Work, Energy & Power

P – Point → In the above paragraph, I point out to the theory of: The Law of Conservation of Energy.

E – Evidence → The evidence that supports the theory is: Joule proved that work and heat are both forms of energy, and scientists discovered various interchangeable forms like kinetic, potential, heat, and light energy.

E – Explanation → Now I explain my point: While energy is the fundamental ability to do work, work itself is the actual force applied over a distance, and power measures the speed or rate at which that work is successfully completed.

L – Link → I link my knowledge of energy to: Real-world applications, such as how mechanical energy constantly shifts between potential and kinetic forms, and how different machines use power to complete tasks at varying speeds.

1. Mohit applied a force and also caused a displacement, as he carried the books up the stairs. Since both conditions for work were satisfied, work was done. Neera applied a force on the cupboard but it did not move, so there was no displacement. As displacement was zero, no work was done in scientific terms.

2. The stretched rubber band possessed elastic potential energy, as it was stored with energy on being stretched (deformed).

3. When the ceiling fan was switched on, electrical energy was transformed into kinetic energy of the rotating blades.

4. Rahul had more power. Power is the rate of doing work (power = work done ÷ time taken). Both did the same work, but Rahul did it in less time, so his power was greater.

5. Work was done when Mohit applied a force and moved the books (work = force × displacement). Energy was the capacity to do this work, which is why everyone felt tired as their energy was spent. Power decided how fast the work was done — Rahul lifting the bag faster showed greater power.

1. Solar energy
   Reason — Kinetic energy, potential energy and chemical energy are forms of energy that a body itself possesses or stores (due to its motion, position or chemical make-up), whereas solar energy is the energy received as radiation from the Sun.
2. Time
   Reason — Force, displacement and work are connected through the relation work = force × displacement, whereas time does not appear in this relation.
3. Friction
   Reason — Work, power and energy are closely related quantities concerned with the doing of work, whereas friction is a force.
4. Light energy
   Reason — Gravitational potential energy, elastic potential energy and kinetic energy are all forms of mechanical energy, whereas light energy is not a form of mechanical energy.
5. Mass
   Reason — Work, time and power are connected through the relation power = work ÷ time, whereas mass is the amount of matter in a body and does not appear in this relation.

1. Work is said to be done when a force is applied on a body and the body is displaced in the direction of the applied force.

2. The shortest distance covered by a body from its initial position to its final position is called displacement.

3. Pushing a wall (the wall does not move, so the displacement is zero and no work is done).

4. One joule is the amount of work done when a force of one newton moves a body by one metre in its own direction (1 J = 1 N × 1 m).

5. Mechanical energy is the energy possessed by a body due to its position or motion.

1. Work is said to be done by a force when it displaces a body (on which it acts) in its own direction.
2. Distance is the total length between two points.
3. Work done will be zero if either the force applied or displacement is zero.
4. One joule is the amount of energy possessed by a body when a force of 1 N moves it by 1 m in its direction.
5. The energy possessed by a body due to its position or motion is called mechanical energy.

1. True

2. False
   Corrected Statement — Gravitational potential energy is directly proportional to mass, so the heavier the body, the more (not less) is its potential energy.

3. True

4. False
   Corrected Statement — In an electric bulb, electrical energy gets converted into light and heat energy, not magnetic energy.

5. False
   Corrected Statement — Power is the amount of work done in unit time (the rate of doing work). The capacity of a body to do work is called energy.

1. Energy can be converted from one form to another.

2. The SI unit of work is joule (J)

3. In loudspeakers, electrical energy gets converted into sound energy.

4. A wound up spring of a watch or a toy car has elastic potential energy in it. As the spring uncoils, it does work in moving the arms of the watch.

5. Kinetic energy is zero when an object is at rest. (It is maximum when the object moves with maximum speed.)

Work done is the product of force and displacement, W = F × s. So, for the same displacement, a greater force does more work, and for the same force, a greater displacement does more work. Hence, work done is directly proportional to both the force applied and the displacement caused in the body.

Energy is the capacity to do work, and energy is spent whenever we do work. While coming home from school, we do work and our energy is used up. As this energy is spent, we feel tired on reaching home.

