Final answer:
To increase gravitational potential energy, the height of an object in a gravitational field must be increased, using the formula PEg = mgh. Work must be done against gravity, which can be then stored as potential energy, and later converted back into kinetic energy. An external force, like a child jumping, can add mechanical energy to a system, resulting in increased potential energy.
Step-by-step explanation:
To increase gravitational potential energy, an object must be lifted to a higher position within a gravitational field, such as that of Earth. Gravitational potential energy (PEg) is calculated using the formula PEg = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. By increasing the height (h), you are doing work against gravity, and thus increasing the gravitational potential energy of the object-Earth system. To double an object's impact speed, you would need to quadruple the height from which it is dropped, as kinetic energy is proportional to the square of the velocity. Work done to lift an object becomes stored as gravitational potential energy, which can be converted back into other forms of energy, like kinetic energy, when the object is released.
When an external force, such as a child pushing off a bed with their legs, does positive work on the system, it adds energy to the system, allowing the child to achieve higher gravitational potential energy with each bounce. This demonstrates that a non-conservative force can increase the mechanical energy of a system. The change in gravitational potential energy is indeed significant in a situation with a box compressing a spring vertically, as it is part of the energy transformations taking place in the system.