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An energy analysis is a simple means of making a prediction of which ball has the greatest speed at the bottom of the incline. The analysis would begin by comparing the total amount of mechanical energy of the two balls. Mechanical energy has two forms - kinetic energy (KE) and potential energy (PE). The kinetic energy depends on mass and speed. Initially, the balls have the same mass and the same speed. The potential energy (PE) depends on mass and height. Initially, the balls have the same mass and the same height. See Dictionary section. You can now make a comparison of the initial amount of mechanical energy of the two balls. Which has the most - A or B? Or are they both the same?
We are told that resistance forces are negligible as the balls roll down the hill. The normal force does not do work on the balls since it acts at right angles to the motion. So the only force doing work is a conservative force - gravity. Since non-conservative forces are not doing work upon the balls; the mechanical energy (ME) of the balls is conserved. The total ME of the balls is the same at the bottom of the hill as it is at the top of the hill. See Know the Law section. You can now make a comparison of the final amount of mechanical energy of the two balls. Which has the most - A or B? Or are they both the same?
Once the balls have reached the bottom of the hill (ground level), the PE is zero. All the mechanical energy possessed by the balls is in the form of KE. Since the two balls have the same ME at the top of the hill, they will also have the same KE at the bottom of the hill. The KE is related to mass and speed. Each ball has the same mass, so the each ball will have the same speed.
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Work - Mechanical Energy Relationships:
If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
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Definition of Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. If an object is moving, then it has kinetic energy. The amount of kinetic energy depends on mass and speed.
Definition of Potential Energy:
Potential energy is the energy stored in an object due to its position. The most common type of potential energy - gravitational potential energy - is the energy stored in an object due to its vertical position relative to the ground or some zero level. The amount of gravitational potential energy depends upon mass and vertical height.
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