1)The increase in potential energy of any system is equal to the output ___.
I still have no idea.
2) The path that an object follows as it is raised does not affect the ___ of the object.
Could it possibly be "final kinetic energy"?
To answer the first question, the increase in potential energy of any system is equal to the output work done on the system. Potential energy is a measure of the stored energy of an object or a system due to its position or condition. The work done on an object or system is the force applied to it multiplied by the distance it is moved in the direction of the force. So, if you want to calculate the increase in potential energy, you can find the output work done on the system by multiplying the force applied to the object by the distance it is moved in the direction of the force.
To answer the second question, the path that an object follows as it is raised does not affect the gravitational potential energy of the object. Gravitational potential energy is derived from an object's position in a gravitational field and is determined solely by its height above the reference point. It does not depend on the specific path taken to raise the object, as long as the change in height is the same. Therefore, the correct answer could be "gravitational potential energy" or simply "potential energy." Final kinetic energy, on the other hand, refers to the energy associated with an object's motion and is unrelated to the path followed while raising the object.