Basics


Types of Energy

Because energy, the ability to do work, appears in such a wide variety of physical systems, there are many different kinds of energy. The division of energy into different types is somewhat arbitrary, but will prove convenient to recognize two very broad categories.
Kinetic energy is energy associated with moving objects, while stored or potential energy is energy waiting to be released.

Our intuition tells us that two factors govern the amount of objects' kinetic energy.

First, heavy objects have more energy than light ones: a bowling ball going with 10 meters per second ( a very fast sprint) carries a lot more kinetic energy than a golf ball going at the same velocity. Kinetic energy is proportional to mass: double the mass, double the kinetic energy.
Second, the faster something is moving, the greater the force it is capable of exerting. A high-speed collision causes more damage than a fender bender in a parking lot. It turns out that an object's kinetic energy increases as the square of its velocity. These ideas lead to the equation for kinetic energy.

In words:
Kinetic energy equals the mass of the moving object times the square of that object's velocity, multiplied by the constant 1/2.

In equation form:

Kinetic energy (in joules) = 1/2 * [mass (in kg)] *[velocity (in m/s)]2

In symbols:

E = 1/2 m v2


Example

What is the kinetic energy of a 4 kg bowling ball rolling down a bowling lane at 10 m/s ? Compare this to that of a 250 g base ball traveling 50 m/s. Which object would hurt more if it hit you, i.e. which object has the greater kinetic energy?

Reasoning:
We have to substitute numbers into the equation for kinetic energy

Solution:

For the 4 kg bowling ball traveling at 10 m/s:

kinetic energy (in joules) = 1/2 mass (in kg) * [ velocity (in m/s)]2


= 1/2 * 4 kg * (10 m/s)2

= 1/2 * 4 kg * 100 m2/s2

= 200 kg m2/s2

= 200 J

For the baseball traveling at 50 m/s:

kinetic energy (in joules) = 1/2 mass (in kg) *[velocity (in m/s)]2

= 1/2 250 (g) * [ 50 m/s]2

= 1/2 * 0.25 (kg) * 2500 m2/s2

= 312.5 kg m2/s2 = 312.5 J


Potential Energy

The kind of energy, that could result in the exertion of a force over a distance, but is not doing so, is called Potential Energy. An object that has been lifted above the surface of the earth possesses an amount of gravitational potential energy exactly equal to the total amount of work you would have to do to lift it from the ground for the present position.

In words:
The gravitational potential energy of any object equals its weight (the force of gravity exerted by the object) times its height above the ground.

In equation form:

gravitational potential energy (in joules) = mass (in kg) * g (in m/s2) * height (in m).

where g is the acceleration due to gravity at the earth's surface.

In symbols:

E = m * g * h



Potential Energy:

Stored energy

Work = weight h

= m g h

Drop box : gravity --> acceleration

At floor level : maximum speed

All Potential Energy is converted to

Kinetic Energy (Energy of motion)

Potential Energy : m g h
Kinetic Energy : 1/2 m v2

Conservation of Energy

Total energy of a system is conserved.


During the swing of a pendulum potential energy is converted to kinetic energy and vice versa.
The potential energy is maximum at the maximum swing of the pendulum, the kinetic energy is maximum when the pendulum is at its lowest point.


Temperature





One example of stored energy:

internal energy ==> vibration of molecules

Thermal Energy
  • solids and fluids : vibration of molecules
  • gases: motion of molecules

Temperature is a measure of the internal energy of a substance

Properties of a substance which depends on the temperature:

  • Volume: (in general, the volume increases with increasing temperature)
  • States: solid - fluid - gas
  • Properties of materials: elasticity, electric resistance, speed of sound

How do we measure temperature?
Since we really don't yet know what temperature is, we have to measure the consequences of it. It is empirically known that when many object get hotter, that they expand. This expansion can be used as a measure for the temperature. Here is one type of thermometers:

Mercury (or Alcohol)Thermometer:
The fluid in the reservoir is in thermal contact with the environment. Heat is exchanged until the temperature of the reservoir and the environment is the equal. The level of the fluid is a measure for the temperature.
Problem: Not very precise since the thermal expansion rate depends on the fluid used. It is limited to a smaller range of temperatures.

Temperature Scale:

The pressure measured by the level h in the gas thermometer is determined at the steam point and the ice point of water. The steam point is defined as 1000  Celsius (C) and the ice point is defined as 00  Celsius (C). Temperatures between are determined by measuring the pressure with the gas thermometer and then interpolating linearly between the boiling and the freezing point.
 
 
All lines approach zero pressure at the temperature -2730C. This is the absolute lowest temperature.
All motion is frozen at this temperature. This temperature is chosen as the zero level of the Kelvin scale. The relation between the Kelvin scale T and the Celsius scale Tc therefore reads

Another scale (used mostly in the US) is the Fahrenheit scale. The steam point is defined as 2120F and the ice-point is defined as 320F. Since the difference of 1800F corresponds to 1000C, the conversion between Fahrenheit and Celsius is

 

A more precise fix point as a reference for the temperature is the triple point of water. At this point, water, water vapor and ice coexist. This point is at 0.010C = 273.16K.

SI Defintion of 1 Kelvin:


 
 

Characteristic Temperatures:


 
 
  Large and small Temperatures:(in Kelvin)
 
 




EXAMPLE 1

What is the temperature 15F in Celcius and Kelvin?

EXAMPLE 2

Most European elementary schools cancel classes when the temperature exceeds 30 degrees Celsius. What is this temperature in Fahrenheit?

Watch the Journey to Absolute Zero

Ch. Elster
Aug 26 14:27:03 EDT 2020