The work done in lifting the stone from the ground gets stored in it as gravitational potential energy. When the stone is dropped, this potential energy changes into kinetic energy. The moving stone uses this kinetic energy to do work on the glass, and so the glass breaks.

Kinetic energy is directly proportional to the square of the speed (KE = $\frac{1}{2}\text{mv}^2$). A fast moving car therefore has a very large kinetic energy. During an accident, this large kinetic energy causes great damage, which makes the accident dangerous and possibly fatal.

A stone or rock lying on the top of a hill possesses gravitational potential energy due to its height. During a landslide, when the rocks fall down, this potential energy changes into kinetic energy. The fast moving rocks can hurt people and damage property, so landslides cause damage in hilly areas.

Kinetic energy is the energy an object possesses due to its motion. For example, flowing water, a flying aircraft, a fast moving football, a moving bus, wind and a running boy all possess kinetic energy.

Gravitational potential energy is the energy stored in an object due to its vertical position or height above the ground. For example, water stored in a dam possesses gravitational potential energy due to its height. It is calculated using equation: PE = m × g × h.

• When you jump on a trampoline, its shape changes and elastic potential energy is stored in it.
• A stretched catapult has stored potential energy, which sends the stone a long distance when released.
• A wound up spring of a watch or a toy car has elastic potential energy that moves the arms of the watch as the spring uncoils.

• Electrical energy is converted into mechanical energy in a washing machine, a fan and an electric motor.
• Electrical energy is converted into sound energy in a loudspeaker.
• Sound energy is converted into electrical energy in a microphone.
• Light energy is converted into electrical energy in a solar cell.
• Chemical energy is converted into electrical energy in a dry cell.
• Electrical energy is converted into light and heat energy in an electric bulb.
• Electrical energy is converted into magnetic energy in an electromagnet.

The power of a source depends on the following two factors.

• The amount of work done by the source.
• The time taken by the source to complete the work.

• In photosynthesis, the light energy of the sun is converted into chemical energy stored in plants. When we eat this food, it is stored in our body as muscular energy, which is then used to do work and gets converted into mechanical energy.
• In a power plant, the chemical energy of fuels like coal is converted into heat energy. This heat boils water to form steam, which moves the shaft of a turbine, so heat energy is converted into mechanical energy. The generator then converts this into electrical energy.
• In an automobile, the chemical energy of the fuel is converted into heat energy, which moves the piston and changes into mechanical energy, finally moving the vehicle as kinetic energy.
• When we stretch a bow, it acquires elastic potential energy. On releasing the string, this potential energy is converted into the kinetic energy of the arrow.
• In a hydroelectric power plant, the potential energy of the water stored at a height is converted into kinetic energy, which moves the turbine and produces electrical energy.

Potential energy is the energy possessed by a body by virtue of its position or configuration. There are two types of potential energy.

• Gravitational potential energy — the energy stored in a body due to its height in the gravitational field. The work done in raising a body to a height is stored in it as gravitational potential energy. It depends on the mass and the height of the body, and is given by PE = m × g × h. Example: water stored in a dam.

• Elastic potential energy — the energy stored in a body when work is done to deform, stretch or compress it. Example: a stretched catapult or a wound up spring of a watch.

Mechanical energy is the energy possessed by a body due to its position or motion. There are two types of mechanical energy.

• Kinetic energy — the energy possessed by a body by virtue of its motion. It depends on the mass and the speed of the body, and is given by KE = $\frac{1}{2}\text{mv}^2$. Example: flowing water and a moving bus.

• Potential energy — the energy possessed by a body by virtue of its position or configuration. It is of two kinds — gravitational potential energy (due to height) and elastic potential energy (due to deformation). Example: water stored in a dam and a stretched catapult.

Work done is given by W = F × s, where F is the force applied and s is the displacement.

• If the force applied is zero (F = 0), then W = 0. For example, a man sleeping on a bed or a child standing and waiting for the school bus applies no force, so no work is done.

• If the displacement is zero (s = 0), then W = 0 even though a force is applied. For example, when a boy pushes a tree or a man pushes a lawn mower on a circular path and stops at the same point, the displacement is zero, so no work is done.

