bike-rider system and rotational kinetic energy \( \frac{1}{2}I\omega^2 \) in the spinning wheels, where \( I \) is the moment of inertia and \( \omega \) is angular velocity. For a typical bike, wheels store about 5-10% of total kinetic energy as rotation, leaving less for forward speed. Jumping off the cliff eliminates rolling, so \( v = \sqrt{2gh} \) purely from translation, yielding higher speed.
Option Analysis
- Vector alignment inefficiency: Incorrect—energy conservation depends on total kinetic forms, not gravity vector matching; work done equals height drop regardless of path in frictionless vacuum.
- Longer distance slows speed: Wrong—final speed from conservation of energy is path-independent (\( v = \sqrt{2gh} \) for pure translation); time differs, but speed does not without dissipation.
- Spacesuit gas friction: False—the problem states no air resistance and cycle has no friction; suit gas provides pressure, not drag in vacuum.
- Wheels gain energy only on cliff: Incorrect—this reverses the truth; wheels rotate down slope (gaining rotational KE), not cliff (pure fall, no rolling contact).
