**Work, Energy & Power**

- 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

- 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

- "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(v**_{2}^{2}- v_{1}^{2})/2

- thus,
**kinetic energy = (1/2)mv**where m in kg, v in m/sec, and KE in Joules^{2}- 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 = -v
_{1}^{2}/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.

- 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 = -v

**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.

- if an object of weight w is lifted a height h, the increase in
potential energy is given by:
**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

- work done in moving a charge from point B to point A, which
are at different potentials:

**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 (V
_{2}/V_{1}), 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

- conduction:

**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
^{-12}J 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 = mc**,^{2}- m_{0}c^{2}

- and as mass changes with its velocity, the equation for the
kinetic energy of a high speed particle had to be modified:

- 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 = 10
^{7}ergs /sec - 1 horsepower = 746 watts

- efficiency of a machine = output work / energy in