1.0 Work: The Physics Definition
In everyday language, "work" might mean studying or sitting at a desk. However, in Physics, Work has a very specific meaning. Work is said to be done only when a force applied on a body produces displacement in the direction of the force.
Concept of Work
Work is a scalar quantity. The amount of work done depends on two factors:
- The magnitude of the Force applied ($F$).
- The Displacement of the body ($s$) in the direction of the force.
S.I. Unit: Joule ($J$)
C.G.S. Unit: Erg ($1\,J = 10^7\,erg$)
Work Formula
$$W = F \times s$$
Where: $W$ = Work Done, $F$ = Force, $s$ = Displacement.
1.1 Conditions for Zero Work
According to the formula, no work is done ($W = 0$) in the following cases:
- No Displacement: If you push a stationary wall, you apply force, but since $s = 0$, the work done is zero.
- Perpendicular Force: If the force is acting at $90^\circ$ to the direction of motion (e.g., a coolie carrying a load on his head while walking on a horizontal platform).
Numerical problems often give force in kgf (kilogram-force). Always convert it to Newtons before calculating work.
$$1\,kgf \approx 10\,N$$ (or $9.8\,N$ if specified in the question).
A boy exerts a force of 25 N to push a box through a distance of 4 metres. Calculate the work done by the boy.
Solution:
1. Given Force ($F$): $25\,N$
2. Given Displacement ($s$): $4\,m$
3. Formula: $W = F \times s$
4. Calculation: $W = 25 \times 4 = 100\,J$
Final Answer: The work done is $100\,Joules$.
The unit Joule is named after the English physicist James Prescott Joule, who discovered the relationship between mechanical work and heat energy!
2.0 Energy: The Capacity to do Work
In Physics, Energy is the ability or capacity of a body to do work. A body that does work loses energy, and the body on which work is done gains energy. Therefore, the units of energy are the same as those of work (Joules).
2.1 Mechanical Energy
Mechanical energy is the most common form of energy associated with the motion or position of an object. It exists in two main forms: Potential Energy and Kinetic Energy.
1. Potential Energy (P.E.)
The energy possessed by a body by virtue of its position or state of configuration.
- Gravitational P.E.: Energy due to height (e.g., water stored in a dam).
- Elastic P.E.: Energy due to deformation (e.g., a compressed spring or a stretched bow).
Gravitational Potential Energy Formula
$$U = m \times g \times h$$
Where: $m$ = mass, $g$ = acceleration due to gravity ($9.8\,m/s^2$), $h$ = height.
2. Kinetic Energy (K.E.)
The energy possessed by a body by virtue of its state of motion. Every moving object, from a speeding bullet to a flowing river, possesses K.E.
Kinetic Energy Formula
$$K = \frac{1}{2} m v^2$$
Where: $m$ = mass of the body, $v$ = velocity of the body.
Note that in the K.E. formula, velocity is squared ($v^2$). This means if you double the speed of a car, its kinetic energy doesn't just double—it becomes four times greater! This is why high-speed crashes are so much more destructive.
A ball of mass 0.5 kg is kicked so that it moves with a velocity of 4 m/s. Calculate its Kinetic Energy.
Solution:
1. Given Mass ($m$): $0.5\,kg$
2. Given Velocity ($v$): $4\,m/s$
3. Formula: $K = \frac{1}{2} m v^2$
4. Calculation: $K = 0.5 \times 0.5 \times (4)^2$
$K = 0.25 \times 16 = 4\,J$
Final Answer: The Kinetic Energy is $4\,Joules$.
The total energy in the universe is constant. Energy cannot be created or destroyed; it only changes from one form to another. This is known as the Law of Conservation of Energy.
3.0 Different Forms of Energy
Energy exists in various forms in nature. According to the Law of Conservation of Energy, energy can be transformed from one form to another, but the total energy of an isolated system remains constant. Here are the primary forms of energy we encounter:
Key Energy Forms
- Chemical Energy: Stored in the bonds of chemical compounds (e.g., food, fuels like coal and petroleum).
