Final answer:
The bicycle's gravitational potential energy does not change as its speed increases on a level surface, because potential energy is determined by height, not horizontal speed. Conservation of energy dictates that the roller coaster example reaches the same final speed when descending the same height, upholding the principle KEi + PEi = KEf + PEf. The standard approximation for g, the acceleration due to gravity, is 10 m/s².
Step-by-step explanation:
As the speed of a bicycle increases from 2 meters per second to 4 meters per second along a level-horizontal surface, the magnitude of the bicycle's gravitational potential energy remains unchanged. This is because gravitational potential energy is solely dependent on the vertical position relative to a reference level, typically the Earth's surface, and not on horizontal motion. Given that the bicycle remains on a level-horizontal surface, there is no change in altitude, and hence no change in gravitational potential energy.
Conservation of Energy
In physics, the conservation of energy principle states that the total energy in an isolated system remains constant. For instance, in the roller coaster example where it starts with an initial speed downhill or uphill, energy conservation implies that it will end up with the same final speed if it descends the same vertical distance because the sum of its potential and kinetic energies will be the same at the start and end points, barring any energy losses. In more technical terms, the initial kinetic energy plus the initial gravitational potential energy equals the final kinetic energy plus the final gravitational potential energy, expressed as KEi + PEi = KEf + PEf.
When applying gravitational potential energy equations, such as PE = mgh (where m is mass, g is the acceleration due to gravity, and h is the height), one commonly uses the approximation g ≈ 10 m/s² for calculations on Earth's surface, as it simplifies numerical computations.