Taking into account the definition of kinetic, potencial and mechanical energy, the correct answer is option B: the gravitational potential energy of the system increases from 2 J to 66 J.
<h3>Kinetic energy</h3>
Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and at rest, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its state of rest by applying a force.
<h3>Potential energy</h3>
On the other hand, potential energy is the energy that measures the ability of a system to perform work based on its position. In other words, this is the energy that a body has at a certain height above the ground.
Gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object to some reference point, the mass, and the force of gravity.
<h3>Mechanical energy</h3>
Finally, mechanical energy is that which a body or a system obtains as a result of the speed of its movement or its specific position, and which is capable of producing mechanical work. Then:
Potential energy + kinetic energy = total mechanical energy
The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces acting on it are conservative (a force is conservative when the work it does on a body depends only on the initial and final points and not the path taken to get from one to the other.)
Therefore, if the potential energy decreases, the kinetic energy will increase. In the same way, if the kinetics decreases, the potential energy will increase.
<h3>Gravitational potential energy of the system in this case</h3>
The principle of conservation of mechanical energy can be applied in this case.
A model train running on an inclined track is part of a closed system that has 316 J of mechanical energy.
The kinetic energy of the train is 314 J at the beginning.
Replacing in the definition of mechanical energy:
Potential energy + 314 J = 316 J
and solving you get:
Potential energy = 316 J - 314 J
<u><em>Potential energy= 2 J</em></u>
Then, the potential energy of the train is 2 J at the beginning.
The kinetic energy of the train is 250 J at the end.
Replacing in the definition of mechanical energy:
Potential energy + 250 J = 316 J
and solving you get:
Potential energy = 316 J - 250 J
<u><em>Potential energy= 66 J</em></u>
Then, the potential energy of the train is 66 J at the end.
Finally, the correct answer is option B: the gravitational potential energy of the system increases from 2 J to 66 J.
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