- Heat (Thermal) Energy: Energy possessed by a body due to the random motion of its molecules.
- Light Energy: A form of electromagnetic radiation that allows us to see.
- Electrical Energy: Energy produced by the movement of electrons through a conductor.
- Sound Energy: Energy produced when an object vibrates and travels through a medium as a wave.
- Nuclear Energy: Energy stored in the nucleus of an atom, released during fission or fusion.
3.1 Energy Interconversion
Devices that convert energy from one form to another are called transducers. Understanding these conversions is vital for modern technology:
| Device | Energy Transformation |
|---|---|
| Electric Bulb | Electrical $\rightarrow$ Light and Heat |
| Solar Cell | Light $\rightarrow$ Electrical |
| Electric Motor | Electrical $\rightarrow$ Mechanical |
| Photosynthesis | Light $\rightarrow$ Chemical |
Einstein's Mass-Energy Relation
$$E = m c^2$$
This formula explains how a small amount of mass ($m$) can be converted into a massive amount of nuclear energy ($E$).
During energy conversion, some energy is always converted into non-useful forms (usually heat due to friction). This is not "lost" in the universe, but it is no longer available to do useful work. We call this the Degradation of Energy.
Trace the energy changes that occur when a person rings an electric bell.
Solution:
1. Chemical Energy (stored in the person's muscles) is converted to Mechanical Energy to press the switch.
2. Once the circuit is closed, Electrical Energy flows through the wires.
3. The electromagnet converts Electrical Energy into Magnetic Energy.
4. The movement of the hammer converts this into Mechanical (Kinetic) Energy.
5. Upon striking the gong, it is finally converted into Sound Energy.
The Sun is the ultimate source of almost all energy on Earth. Fossil fuels, wind energy, and even the food you eat are essentially "packaged" solar energy from millions of years ago!
4.0 Power: The Rate of Doing Work
While Work tells us the total amount of energy transferred, Power tells us how fast that work was done. For example, if two students climb the same flight of stairs, the one who reaches the top first has more power, even though they both did the same amount of work.
What is Power?
Power is defined as the rate of doing work or the rate at which energy is consumed.
- S.I. Unit: Watt ($W$). ($1\,Watt = 1\,Joule / 1\,second$)
- Higher Units: Kilowatt ($kW = 10^3\,W$) and Megawatt ($MW = 10^6\,W$).
- Commercial Unit: Horsepower ($1\,hp = 746\,W$).
Power Formula
$$P = \frac{W}{t}$$
Where: $P$ = Power, $W$ = Work Done, $t$ = Time taken.
4.1 Household Electricity Consumption
The electricity bill you receive at home is not based on "Power" but on the total Energy consumed over a month. The commercial unit for this energy is the kilowatt-hour (kWh), commonly known as a "Unit".
Understanding 1 kWh
One kilowatt-hour is the amount of electrical energy consumed by an appliance of power 1 kW when it is used for 1 hour.
$1\,kWh = 3.6 \times 10^6\,J$
Remember that **Watt ($W$)** is a unit of Power, while **Watt-hour ($Wh$)** or **kWh** is a unit of Energy.
Think of Power as the speed of a car and Energy as the total distance travelled.
A machine does 1200 Joules of work in 2 minutes. Calculate its power.
Solution:
1. Work Done ($W$): $1200\,J$
2. Time ($t$): $2\,minutes = 2 \times 60 = 120\,seconds$ (Must convert to seconds!)
3. Formula: $P = W / t$
4. Calculation: $P = 1200 / 120 = 10\,W$
Final Answer: The power of the machine is $10\,Watts$.
The term "Horsepower" was created by James Watt to compare the output of steam engines with the power of draft horses. He determined that a horse could turn a mill wheel 144 times in an hour, which he estimated as 33,000 foot-pounds per minute!