Work and Energy

This chapter explains the concepts of work, energy, and power in science. It covers how work is done, how energy changes form, and how we measure power and energy usage in our daily lives.

🔹 1. What is Work in Science?

✅ Work is said to be done when:

A force is applied on an object, and
The object moves in the direction of the force.

📗 Conditions for Work:

Situation	Is Work Done?	Reason
Pushing a wall (no movement)	❌ No	Displacement is zero
Lifting a bag upward	✅ Yes	Force and displacement exist
Carrying a bag on your head and walking straight	❌ No	No displacement in direction of force

📘 Formula for Work Done:

$\text{Work} = \text{Force} \times \text{Displacement in the direction of force}$

Unit: Joule (J)
1 Joule = 1 Newton × 1 metre = Work done when a force of 1 N moves an object by 1 m.

📘 Subject: Science
Chapter: Work and Energy
Topic: Work Done by Force

🧠 Explanation:
When a force moves an object through a distance in the same direction as the force, work is said to be done. The formula for work is:

Work = Force × Displacement

Here,
Force = 7 newton (N)
Displacement = 8 meters (m)

🧮 Solution:

Work = 7 × 8
     = 56 joules (J)

✅ Final Answer:
Work done = 56 joules (J)

🔹 2. Positive, Negative, and Zero Work

Type of Work	Condition	Example
Positive Work	Force and displacement in same direction	Pushing a trolley forward
Negative Work	Force and displacement in opposite direction	Friction, lifting against gravity
Zero Work	No displacement or force is perpendicular	Holding a bag, pushing a wall

🧠 Answer:
Work is said to be done when a force is applied on an object and the object moves in the direction of the force. If there is no movement, no work is done.

🧠 Answer:
The formula for work done is:

Work = Force × Displacement

This formula is used when force and displacement are in the same direction.

🧠 Answer:
When a force of 1 newton moves an object by 1 meter in the direction of the force, the work done is 1 joule.
So,

1 joule = 1 newton × 1 meter

📘 Subject: Science
Topic: Work Done by Force

🧠 Explanation:
Work is calculated using the formula:

Work = Force × Displacement

Here,
Force = 140 N
Displacement = 15 m

🧮 Solution:

Work = 140 × 15
     = 2100 joules (J)

✅ Final Answer:
Work done = 2100 joules (J)

🔹 3. What is Energy?

✅ Energy is the capacity to do work.

If a body has energy, it can do work.

SI Unit: Joule (J)
Other units: kilojoule (kJ), calorie (used in food), kilowatt-hour (used in electricity)

🔹 4. Kinetic Energy (KE)

Energy possessed by a body due to its motion.

📘 Formula:

$KE = \frac{1}{2}mv^2$

Where:

m = mass of object (kg)
v = velocity of object (m/s)

🔹 5. Potential Energy (PE)

Energy possessed by a body due to its position or configuration.

📘 Formula:

$PE = mgh$

Where:

m = mass (kg)
g = gravitational acceleration (9.8 m/s²)
h = height (m)

🧠 Answer:
The energy possessed by a moving object due to its motion is called kinetic energy. Any object which is moving has kinetic energy.

🧠 Answer:
The kinetic energy (K.E.) of an object is given by the formula:

K.E. = (1/2) × mass × velocity²

Where,
mass = mass of the object (in kg)
velocity = speed of the object (in m/s)

📘 Given:
Kinetic Energy = 25 J when velocity = 5 m/s

📌 Case 1: Velocity is doubled
New velocity = 2 × 5 = 10 m/s

Kinetic energy is proportional to the square of velocity:

New K.E. = 25 × (10² / 5²)
         = 25 × (100 / 25)
         = 25 × 4
         = 100 J

✅ K.E. when velocity is doubled = 100 J

📌 Case 2: Velocity is tripled
New velocity = 3 × 5 = 15 m/s

New K.E. = 25 × (15² / 5²)
         = 25 × (225 / 25)
         = 25 × 9
         = 225 J

✅ K.E. when velocity is tripled = 225 J

🔹 6. Law of Conservation of Energy

Energy can neither be created nor destroyed. It can only be converted from one form to another.

