2 energy questions to fill in the blank:

1) The path that an object follows as it is raised does not affect the _____ of the object.

2) The increase in potential energy of any system is equal to the output _____.

1) The path that an object follows as it is raised does not affect the **potential energy** of the object.

To understand why the path does not affect the potential energy, we need to consider the concept of work. The potential energy of an object is determined by its position relative to other objects in a gravitational field. It represents the stored energy that can be converted into other forms of energy when the object falls or is released.

When an object is raised, work is done against gravity to increase its potential energy. The work done is equal to the force applied on the object multiplied by the distance it is raised. The force is the weight of the object, which is equal to the mass of the object multiplied by the acceleration due to gravity.

Regardless of the path taken to raise the object, the force and the distance moved vertically against gravity determine the work done and hence the increase in potential energy. As long as the vertical distance is the same for two different paths, the potential energy gained will be the same. Therefore, the path does not affect the potential energy of the object.

2) The increase in potential energy of any system is equal to the output **work**.

Potential energy and work are intrinsically connected. When work is done on a system, it results in a change in its potential energy. In the case of raising an object, work is done against gravity, increasing the object's potential energy.

The relationship between the work done and the change in potential energy is described by the work-energy theorem. According to this theorem, the work done on an object is equal to the change in its kinetic energy plus the change in its potential energy.

In this case, since the object is being raised against gravity, the change in kinetic energy can be assumed to be negligible. Therefore, the work done is equal to the change in potential energy.

Hence, the increase in potential energy of any system is equal to the output work done on that system.