Hence, work done becomes zero if either the force applied or the displacement is zero.

1. Work done in one trip = Force × displacement = (m × g) × h.

Force (F) = m × g
= 20 × 10
= 200 N

Work in one trip = 200 × 10 = 2000 J

Total work for 5 trips = 5 × 2000 = 10000 J

So, the total work done by Manav is 10000 J.

2. The water in the raised tank possesses gravitational potential energy. This is because it is stored at a height above the ground, so it has energy by virtue of its position.

3. When the motor lifts the water, electrical energy is converted into mechanical energy.

4. Power is the rate of doing work (power = work done ÷ time taken). The motor does the same work as Manav, but it completes the work in much less time. Since less time means more power, the motor is more powerful than Manav.

5. No, all the energy from his body is not converted into useful mechanical work. When Manav carries the water, part of his muscular energy is used to lift the water, while the remaining energy is mainly converted into thermal/internal energy and dissipated as heat. This is why he feels tired.

1. While playing golf, the moving golf club has kinetic energy. When it hits the stationary ball, it does work on the ball, and some of the club's kinetic energy is transferred to the ball. The energy moves from the club to the ball but stays in the same (kinetic) form.

2. Thermal energy gets transferred in three ways — conduction, convection and radiation.

3. In a solar panel (solar cell), the light energy coming from the Sun gets converted into electrical energy.

Work done is given by W = F × s. The child applies the same force on both boxes, so the work done depends on the displacement. The lighter box moves a greater displacement. As work done is directly proportional to displacement, more work is done on the lighter box because it is displaced farther.

At the highest point, the bob is momentarily at rest at the greatest height, so its potential energy is maximum and kinetic energy is zero. At the lowest point, the bob moves fastest, so its kinetic energy is maximum and its potential energy is minimum. If the lowest point is chosen as the zero reference level, its potential energy there is taken as zero. At every point, the total mechanical energy (PE + KE) remains constant, neglecting friction and air resistance.

Given,

Force (F) = 100 N

Height (h) = 5 m

Work done (W) = F × h

= 100 × 5

= 500 J

So, the work done is 500 J.

Given,

Energy (E) = 60 J

Time (t) = 2 s

$$\begin{aligned}\text {Power (P)} = \frac{\text E}{\text t} \\[1em] = \frac{60}{2} \\[1em] = 30\text{ W}\end{aligned}$$

So, the power of the bulb is 30 W.

Materials required: A toy car and a flat board or plank to act as a ramp.

Steps

• Place one end of the board on a few books to make a sloping ramp.
• Hold the toy car at the top of the ramp and let it stay there for a moment. At this height, the car has gravitational potential energy.
• Release the car so that it rolls down the ramp on its own.

Observation As the car rolls down, its height decreases and its speed increases. The potential energy of the car at the top is transformed into kinetic energy as it moves down, and the kinetic energy is maximum at the bottom of the ramp. This shows the transformation of energy from potential to kinetic.

Plan: Fix a pulley to a strong beam above the roof tank. Pass a rope over the pulley and tie a bucket to one end of the rope. Fill the bucket with water at the ground and stand on the roof. Pull the rope downward to raise the bucket of water up to the tank, then empty it into the tank.

Science behind it: A pulley system provides mechanical advantage. The load is supported by more than one section of the rope, so a smaller effort force is required to lift the bucket, although a greater length of rope has to be pulled. Pulling downward also makes the task easier because the person can use body weight while applying the force.

1. In science, work is said to be done by a force when it displaces a body (on which it acts) in its own direction.

2. When Neelam pushes a wall, she applies a force but the wall does not move. As there is no displacement, no work is done in the scientific sense.

3. For work to be done, a force must be applied on the body and the body must move (be displaced) in the direction of the applied force.

4. While carrying the bag upstairs, a force is applied to lift the bag against gravity and the bag is displaced upward. As both a force and a displacement are present, work is done.

