Work, Energy and Energy and Notes Power - Work, Energy

Work, Power, and Measurement

Work is defined as the displacement produced by a force. Scientifically, work is done only when an applied force makes a body move. The amount of work is the product of the magnitude of the force and the displacement in the direction of that force, expressed as $W = F \times S \cos(\theta)$. Work is a scalar quantity and its S.I. unit is the joule ($J$), defined as the work done by a force of $1\,newton$ displacing a body through $1\,metre$. In the C.G.S. system, the unit is the erg, where $1\,J = 10^7\,erg$. Work is zero if there is no displacement ($S = 0$) or if the displacement is normal to the direction of force ($\theta = 90^\circ$).

Power ($P$) is the rate of doing work, calculated as $P = \frac{W}{t}$. It can also be measured as the product of force and average speed ($P = F \times v$). The S.I. unit for power is the watt ($W$). Other units include the kilowatt ($1\,kW = 10^3\,W$), megawatt ($1\,MW = 10^6\,W$), gigawatt ($1\,GW = 10^9\,W$), and horse power ($1\,HP = 746\,W$). Unlike work, power depends on the time taken to complete the task.

Energy, Units, and Equations

Energy is the capacity to do work and is a scalar quantity measured in joules. Mechanical energy consists of Potential Energy ($U$) and Kinetic Energy ($K$). Gravitational Potential Energy ($P.E.$) is the work done in lifting a body against gravity: $U = mgh$. Elastic Potential Energy is stored due to a change in shape or configuration. Kinetic Energy ($K.E.$) is the energy of a body in motion: $K = \frac{1}{2}mv^2$. The Work-Energy Theorem states that the work done on a body is equal to the increase in its kinetic energy ($W = \Delta K$). Momentum ($p$) and kinetic energy are related by $p = \sqrt{2mK}$ or $K = \frac{p^2}{2m}$.

Various units are used for specific energy forms: the calorie for heat ($1\,calorie = 4.18\,J$), the kilowatt hour ($1\,kWh = 3.6 \times 10^6\,J$) for electrical energy, and the electron volt ($1\,eV = 1.6 \times 10^{-19}\,J$) for atomic particles. Kinetic energy manifests in translational, rotational, or vibrational forms depending on the type of motion.

Conservation and Transformation of Energy

The principle of conservation of energy states that energy can neither be created nor destroyed; it only changes from one form to another. In a closed system without friction, the total mechanical energy ($K + U$) remains constant. This is verified for a freely falling body where potential energy decreases and kinetic energy increases proportionally during the fall. For a simple pendulum, energy oscillates between potential at the extreme positions and kinetic at the mean position. Einstein's mass-energy relation ($E = mc^2$) describes the conversion of mass into nuclear energy. Energy degradation or dissipation refers to the conversion of useful energy into non-useful forms like heat due to friction.

Questions & Discussion

The transcript contains several conceptual questions and numerical problems. Question: When is work said to be done by a force? Answer: It is done only when the force causes a displacement. Discussion: Does a coolie carrying a load on horizontal ground do work against gravity? Answer: No, because the displacement is normal to the force of gravity ($\theta = 90^\circ$). A specific numerical example calculates the power of a heart beating 72 times in one minute doing $1\,J$ per beat, yielding a power of $1.2\,W$. Another problem shows that if a car's speed is halved, its kinetic energy becomes one-fourth. The difference between work done in pulling a block up a slope ($600\,J$) and its potential energy gain ($450\,J$) is accounted for by the work done against friction ($150\,J$).