A Numerical Scale of Energy

Energy comes in a variety of forms, and physicists didn't discover all of them right away. They had to start somewhere, so they picked one form of energy to use as a standard for creating a numerical energy scale. (In fact the history is complicated, and several different energy units were defined before it was realized that there was a single general energy concept that deserved a single consistent unit of measurement.) One practical approach is to define an energy unit based on heating water. The SI unit of energy is the joule, J, (rhymes with cool), named after the British physicist James Joule. One Joule is the amount of energy required in order to heat 0.24 g of water by 1 °C. The number 0.24 is not worth memorizing.

Note that heat, which is a form of energy, is completely different from temperature, which is not. Twice as much heat energy is required to prepare two cups of coffee as to make one, but two cups of coffee mixed together don't have double the temperature. In other words, the temperature of an object tells us how hot it is, but the heat energy contained in an object also takes into account the object's mass and what it is made of.¹

¹In standard, formal terminology, there is another, finer distinction. The word heat is used only to indicate an amount of energy that is transferred, whereas thermal energy indicates an amount of energy contained in an object. I'm informal on this point, and refer to both as heat, but you should be aware of the distinction.

Later we will encounter other quantities that are conserved in physics, such as momentum and angular momentum, and the method for defining them will be similar to the one we have used for energy: pick some standard form of it, and then measure other forms by comparison with this standard. The flexible and adaptable nature of this procedure is part of what has made conservation laws such a durable basis for the evolution of physics.

Heating a swimming pool.

Irish coffee.

Once a numerical scale of energy has been established for some form of energy such as heat, it can easily be extended to other types of energy. For instance, the energy stored in one gallon of gasoline can be determined by putting some gasoline and some water in an insulated chamber, igniting the gas, and measuring the rise in the water's temperature. (The fact that the apparatus is known as a bomb calorimeter will give you some idea of how dangerous these experiments are if you don't take the right safety precautions.) Here are some examples of other types of energy that can be measured using the same units of joules:

type of energy	example
chemical energy released by burning	About 50 MJ are released by burning a kg of gasoline
energy required to break an object	When a person suffers a spiral fracture of the thighbone (a common type in skiing accidents), about 2 J of energy go into breaking the bone.
energy required to melt a solid substance	7 MJ are required to melt 1 kg of tin
chemical energy released by digesting food	A bowl of Cheeries with milk provides us with about 800 kJ of usable energy
raising a mass against the force of gravity	Lifting 1.0 kg through a height of 1.0 m requires 9.8 J
nuclear energy released in fission	1 kg of uranium oxide fuel consumed by a reactor releases 2 × 1012 J of stored nuclear energy

It is interesting to note the disproportion between the megajoule energies we consume as food and the joule-sized energies we expend in physical activities. If we could perceive the flow of energy around us the way we perceive the flow of water, eating a bowl of cereal would be like swallowing a bathtub's worth of energy, the continual loss of body heat to one's environment would be like an energy-hose left on all day, and lifting a bag of cement would be like flicking it with a few tiny energy-drops. The human body is tremendously inefficient. The calories we burn in heavy exercise are almost all dissipated directly as body heat.

You take the high road and I'll take the low road.

It's impressive to note the complete impossibility of solving this problem using only Newton's laws. Even if the shape of the track had been given mathematically, it would have been a formidable task to compute the balls' final speed based on vector addition of the normal force and gravitational force at each point along the way.

Discussion Questions

A	I'm not making this up. XS Energy Drink has ads that read like this: All the Energy ... Without the Sugar! Only 8 Calories! Comment on this.