5. The two factors that determine the amount of work done are the force applied and the displacement caused (W = F × s).

1. The energy of a moving object is called kinetic energy.

2. The energy stored in an object due to its height is called gravitational potential energy.

3. In a dam, the potential energy of the water changes into kinetic energy, which then turns the turbine.

4. The process of energy changing from one form to another is called energy transformation (or energy conversion).

5. No, energy can neither be created nor destroyed. It only changes from one form to another. This is the law of conservation of energy.

1. The formula to calculate work done is, work = force × displacement.

2. Energy is the capacity to do work. When work is done on a body, its energy increases, and when a body does work, its energy is spent. Work and energy have the same unit, the joule.

3. Mechanical energy is the sum of the kinetic energy and the potential energy of a body.

4. The formula to calculate power is $\text P = \frac{\text W}{\text t}$, that is, $\text {Power} = \frac{\text{work done}} {\text {time taken}}$.

5. The person who does the work faster (in less time) has more power.

1. Energy is the capacity of a body to do work, while power is the rate of doing work.

2. The SI unit of energy is the joule (J) and the SI unit of power is the watt (W).

3. Power is called the rate of doing work because it is equal to the work done divided by the time taken $\text P = \left(\frac{\text W}{\text t}\right)$. It tells how much work is done in unit time, that is, how fast work is done.

4. Yes. If a machine does only a small amount of work but in a very short time, its power $\left(\frac{\text {work}}{\text{time}}\right)$ becomes high. So a machine can have high power even without doing much total work.

5. A geyser heating water over a long time uses high energy slowly, whereas a stretched rubber band snapping back releases low energy very quickly.

1. Work is said to be done only when a force is applied and the body shows displacement in the direction of the force.
2. The SI unit of work is joule (J).
3. Energy possessed by a body due to its motion is called kinetic energy.
4. The rate at which work is done is called power.
5. The law of conservation of energy states that energy can neither be created nor destroyed, it only changes from one form to another.

1. True

2. True

3. True

4. False
   Corrected Statement — The commercial unit of energy used by electricity boards is the kilowatt-hour (kWh), not the joule.

5. True

The two conditions necessary for work to be done are:

• A force must be applied on the body.
• The body must move (be displaced) in the direction of the applied force.

The gravitational potential energy of an object depends on two factors:

• Mass (or weight) of the body — it is directly proportional to the mass.
• Height from the level of the ground — it is directly proportional to the height.

In uniform circular motion, the centripetal force is always directed towards the centre of the circular path, while the instantaneous displacement is along the tangent to the path. Thus, the force and displacement are perpendicular to each other, so the work done by the centripetal force is zero. Also, because the speed remains constant, the kinetic energy does not change and the net work done is zero.

• In an electric bulb, electrical energy is converted into light and heat energy.
• In a ceiling fan, electrical energy is converted into mechanical (kinetic) energy of the rotating blades.

Given,

Mass of the body (m) = 2 kg

Height (h) = 5 m

g = 9.8 ms^-2

Potential energy (PE) = m × g × h

= 2 × 9.8 × 5

= 98 J

So, the potential energy gained is 98 J.

One watt is the power of a body or a machine if it does 1 joule of work in 1 second (1 W = 1 Js^-1).

Given,

Volume of water = 100 litres = 0.1 m³

Mass of water (m) = volume × density
= 0.1 × 1000
= 100 kg

Height (h) = 20 m,
Time (t) = 50 s,
Acceleration due to gravity (g) = 9.8 m s⁻²

Work done = PE
= m × g × h
= 100 × 9.8 × 20
= 19600 J

$$\begin{aligned}\text P = \frac{\text W}{\text t} \\[1em] = \frac{19600}{50} \\[1em] = 392 \text { W}\end{aligned}$$

So, the power of the pump is 392 W.

A simple pendulum has a heavy bob tied to a thread whose other end is fixed to a rigid support. When the bob is displaced to an extreme position, it has maximum potential energy and zero kinetic energy. As it swings down towards the mean position, its potential energy changes into kinetic energy. At the mean position, its kinetic energy is maximum and potential energy is zero. As it rises to the other extreme position, the kinetic energy again changes back into potential energy.

At every point of the swing, the total mechanical energy (potential energy + kinetic energy) remains constant. This shows that energy is only transformed from one form to another and is neither created nor destroyed, which verifies the law of conservation of energy.