✅ Example:

In a pendulum:
At the highest point → Maximum potential energy
At the lowest point → Maximum kinetic energy
Total mechanical energy (PE + KE) remains constant

🔹 7. Power

✅ Power is the rate of doing work.

$\text{Power} = \frac{\text{Work Done}}{\text{Time Taken}}$

SI Unit: Watt (W)
1 Watt = 1 Joule / 1 second
Common Units:

Kilowatt (kW) = 1000 W
Horsepower (HP) = 746 W

🧠 Answer:
Power is the rate of doing work or the rate of using energy. It tells how fast work is being done.

Power = Work done / Time taken

🧠 Answer:
When 1 joule of work is done in 1 second, the power is said to be 1 watt.

1 watt = 1 joule / 1 second

📘 Given:
Work done (energy used) = 1000 J
Time taken = 10 seconds

🧮 Solution:

Power = Work / Time
      = 1000 J / 10 s
      = 100 watts

✅ Final Answer:
Power of the lamp = 100 watts

🧠 Answer:
Average power is the total work done divided by the total time taken.

Average Power = Total work done / Total time taken

🔹 8. Commercial Unit of Energy

✅ Electrical energy is measured in kilowatt-hour (kWh).

$1 \, \text{kWh} = 1000 \, \text{W} \times 3600 \, \text{s} = 3.6 \times 10^6 \, \text{J}$

1 unit of electricity = 1 kWh

📊 Summary of Important Formulas

Concept	Formula	Unit
Work	Work = Force × Displacement	Joule (J)
Kinetic Energy	KE = ½ mv²	Joule (J)
Potential Energy	PE = mgh	Joule (J)
Power	Power = Work / Time	Watt (W)
Commercial Energy	1 kWh = 3.6 × 10⁶ Joules	kWh / J

🧠 Key Points to Remember

No movement = no work.
Kinetic energy increases with square of speed.
Power measures how fast work is done.
Energy is conserved in all processes.
1 HP = 746 W; 1 kWh = 1 Unit of electricity.

Exercise

Suma is swimming in a pond: Yes, work is done because her muscles apply force and her body moves forward.
A donkey is carrying a load on its back: No work is done by the donkey on the load because the force is vertical (upward) while motion is horizontal.
A windmill is lifting water from a well: Yes, work is done as water is moved upward by the force of the windmill.
A green plant is carrying out photosynthesis: No mechanical work is done since there is no displacement involved by an applied force.
An engine is pulling a train: Yes, work is done as the engine applies force and the train moves.
Food grains are getting dried in the sun: No mechanical work is done as there is no force causing displacement.
A sailboat is moving due to wind energy: Yes, work is done as wind applies force and moves the boat forward.

🧠 Answer:
The work done by gravity depends only on the vertical displacement. Since the object comes back to the same height, the net vertical displacement is zero. Hence,

✅ Work done by gravity = 0 J

🧠 Answer:
The battery converts chemical energy into electrical energy. The electric energy flows through the wire and is converted into light energy and heat energy by the bulb.

📘 Given:
Mass = 20 kg, Initial velocity = 5 m/s, Final velocity = 2 m/s

🧠 Formula:
Work done = Change in kinetic energy

W = (1/2) × m × (v² - u²)

🧮 Calculation:

W = (1/2) × 20 × (2² - 5²)
   = 10 × (4 - 25)
   = 10 × (-21)
   = -210 J

✅ Final Answer: Work done = -210 J (negative because kinetic energy decreased)

🧠 Answer:
Since the object is moved horizontally and there’s no change in height, there is no displacement in the direction of gravitational force.

✅ Work done by gravity = 0 J

🧠 Answer:
No, this does not violate the law. As the object falls, its potential energy is converted into kinetic energy. The total mechanical energy (P.E. + K.E.) remains constant.

✅ Energy is conserved.

🧠 Answer:
While riding a bicycle, the muscular energy (chemical energy from food) of the rider is converted into:

Kinetic energy of the bicycle (motion)
Heat energy due to friction
Sound energy (sometimes)

🧠 Answer:
No work is done on the rock because it does not move. But energy is still used by the body. That energy is used by the muscles and gets converted into heat energy and causes tiredness.

