This chapter explains the scientific relationship between work, energy, and power. It clarifies how these terms, often used loosely in daily life, have specific mathematical definitions and units that help us understand the physical world.
10.1 Work
In physics, work has a specific meaning that differs from mental or physical exhaustion. While studying for hours or holding a heavy bag without moving might feel like hard work, scientifically, no work is performed in these cases because there is no movement of the object.
10.1.1 NOT MUCH ‘WORK’ IN SPITE OF WORKING HARD!
Common activities that do not count as “work” in science include:
- Stationary effort: Pushing against a massive wall or rock that does not move. Because the displacement is zero, the work done is zero.
- Static loading: Standing still with a heavy load on your head. Despite feeling tired, you aren’t moving the load, so no scientific work is done.
- Mental tasks: Activities like thinking, reading, or drawing while sitting.
In contrast, activities like climbing a staircase or pulling a cart are considered work because they involve both force and movement.
10.1.2 SCIENTIFIC CONCEPTION OF WORK
For work to be done in the scientific sense, two conditions must be met:
- A force must act on the object.
- The object must be displaced (moved).
If either force or displacement is zero, the total work done is zero.
10.1.3 WORK DONE BY A CONSTANT FORCE
Work is defined as the product of the force applied and the distance moved in the direction of that force.
Work (W) = Force (F) × Displacement (s)
Key Points:
- Units: The unit of work is Newton-metre ($Nm$) or Joule (J).
- 1 Joule: Defined as the work done when a force of $1~N$ displaces an object by $1~m$ along its line of action.
- Positive Work: When force and displacement are in the same direction.
- Negative Work: When force acts opposite to the direction of motion (like friction or brakes).
- Zero Work: When force and displacement are perpendicular (at $90^{\circ}$) or if either is zero.
Questions and Answers
- Question: When do we say that work is done?
- Work is done when a force acts on an object and causes it to move through a distance.
- Question: Write an expression for work done when a force acts in the direction of displacement.
- $W = F \times s$
- Question: Define 1 J of work.
- $1~J$ is the amount of work done on an object when a force of $1~N$ displaces it by $1~m$ in the direction of the force.
- Question: A pair of bullocks exerts a force of 140 N on a plough. The field is 15 m long. How much work is done?
- Force = $140~N$, Displacement = $15~m$.
- Work = $140 \times 15 = 2100~J$.
10.2 Energy
Energy is the capacity to do work. An object that possesses energy can exert a force on another object to perform work. When work is done, energy is transferred from the object doing the work to the object being worked upon.
- Unit: The unit of energy is the same as work, which is the Joule (J).
- Source: The Sun is our primary natural source of energy; other sources include the earth’s interior, tides, and atomic nuclei.
10.2.1 FORMS OF ENERGY
Energy exists in various forms, such as:
- Mechanical Energy: The sum of Potential and Kinetic energy.
- Other Forms: Heat, Chemical, Electrical, and Light energy.
10.2.2 KINETIC ENERGY
Kinetic energy is the energy possessed by an object due to its motion. Any moving object, whether it is a speeding car or a blowing wind, possesses this energy.
Kinetic Energy (Ek) = 1/2 × m × v²
(Where $m$ is mass and $v$ is velocity)
Questions and Answers
- Question: What is the kinetic energy of an object?
- It is the energy an object has because it is moving.
- Question: Write the expression for kinetic energy.
- $E_k = \frac{1}{2}mv^2$
- Question: An object of mass 15 kg is moving with a velocity of 4 m/s. What is its kinetic energy?
- $E_k = \frac{1}{2} \times 15 \times 4^2 = 120~J$.
10.2.3 POTENTIAL ENERGY
Potential energy is the energy stored in an object due to its position or configuration.
- Examples: A stretched rubber band, a compressed spring, or a bow ready to release an arrow.
10.2.4 POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT
When an object is raised to a height, work is done against gravity. This stored energy is called Gravitational Potential Energy.
Potential Energy (Ep) = m × g × h
(Where $m$ is mass, $g$ is gravity, and $h$ is height)
The work done depends only on the vertical height difference, not the path taken to reach that height.
10.2.5 ARE VARIOUS ENERGY FORMS INTERCONVERTIBLE?
Energy can change from one form to another. For example, in a falling object, Potential Energy converts into Kinetic Energy. In plants, solar energy converts into chemical energy (food).
10.2.6 LAW OF CONSERVATION OF ENERGY
This law states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The Total Mechanical Energy (sum of P.E. and K.E.) of a system remains constant.
mgh + 1/2 mv² = Constant
10.3 Rate of Doing Work
Power measures the speed at which work is done. It is the rate of doing work or the rate of energy consumption.
Power (P) = Work (W) / Time (t)
- Unit: The SI unit is the Watt (W).
- 1 Watt: The power of an agent that does $1~J$ of work in $1~s$.
- Commercial Unit: Kilowatt ($1~kW = 1000~W$).
- Average Power: Calculated as the total work done divided by the total time taken.
Questions and Answers
- Question: What is power?
- Power is the rate at which work is performed or energy is transferred.
- Question: Define 1 watt of power.
- It is the power of an agent that does work at the rate of 1 Joule per second ($1~J/s$).
- Question: A lamp consumes 1000 J of energy in 10 s. What is its power?
- Power = $1000~J / 10~s = 100~W$.
- Question: Define average power.
- Average power is the total energy consumed divided by the total time taken.
Exercise: Solved Questions
- A donkey carries a load; is work done?
- No. The force of gravity is vertical, but the displacement is horizontal. The angle is $90^{\circ}$, so work is zero.
- Work done by gravity on an object in a curved path (returning to the same height)?
- Zero. Since the initial and final points are on the same horizontal line, vertical displacement is zero.
- Does a falling object violate the conservation of energy?
- No. As it falls, Potential Energy decreases, but Kinetic Energy increases by the same amount, keeping the total energy constant.
- A person holding hay on his head for 30 minutes gets tired. Is work done?
- No. Although energy is spent by muscles, there is no displacement of the load.
- Calculate energy used by a 1500 W heater in 10 hours.
- Energy = Power $\times$ Time = $1.5~kW \times 10~h = 15~kWh$ (15 units).
- Find energy in joules for 250 units.
- $1~unit = 3.6 \times 10^6~J$.
- $250~units = 250 \times 3.6 \times 10^6 = 9 \times 10^8~J$.
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