CBSE Class 9 Science: Work and Energy

Understanding Scientific Work

In our daily lives, we use the term 'work' for any physical or mental effort. However, in physics, work is done only when two conditions are met:

1. A force must act on an object.
2. The object must be displaced (i.e., it must move).

If you push a wall with all your might but it doesn't move, you've done zero work scientifically, even though you feel tired! The amount of work done is calculated by multiplying the force by the displacement in the direction of the force.

Formula:
Work Done (W) = Force (F) × Displacement (s)
W = F × s

The SI unit of work is the Joule (J). One Joule is the amount of work done when a force of 1 Newton displaces an object by 1 meter.

Work can be positive, negative, or zero:

• Positive Work: When the force and displacement are in the same direction (e.g., pushing a box across the floor).
• Negative Work: When the force acts opposite to the direction of displacement (e.g., work done by friction on a moving car).
• Zero Work: When the force is perpendicular to the displacement (e.g., a satellite orbiting Earth) or when there is no displacement.

Energy: The Capacity to Do Work

Energy

The ability or capacity to do work. An object that possesses energy can exert a force on another object to do work. The SI unit of energy is the same as work: the Joule (J).

Kinetic Energy (KE)

The energy possessed by an object due to its motion. The faster an object moves, the more kinetic energy it has. Its formula is KE = ½ mv².

Potential Energy (PE)

The energy stored in an object due to its position or configuration. The most common example is gravitational potential energy, which an object has due to its height above the ground. Its formula is PE = mgh.

Mechanical Energy

The sum of the kinetic energy and potential energy of an object. It is the energy associated with the motion and position of an object.

Worked Examples: Calculating Kinetic and Potential Energy

• Problem 1: Calculating Kinetic Energy A cricket ball of mass 150 g is moving with a velocity of 30 m/s. Calculate its kinetic energy. Step 1: Identify given values and convert to SI units. Mass (m) = 150 g = 150 / 1000 kg = 0.15 kg Velocity (v) = 30 m/s Step 2: Write the formula for Kinetic Energy. KE = ½ mv² Step 3: Substitute the values into the formula. KE = ½ × 0.15 kg × (30 m/s)² Step 4: Calculate the final value. KE = 0.5 × 0.15 × 900 KE = 67.5 J Final Answer: The kinetic energy of the cricket ball is 67.5 Joules.
• Problem 2: Calculating Potential Energy A bag of rice weighing 5 kg is lifted to a height of 2 m. Calculate the work done, which is stored as potential energy. (Take g = 9.8 m/s²) Step 1: Identify the given values. Mass (m) = 5 kg Height (h) = 2 m Acceleration due to gravity (g) = 9.8 m/s² Step 2: Write the formula for Potential Energy. The work done in lifting the object is stored as its gravitational potential energy (PE). PE = mgh Step 3: Substitute the values into the formula. PE = 5 kg × 9.8 m/s² × 2 m Step 4: Calculate the final value. PE = 98 J Final Answer: The potential energy stored in the bag of rice is 98 Joules.

The Law of Conservation of Energy

1. State the Law — The law of conservation of energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In an isolated system, the total energy always remains constant.
2. Example: A Freely Falling Body — Let's consider an object of mass 'm' held at a height 'h' above the ground. We will analyze its energy at three different points during its fall.
3. Point A: At Maximum Height (h) — The object is stationary, so its initial velocity (u) is 0. - Kinetic Energy (KE) = ½ mu² = 0 - Potential Energy (PE) = mgh - Total Mechanical Energy = KE + PE = 0 + mgh = mgh
4. Point B: In the Middle of the Fall — Let's say the object falls a distance 'x'. Its height from the ground is now (h-x). Its velocity 'v' can be found using v² = u² + 2as, so v² = 2gx. - Kinetic Energy (KE) = ½ mv² = ½ m(2gx) = mgx - Potential Energy (PE) = mg(h-x) - Total Mechanical Energy = KE + PE = mgx + mg(h-x) = mgx + mgh - mgx = mgh
5. Point C: Just Before Hitting the Ground — The object has fallen the full height 'h'. Its height from the ground is 0. Its final velocity 'v' can be found using v² = u² + 2as, so v² = 2gh. - Kinetic Energy (KE) = ½ mv² = ½ m(2gh) = mgh - Potential Energy (PE) = mg(0) = 0 - Total Mechanical Energy = KE + PE = mgh + 0 = mgh
6. Conclusion — At all three points (Top, Middle, and Bottom), the total mechanical energy of the object remains constant (mgh). The potential energy at the top is completely converted into kinetic energy at the bottom, perfectly demonstrating the law of conservation of energy.

Key Points for Your Exams

• Zero Work Condition: This is a very common question! Remember, if the force is perpendicular to displacement (like a person carrying a suitcase and walking horizontally) or if displacement is zero, the work done is zero in the scientific sense.
• Units are Crucial: Always convert given quantities to their SI units before calculation. Mass must be in kilograms (kg), velocity in meters per second (m/s), and height/distance in meters (m) to get the final answer in Joules (J).
• Work vs. Energy: Work is the process of transferring energy. Energy is the capacity to do work. They share the same unit (Joule) but are distinct concepts.
• Negative Work: Don't forget that work done by friction or air resistance is always negative because these forces act in the direction opposite to the motion.

Practice Questions with Solutions

• Q: A force of 10 N acts on an object. The object is displaced through 5 m in the direction of the force. What is the work done? A: Step 1: Identify the given values. Force (F) = 10 N, Displacement (s) = 5 m. Step 2: Write the formula for work done. W = F × s. Step 3: Substitute the values and calculate. W = 10 N × 5 m = 50 J. Final answer: The work done is 50 Joules.
• Q: An object of mass 15 kg is moving with a uniform velocity of 4 m/s. What is the kinetic energy possessed by the object? A: Step 1: Identify the given values. Mass (m) = 15 kg, Velocity (v) = 4 m/s. Step 2: Write the formula for kinetic energy. KE = ½ mv². Step 3: Substitute the values into the formula. KE = ½ × 15 kg × (4 m/s)² = 0.5 × 15 × 16. Step 4: Calculate the final value. KE = 120 J. Final answer: The kinetic energy of the object is 120 Joules.
• Q: Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 m/s². A: Step 1: The energy possessed by the object due to its height is its potential energy. Identify the given values: Mass (m) = 10 kg, Height (h) = 6 m, g = 9.8 m/s². Step 2: Write the formula for potential energy. PE = mgh. Step 3: Substitute the values and calculate. PE = 10 kg × 9.8 m/s² × 6 m = 588 J. Final answer: The potential energy of the object is 588 Joules.
• Q: A battery lights a bulb. Describe the energy changes involved in the process. A: Step 1: Identify the initial form of energy. A battery stores energy in chemical form. Step 2: Trace the first energy conversion. When the circuit is completed, the chemical energy inside the battery is converted into electrical energy, which flows through the wires. Step 3: Trace the final energy conversion. When the electrical energy reaches the bulb's filament, it is converted into two main forms: light energy (which makes the bulb glow) and heat energy (which is why the bulb feels warm). Final answer: The energy transformation is: Chemical Energy → Electrical Energy → Light Energy + Heat Energy.

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