# Energy

### What is Energy? Energy can take many forms and is always conserved. Potential energy is the energy due to position. Kinetic energy is the energy due to motion. In many systems, potential and kinetic energy are converted to each other.

Energy, a word that is commonly used in everyday language, has a very specific meaning in the physical sciences. At its most basic, work (w) is energy that is transferred when a force acts on an object over a distance. When a person pushes a shopping cart through a store, they are doing work on the cart. Energy is the capacity to do work. Doing work transfers energy. Energy can take many different forms, and these forms can be categorized as either potential energy or kinetic energy.

Potential energy (PE) is the energy of an object based on its position. A familiar example is gravitational potential energy. A 1.0-kg ball held 1.0 m above the ground. has the potential to fall to Earth because of the attractive force of gravity between the ball and Earth. Thus, the ball held aloft has potential energy. The gravitational potential energy (PEgrav) of an object is proportional to its mass (m) and the height (h) between it and any surface that is designated as the zero level of energy. Often, Earth's surface is designated as the level of zero gravitational energy. The greater the distance between the ball and the surface below, the more potential energy the ball has. The potential energy of the ball is therefore the product of its mass, the acceleration due to gravity, g, equal to approximately 9.8 m/s2, and the height above Earth's surface.
\begin{aligned}PE_{\rm{grav}}&=mgh\\&=(1.0\;{\rm{kg})}(9.8\;{\rm{m/s}}^{2})(1.0\;{\rm{m})}\\&=9.8\;{\rm{J}}\end{aligned}
In the equation for gravitational potential energy, the SI unit of energy is a joule (J), which is equal to 1 kg · m2/s2. If the ball is released, it starts to move toward Earth. As it moves closer to Earth, the distance between the ball and Earth is decreased and its potential energy is decreased. Energy can neither be created nor destroyed; the energy in the universe is always conserved. Therefore, if the potential energy of the ball decreases, another form of energy must increase. Kinetic energy (KE) is the energy of an object in motion. The kinetic energy of a falling ball increases as the ball moves toward the ground because its speed is increasing. The amount of kinetic energy in a system is proportional to the square of the velocity (v).
$KE=\frac12mv^{2}$
Recall that a falling object accelerates due to gravity, and the acceleration increases the velocity of the object. Thus, as an object falls, it gains kinetic energy. A ball released from a height, h, will convert potential energy to kinetic energy as it falls toward Earth. At the point of impact, most of the kinetic energy is converted to elastic energy, which causes the ball to bounce back up, but some kinetic energy is converted to thermal energy.
The kinetic energy of the falling ball comes from the potential energy of the ball held aloft. Upon release of the ball, some of the potential energy is converted to kinetic energy. As the ball moves closer and closer to Earth, more and more of the potential energy is converted to kinetic energy. The ball moves faster and faster until the ball eventually hits the ground and stops moving. The force of hitting the ground causes the ball to compress and deform. Some of the kinetic energy is converted to elastic energy (also called elastic potential energy), energy stored as a result of a material's deformation. The elastic energy causes the ball to return to its original spherical shape, which converts the elastic energy back into kinetic energy as the ball bounces back up.

### Work versus Heat Energy transferred over a distance is work; the energy of molecular motion is thermal energy. The transfer of thermal energy is called heat.

Consider a ball that is dropped from a height and bounces on the ground. If 100 percent of the potential energy of the bouncing ball were converted to kinetic energy, then to elastic energy, and then back to kinetic energy, the ball would travel back up to its original starting height and would continue to bounce forever. This does not happen—the ball reaches a lower and lower height each time it bounces, until it eventually stops bouncing altogether. Because the ball reaches a lower height above the surface after each bounce, it has less potential energy at the top of each bounce. Energy is always conserved, so the missing potential energy must instead have been converted into another form of energy, which does not return to kinetic energy upon bouncing. The energy that is missing has been converted to thermal energy.

Thermal energy is the kinetic energy of the particles that make up a system. It is the energy associated with the particle motion, which includes translational motion, the movement of a particle in space, and vibration of the particles. Thermal energy is part of a system's internal energy, which is the sum of all kinetic energy and potential energy of the particles in a system.

A transfer of thermal energy is called heat. As a material absorbs heat, its thermal energy increases, and this causes the material's molecules to vibrate faster. Temperature is a measure of the average kinetic energy of the particles of a substance. An increase in thermal energy means increased molecular motion, which is measured as an increase in the material's temperature. The particles of a substance with increased temperature have a higher kinetic energy.

When a ball strikes the ground, the temperature of the ball and the ground both rise slightly because the molecules near the point of impact absorb some of the ball's kinetic energy and begin to vibrate faster. The energy converted into thermal energy that causes this temperature increase cannot also be converted into elastic energy. The kinetic energy just before impact is equal to the elastic energy at impact plus the increase in thermal energy of the ball and the ground:
${PE_{\rm{initial}}}={KE_{\rm{impact}}}=\rm{elastic\;energy}_{\rm{impact}}+\rm{thermal\;energy}$ Right before impact, the molecules in the ball and the molecules in the ground are vibrating at one speed. At the point of impact, the KE is transferred to elastic energy as the ball deforms, but some KE is transferred to thermal energy, increasing the speed of the molecular vibrations, and therefore the temperature of both the ball and the ground.
The kinetic energy of the ball just before it hits the ground is therefore greater than the elastic energy of the ball at the time of impact, when it is at its most deformed. This means the elastic energy at impact is less than the initial potential energy of the ball, so the ball cannot bounce all the way back to its starting height.