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An energy analysis begins by first identifying which types of forces are doing net work upon the object. In the case of the sledder, frictional forces (friction and air resistance) are said to be negligible. The normal force acts perpendicular to the sledder's motion and does not do work upon the sledder. So gravity - a conservative force - is the only force doing work upon the sledder.
Since the work being done on the sledder is being done by a conservative force, the total mechanical energy will be conserved. See Know the Law section. The amount of total energy - KE plus PE - at the beginning of the motion will be the same amount at every location along the path of the sledder.
The goal will be to determine the amount of energy at one of the locations so that the energy at all locations can be determined. The obvious starting point is location A since the height and speed is known for this location. Once the KE and PE of the sledder are determined for location A (see Formula Frenzy section), the total amount of energy will be known. The height at locations B can be used to determine the PE at this location. The KE simply makes up the difference between the total energy and the PE. And of course at location C, there is no potential energy since the projectile is at ground level (or a pico-meter above); all the energy is in the form of KE. Location D is the final resting position, so the KE is 0 J at this location and the energy is in the form of PE. The height at location D can be calculated using the potential energy formula.
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Energy Conservation:
If the only forces doing net work upon an object are conservative forces (such as gravity and spring forces), then the mechanical energy of the object will be conserved. The energy may change from one form to another - potential to kinetic or vice versa; but the total amount of the two forms together will be unchanging.
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The amount of kinetic energy (KE) possessed by an object depends upon its mass (m) and its velocity (v). The formula is
KE = 0.5 • m • v2
The amount of potential energy (PE) possessed by an object depends upon its mass (m) and its height (h). The formula is
PE = m • g • h
where g is the gravitational field strength (9.8 N/kg on Earth).
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