work, energy & power

Work, Energy & Power

see also:

Frictional force:

whenever an object moves while in contact with another, frictional forces oppose the relative motion as as result of adhesion of one surface to another & by the interlocking of the irregularities of the rubbing surfaces
friction thus increases work necessary & transforms kinetic energy into heat energy
the force of frictional resistance depends upon the properties of the surfaces & upon the force keeping the surfaces in contact
kinetic friction (sliding frictional forces):
- frictional force is parallel to the surfaces sliding over one another
- frictional force is proportional to the force which is normal (perpendicular) to the surfaces & which presses them together
- frictional force is almost independent of the area of the surface of contact
- frictional force is almost independent of the speed of sliding, provided that the resulting heat does not alter the condition of the surfaces
- frictional force depends on the nature of the surfaces which can be represented by:
  - coefficient of kinetic friction = frictional force / perpendicular force
  - ie. coefficient of kinetic friction = force just sufficient to move the object at constant speed / weight of the object
static friction:
- when there is no relative motion between the two surfaces in contact, the friction is called static friction & can have any value from zero up to the limiting friction value.
limiting friction:
- if a stationary object is pushed, the force required to make it move & thus overcome the static friction equals the limiting friction.
- same laws apply as for kinetic friction, except of course that relating to speed
- coefficient of static (limiting) friction = limiting frictional force / perpendicular force

Work:

although work is the product of 2 vector quantities, force and displacement, it is a scalar quantity
work = average force x displacement (work is newton-meter = Joule)
work is the area under the curve of a force vs displacement graph

Energy:

"that property of a body or system of bodies by virtue of which work can be performed"
energy can exist in many forms & can be transformed from one form to another
types of energy:
- kinetic energy:
  - energy possessed by an object by virtue of its motion
  - work done on a body in accelerating it results in a change in the body's kinetic energy:
    - change in kinetic energy = work done = Fs = mas = m(v₂² - v₁²)/2
  - thus, kinetic energy = (1/2)mv² where m in kg, v in m/sec, and KE in Joules
    - eg. doubling the speed of a car, quadruples the work need to be done by brakes in stopping it, and from the above equations, the stopping distance = -v₁² /2a, where a is the deceleration, and thus stopping distance is proportional to the square of the speed, although in practice, as brake linings heat up, they become less efficient at higher speeds & thus the increase in stopping distance is even greater than this.
- potential energy:
  - energy of position or configuration
  - gravitational potential energy:
    - if an object of weight w is lifted a height h, the increase in potential energy is given by:
      - change in potential energy = weight x height lifted = mgh, where m in kg, g = gravity force, h in meters
    - the potential energy of an object at high altitude with respect to earth is given by:
      - potential energy = G x MassEarth x MassObject x (1/R - 1/r)
        
        G = gravitational constant
        
        R = radius of earth
        
        r = distance of body to centre of earth
      - thus weight vs distance from earth is a hyperbolic function, with it decreasing to ~1/5th by the time an object goes from earth's surface to a distance of 1 earth radius away from the surface and to ~ 1/10th when it gets to 2 earth radius distance from the surface.
  - electrical potential energy:
    - work done in moving a charge from point B to point A, which are at different potentials:
      - work done = q(potential at A - potential at B), potential in volts, charge in coulomb, work done in Joules
    - electrical potential energy = charge x potential
    - the energy gained by an electron in falling through a potential drop of 1 volt = 1 electron volt (eV) = 1.6x10^-19 J
- thermal energy:
  - objects have an internal energy as a result of the oscillations of particles within it
  - heat energy is disordered energy and has two components:
    - energy - enthalpy:
    - measure of disorder - entropy:
      - change in entropy = change in heat / absolute temperature (for a reversible process)
      - change in entropy for an expanding gas = nRln (V₂/V₁), where n = no. mole, R=gas constant, V = volume
      - entropy = Boltzmann's constant x ln(w),
        
        where w = probability that the system exists in the state it is in relative to all possible states it could be in
        
        for a gas, w = (constant x volume)^{N molecules}, thus, entropy = kN(ln c +ln V)
  - 1st law of thermodynamics:
    - when heat is transformed into any other form of energy, or when other forms of energy are transformed into heat, the total energy (heat plus other forms) is constant
  - 2nd law of thermodynamics:
    - it is impossible for an engine unaided by external energy to transfer heat from one body to another at a higher temperature.
  - 3rd law of thermodynamics:
    - it is impossible to reach the temperature of zero degrees Kelvin
  - specific heat of a substance = the heat needed to change the temperature of a unit mass of a substance by one degree
  - molar heat capacity = specific heat of a substance per mole of substance
  - not all heat a substance receives raises its temperature:
    - heat of fusion = heat per unit mass needed to change a substance from solid to liquid state
    - heat of vaporisation = heat per unit mass needed to change a substance from liquid to vapor state
  - heat energy may be transferred from one object to another by either:
    - conduction:
      - rate of heat transfer = thermal conductivity of material x surface area x avg. temperature gradient
    - convection:
      - transfer of heat by convective circulation of liquid or a gas associated with pressure differences, most commonly brought about by local changes in density
      - a rise in temperature is accompanied by a decrease in density in most liquids
      - if the pressure differences are produced mechanically such as with fan, it is said to be forced convection
    - radiation
    - see also heat in climate
the law of conservation of energy:
- when energy is given to a body, the process is a transfer of energy from one body to another, no energy is created or destroyed, it merely changes from one form to another
- however, Einstein correctly predicted that mass and energy is equivalent, and thus in certain nuclear reactions, a particle may receive energy of the order of 10^-12J at the expense of a decrease in mass of the reactants
  - and as mass changes with its velocity, the equation for the kinetic energy of a high speed particle had to be modified:
    - kinetic energy = mc² - m₀c²,

Power:

the time rate of doing work
average power = work performed / time elapsed = force x displacement / time elapsed = force x velocity
1 watt = 1 newton-meter per second = 1 Joule / sec = 10⁷ ergs /sec
1 horsepower = 746 watts

Efficiency:

efficiency of a machine = output work / energy in