Elastic potential energy is the energy stored in a spring. The amplitude of the force required to stretch a spring is given by F = − kx, where x is the distance of the deformation (or compression) of a spring from the unloaded position and k is the spring constant. The spring constant is a measure of spring stiffness, with stiffer springs having larger k-values. The potential energy stored in a spring is given by P. E. = (1/2) kx 2. Photo: The mechanical equivalent of heat: In James Prescott Joule`s famous experiment, a falling weight (1) pulls on a rope that passes over a pulley (2). The rope turns an axis (3) that a paddle turns in a sealed container of water (4). When the paddle turns, the water warms up. Joule proved that the thermal energy obtained by water was exactly the same as the potential energy lost by weight. Potential energy, also known as stored energy, is the ability of a system to perform work based on its position or internal structure. Examples include energy stored in a ram at the top of its path, or energy stored in a coiled spring. Potential energy is measured in joules.

Reasonable conjecture doesn`t quite cut mustard into science. We really need to make sure that the energy we start with in a closed system is the same as the energy we end up with. How do we know? One of the first to experimentally confirm the law of conservation of energy was the English physicist James Prescott Joule (1818-1889), who used an ingenious device to find what he called «the mechanical equivalent of heat.» He used a falling weight to drive a large paddle wheel sealed in a container of water. He calculated the potential energy of weight (the energy it had because of its height above the ground) and argued that when the weight fell, it transferred pretty much all of its energy to the kinetic energy in the paddle wheel. When the paddle wheel turned, it stirred the water in the container and heated it by a small but significant amount. We now know how much energy it takes to heat a certain mass of water by a certain number of degrees, allowing Joule to determine how much energy the water has gained. To his delight, he found that this number corresponded exactly to the energy lost by weight loss. Joule`s brilliant work on energy was recognized when the International Energy Science Unit (the Joule) was named in his honor. Albert Einstein`s famous equation E=mc2 shows that energy and mass are different forms of the same thing. Generally speaking, you can convert a small amount of mass into a large amount of energy (like in a nuclear power plant, where large atoms break, releasing energy in the process). Einstein`s equation shows us that sometimes we have to include mass in the conservation of energy. In a nuclear reaction, we start with one set of atoms (a certain amount of energy in the form of mass) and end with another set of atoms (a different amount of energy trapped in their mass) plus the energy released as heat.

If we take into account the mass of the atoms before and after the reaction, as well as the energy released in the process, we find that the conservation of energy is exactly filled. Since mass is a form of energy, it is clear that we cannot destroy mass or create it out of nothing, just as we cannot create or destroy energy. You will sometimes see that this is called mass conservation. It is also possible to determine the change in the internal energy of the system with the equation: [math]Delta U = W + Q[/math] No! To push the car, you have to work against gravity. Your body needs to use energy to work. Most of the energy your body uses comes from the car when you push it up. The energy your body loses is about the same as the work it does against gravity. And the energy savings of the car are the same as the work done. So no energy is created or destroyed here: you simply convert the energy stored as fuel in your body into potential energy stored by the car (due to its height). In the early 20th century, Einstein discovered that even mass is a form of energy (this is called mass-energy equivalence). The amount of mass is directly related to the amount of energy determined by the most famous formula of physics: in the everyday world, «work» is something you do to make money; In physics, work has a different meaning. When you do useful work with force (push or pull), like moving a car uphill, we say you`re doing work, and it costs energy.

If you push a car uphill, it has more potential energy up the hill than at the bottom. Have you violated energy conservation by generating potential energy out of thin air? According to the definition of work, Newton`s second law of motion and kinematics, W = Fx = max and v f 2 = v o 2 + 2 ax or a = ( v f 2 − v o 2)/2 x. Replace the last expression for acceleration in the expression for the job to get W = m ( v f 2 − v o 2) or W = (1/2) mv f 2 − (1/2) mv o 2. The right side of the last equation gives the definition of kinetic energy: K. E. = (1/2) mv 2 Kinetic energy is a scalar quantity with the same units as labor, joules (J). For example, a mass of 2 kg moving at a speed of 3 m / s has a kinetic energy of 9 J. Fill up a car with gasoline and you have a closed system. All available energy is trapped in chemical form in the gas of your tank. When gas flows into your engine, it burns with oxygen in the air. The chemical energy contained in the gas is first converted into thermal energy: the burning fuel produces expanding hot gas, which pushes the pistons into the cylinders of the engine.

In this way, heat is converted into mechanical energy. The pistons rotate the crankshaft, gears and drive shaft and finally the wheels of the car. When the wheels turn, they accelerate the vehicle along the road, giving it kinetic energy (kinetic energy). If a car were 100% efficient, all the chemical energy originally trapped in gasoline would be converted into kinetic energy. Unfortunately, energy is wasted at every step of this process. A part is lost by friction when the metal parts rub and wear against each other and heat up; Some of the energy is lost in the form of noise (cars can be quite noisy – and sound is energy that must come from somewhere) Not all the energy produced by the car moves you on the road: many things have to push against the air (so they are lost by air resistance or drag), while some are used to power things like headlights, Air conditioning and so on. However, if you measure the energy with which you start (in gasoline) and calculate how much energy you finish and lose along the way (all the useful kinetic energy and the unnecessary energy lost through friction, sound, air resistance, etc.), you will find that the energy count is always balanced: the energy you start with is the energy, with which you finish. There are even simpler and more familiar ways to report energy savings. «No pain, no gain» is a rough everyday equivalent: if you want something, you have to work for it.

«There is no free meal» and «You don`t get anything for free» are other examples. The amount of energy in a system is therefore determined by the following equation: However, energy saving is more than a general rule that persists in its validity. It can be shown that it follows mathematically from the uniformity of time. If one moment of time were particularly different from any other time, identical physical phenomena occurring at different times would require different amounts of energy, so the energy would not be conserved. A «closed system» is a bit like a box sealed around everything we study: no energy can seep into the box from the inside (or be inserted into the box from the outside). Joule builds on the earlier work of the Anglo-American physicist Benjamin Thompson (1753–1814), also known as Earl Rumford. While working in a German artillery factory, Rumford noticed that the guns became hot when pierced. He soon realized that heat was not a magical property of metal (as many people suspected), but came from the mechanical and frictional process of drilling: the more you drilled, the hotter the metal became.