Final answer:
Mass and energy are directly proportional as illustrated by Einstein's equation E=mc², and in mechanical systems, total energy is constant but can change form between potential and kinetic energy. Height affects potential energy due to the work done against gravity.
Step-by-step explanation:
The relationship between mass and energy is famously captured in Albert Einstein's equation E = mc², where E stands for energy, m stands for mass, and c is the speed of light. This equation implies that mass can be converted into energy and energy can be converted into mass. Therefore, the amount of energy contained within a system is directly proportional to its mass. Moreover, in terms of gravitational potential energy, the height of an object is directly proportional to the energy because energy increases with height due to the work done against the gravitational field.
In a mechanical system, such as a block attached to a spring, the total energy of the system, which is a combination of potential and kinetic energy, is constant and can be represented by the equation ETotal = (1/2)kA², where ETotal is the total energy, k is the spring constant, and A is the amplitude. The total energy is also proportional to the mass of the block since the kinetic energy component involves the mass.