Work, Energy & Power

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
• 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,
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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