📘 Given:
1 unit = 1 kilowatt-hour (kWh) = 3.6 × 10⁶ J

🧮 Solution:

Energy = 250 × 3.6 × 10⁶ J
       = 9 × 10⁸ J

✅ Final Answer: 9 × 10⁸ joules

📘 Given: m = 40 kg, h = 5 m, g = 9.8 m/s²

🧠 Formula: PE = m × g × h

PE = 40 × 9.8 × 5
   = 1960 J

✅ Final Answer: Potential Energy = 1960 joules

🧠 Answer:
The satellite moves in a circular path around the Earth. The force of gravity acts towards the center (radially), while displacement is along the tangent. So, the angle between force and displacement is 90°, and:

✅ Work done by gravity = 0 J

🧠 Answer:
Yes. According to Newton’s first law, an object in motion will continue in uniform motion unless an external force is applied. So, an object can be displaced without force if no resistance or friction is present.

🧠 Answer:
Scientifically, no work is done because there is no displacement of the bundle. The person gets tired because of internal muscular energy usage, but no mechanical work is done.

📘 Given:
Power = 1500 W = 1.5 kW, Time = 10 hours

🧠 Solution:
Energy = Power × Time

Energy = 1.5 kW × 10 h
       = 15 kWh

✅ Final Answer: Energy used = 15 kWh

🧠 Answer:
When the pendulum is pulled to one side, it gains potential energy. As it is released, the energy changes into kinetic energy at the lowest point. Then again it turns back into potential energy on the other side. The total energy remains constant.
✅ Law of conservation of energy is verified.

🧠 Answer:
Work done = Loss in kinetic energy

W = (1/2) × m × v²

This is the amount of work required to stop the object.

📘 Given:
Mass m = 1500 kg, Speed v = 60 km/h = 16.67 m/s

🧠 Formula: W = (1/2) × m × v²

W = (1/2) × 1500 × (16.67)²
  ≈ 0.5 × 1500 × 278
  ≈ 750 × 278
  ≈ 208500 J

✅ Final Answer: Work required ≈ 208,500 joules

Case 1: Force is upward
→ Work done = Zero (force is perpendicular to displacement)
Case 2: Force is east (same as displacement)
→ Work done = Positive
Case 3: Force is west (opposite to displacement)
→ Work done = Negative

🧠 Answer:
Yes, Soni is correct. If all the forces acting on an object cancel each other (net force is zero), then the object will not accelerate. It will remain at rest or move with uniform velocity.

📘 Given:
Power = 4 × 500 = 2000 W, Time = 10 h = 36000 s

🧮 Solution:

Energy = Power × Time
       = 2000 × 36000
       = 72,00,000 J

✅ Final Answer: 7.2 × 10⁶ joules

🧠 Answer:
As the object hits the ground, its kinetic energy is converted into:

Sound energy
Heat energy
Slight deformation (mechanical energy)

✅ Energy is not destroyed but transformed.

📘 Chapter Overview

🔹 1. What is Work in Science?

✅ Work is said to be done when:

📗 Conditions for Work:

📘 Formula for Work Done:

🔹 2. Positive, Negative, and Zero Work

🔹 3. What is Energy?

✅ Energy is the capacity to do work.

🔹 4. Kinetic Energy (KE)

📘 Formula:

🔹 5. Potential Energy (PE)

📘 Formula:

🔹 6. Law of Conservation of Energy

✅ Example:

🔹 7. Power

✅ Power is the rate of doing work.

🔹 8. Commercial Unit of Energy

✅ Electrical energy is measured in kilowatt-hour (kWh).

📊 Summary of Important Formulas

🧠 Key Points to Remember

Exercise

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📘 Chapter Overview

🔹 1. What is Work in Science?

✅ Work is said to be done when:

📗 Conditions for Work:

📘 Formula for Work Done:

🔹 2. Positive, Negative, and Zero Work

🔹 3. What is Energy?

✅ Energy is the capacity to do work.

🔹 4. Kinetic Energy (KE)

📘 Formula:

🔹 5. Potential Energy (PE)

📘 Formula:

🔹 6. Law of Conservation of Energy

✅ Example:

🔹 7. Power

✅ Power is the rate of doing work.

🔹 8. Commercial Unit of Energy

✅ Electrical energy is measured in kilowatt-hour (kWh).

📊 Summary of Important Formulas

🧠 Key Points to Remember

Exercise

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