2d: Energy and Power

Energy is the capacity to do work and it is measured in Joules; J = kg m2/s2. Other common units of energy are the Btu (British thermal unit); the calorie (1 cal = 4.18 J); the food calorie (1 kcal = 1000 cal = 4186.8 J); the kilowatt-hour (1 kWh = 3,600,000 J). Notice that the calories listed for food are actually a thousand scientific calories each.

There are many forms of energy (all measured in Joules) and you can convert from one form to another. The capacity of a musical instrument for converting mechanical energy of vibration (a vibrating guitar string for example) into vibrations in the air determines how loud the instrument will sound.

  • Work is one form of energy. Work is defined scientifically as force times the displacement caused by the force; W = Fd. We only count the part of the force that acts in the same direction as the displacement; so a force acting perpendicular to a displacement does not do work. Likewise, if something doesn’t move, no work is done.
  • Kinetic energy is energy of motion. If we do work on a ball (apply a force over a distance) and then release it the ball will have kinetic energy. Kinetic energy is directly proportional to mass (double the mass of an object at the same speed and you have twice as much energy) and directly proportional to velocity squared (double the speed of an object and you have four times as much kinetic energy); KE = 1/2 mv2.
  • Gravitational potential energy is the energy (work) you can get out of an object due to letting it fall. Or if you do work in lifting a mass against the pull of gravity you store up energy that you can get back by letting it fall. Gravitational potential energy is directly proportional to mass and how high it is: GPE = mgh, where g = 9.8 m/s2 is the acceleration of gravity.
  • You can do work on a spring by either stretching it or compressing it a distance x in which case there is stored spring potential energy. The stiffness of a spring is given by a constant, κ, and the energy stored is SPE = 1/2 κ x2.
  • Electromagnetic radiation is energy carried in the form of electromagnetic waves. Examples of electromagnetic waves are light, radio signals, Wi-Fi signals, blue tooth, cell phone signals, x-rays, gamma rays, microwaves, infrared, ultraviolet, etc. The difference between each kind of electromagnetic wave is the size of the wavelength and the energy it carries. Except for visible light, we cannot detect electromagnetic waves. In general we need some electronic device to detect electromagnetic signals. For example a car radio turns electromagnetic waves from the radio station into audible sound waves.
  • chemical reaction occurs when two or more atoms interact by re-arranging where their electrons are located (they may share electrons, donate or borrow electrons, or have other complicated interactions). When this happens energy may be emitted or absorbed in the form of heat and/or electromagnetic waves. A burning candle is an example; the molecules making up the candle are interacting with oxygen and giving off heat (increased random molecular energy) and light (electromagnetic energy). The chemical energy stored in a battery is another example; molecules in the battery can combine in a way to give energy to a flow of electrons in a wire.
  • As Einstein famously showed, there are certain types of changes in the nucleus of some atoms that give off heat. This nuclear energy comes from the atom changing a very small amount of mass directly into energy via E = mc2, where c is the speed of light. In other words, in certain special atoms (called radionuclides) something happens to make the atom either randomly split or give off part of its nucleus. If you could weigh the pieces after the reaction you would find a tiny bit of mass was missing. It is this mass that has been turned into energy via Einstein’s famous equation. This is the energy used in nuclear reactors and also the energy source of the sun.

In the above examples there is only one mass or object involved. But we know all matter is made of atoms and chemically bound combination of atoms called molecules that are too small to see, even in a microscope. In a solid these atoms are not stationary but vibrate around an equilibrium position. For liquids and gasses they move relative to each other as you saw in the pressure simulation. In both cases the average kinetic energy is proportional to something we call temperature. Temperature is not a type of energy but is proportional to energy and is measured in Fahrenheit, Celsius or Kelvin.

In addition to random kinetic energy molecules can bend, vibrate and rotate in both solids, liquids and gasses. If we place an object that has a high temperature (high internal random motion) in contact with an object that has a low temperature (low random internal motion) energy will flow from the high temperature object to the low temperature object (the molecules of each will bump into each other so they eventually have the same average random energy). When this happens we call the energy that moves from the hot object to the cold object heat which is measured in Joules. Notice that heat and temperature are not the same thing. Heat is a flow of energy (measured in Joules) and temperature is a number in Celsius that is proportional to the internal kinetic energy of the molecules making up a substance.

There is one other term, related to energy, which is how fast energy is being used or delivered. The rate at which energy is used or work done is called power and it is measured in Watts and horsepower (1 hp = 746 Watts). In the US we use Watts for electrical power but hp for mechanical power. It would make more sense to either measure light bulbs in hp or cars in Watts so that everything had the same units. Power is directly proportional to the amount of energy delivered and inversely proportional to the time it takes to deliver the energy; P = W/t. So accelerating your car up to a certain speed will require the same amount of energy regardless of whether you do it slowly or rapidly. But in order to accelerate faster (reach the same kinetic energy in a shorter time) you need a motor that is more powerful.

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