Work Done · Kinetic & Potential Energy · Conservation of Energy · Power · Pulley, Lever & Inclined Plane
In earlier chapters, you learnt how forces change the motion of objects using kinematic equations and Newton's laws. But when forces change with time or act in complicated ways, applying these laws directly can become difficult. Is there a simpler and more powerful way to understand such situations?
In this chapter, you will explore the ideas of work, energy and power, which often allow us to analyse motion and interactions more easily. You will also learn about simple machines, which help us perform tasks with less effort and more convenience.
Food provides energy to walk and work. Chemical energy in food powers our muscles.
Electricity provides energy to rotate a fan, power lights and run machines.
Fuel provides energy to move a car. Chemical energy is converted to kinetic energy.
Consider a wheat bag of mass 5 kg on the floor. To lift it slowly to a height of 1 m, you must apply an upward force equal to mg. The force acts upwards as the bag is displaced 1 m in the direction of the force. In everyday language, you did some work.
If you lift 3 such bags one after the other to the same height, you do 3 times more work. If you lift a single bag to 3 m height, you also do 3 times more work. This tells us work depends on both force and displacement.
1 joule of work is done when a constant force of 1 newton displaces an object by 1 metre in the direction of the force.
If no force acts on an object, no work is done on it.
Pushing a rigid wall -- no displacement, so zero work on the wall (even though you feel tired!).
A girl carrying a box while walking -- upward force, horizontal movement. Work done by her force = zero.
When displacement is in the same direction as the applied force. Example: Pushing a wheelchair forward.
When displacement is opposite to the applied force. Example: A goalkeeper stopping a football.
Question: A girl lifts a dumbbell and slowly lowers it down. When does she do positive and negative work?
Answer: When moving the dumbbell up, force and displacement are in the same direction → positive work. When moving it down, force (upward) is opposite to displacement (downward) → negative work.
Question: A goalkeeper's hand moved back by 15 cm as she stopped a ball with a force of 200 N. Work done?
Answer: W = F × s = 200 N × (−0.15 m) = −30 J
The work is negative because the ball moves opposite to the force applied by the goalkeeper.
Enter the force, distance, and angle to calculate work done. See whether work is positive, negative, or zero!
When a force is applied and an object is displaced, work is done on it. Does this cause the object to gain capacity to do further work?
A fielder throws a ball. The moving ball hits the wicket, making it fall. The ball gained energy from the work done by the fielder.
A flowerpot raised to a height can damage objects below if it falls. It gained energy from the work done in raising it.
An object having the capacity to do work is said to possess energy. When positive work is done on an object, it gains energy. The object can then use that energy to apply a force on another object.
Question: In a carrom game, a player pockets the black coin using the striker and white coin. Identify work and energy changes at each collision.
Answer: The striker does positive work on the white coin (increasing its energy). By Newton's third law, the white coin does negative work on the striker (decreasing its energy). Similarly, the white coin does positive work on the black coin, while the black coin does negative work on the white coin.
Energy is the capacity to do work. It can exist in many forms and it is possible to change energy from one form to another.
Energy due to motion or position of objects
Energy related to motion of charges
Energy that makes things warm or hot
Energy that allows us to see
Energy of vibrations of air or other molecules
Energy stored in the nuclei of atoms
Energy stored in chemical bonds between atoms
Electrical energy → Light energy
Electrical energy → Thermal energy
Chemical energy → Mechanical energy
Mechanical energy → Sound energy
The energy possessed by an object due to its motion is called kinetic energy. All moving objects possess kinetic energy -- a moving bicycle, a rolling ball, a speeding car.
Consider an object of mass m starting from rest (u = 0) and acquiring velocity v under force F. Using kinematics (v² = u² + 2as) and Newton's second law (F = ma), we derive:
Question: A cricket ball (mass 0.2 kg) is bowled at 154.8 km/h. Calculate its kinetic energy.
Answer: v = 154.8 km/h = 43 m/s
K = ½ × 0.2 × 43² = ½ × 0.2 × 1849 = 184.9 J
Question: A jet (mass 15,000 kg) is stopped by a wire exerting 367,500 N over 100 m. Find the aircraft's initial velocity.
Answer: Using work-energy theorem:
½ × 15000 × v² - 0 = -(-367500 × 100)
7500 × v² = 36,750,000 → v² = 4900 → v = 70 m/s = 252 km/h
Switch between tabs to calculate kinetic or potential energy. See how your energy compares to real-world examples!
Energy can be stored not only due to motion but also due to the shape or position of an object. A stretched rubber band can shoot a stone. A bent bow can launch an arrow. A compressed spring can push an object.
The energy stored by an object as a result of its deformation or in a system of objects due to their relative positions is called potential energy.
Stretched rubber band / bent bow stores energy in its shape. When released, it converts to kinetic energy of the projectile.
A compressed or stretched spring stores energy. When released, it can push an object with stored energy.
Two magnets separated from each other store energy due to their relative positions.
A ball lifted to a height stores gravitational potential energy in the Earth-ball system.
Consider an object of mass m on the ground (potential energy = 0). To raise it to height h, we apply force mg over distance h:
Question: A fielder throws a ball (200 g) 10 m high in celebration. What is its potential energy at the top? (g = 10 m/s²)
Answer: U = mgh = 0.2 × 10 × 10 = 20 J
The sum of kinetic energy and potential energy is called mechanical energy. Let us find what happens to mechanical energy as an object falls freely.
An object of mass m is dropped from height h (initial velocity = 0):
PE = mgh, KE = 0
Total = mgh
PE = mgh', KE = ½mg²t²
Total = mgh
PE = 0, KE = mgh
Total = mgh
Watch the pendulum swing and see how PE and KE exchange at each position. Adjust the height with the slider!
Question: What is the velocity of a child at the bottom of a slide of height h?
Answer: At top: PE = mgh. At bottom: KE = ½mv²
By conservation: mgh = ½mv² → v² = 2gh → v = √(2gh)
The velocity depends only on height h -- the shape of the slide or mass of the child does not matter!
Question: A truck (10,000 kg) at 72 km/h has brake failure. It enters a 30° escape ramp (sand force = 50,000 N). Find minimum ramp length. (g = 10 m/s², hint: truck rises 1 m for every 2 m along ramp)
Answer: v = 20 m/s, Initial KE = ½ × 10000 × 400 = 2,000,000 J
Height gained = d/2. Final PE = mg × d/2 = 50,000d
Work by sand = −50,000d
Using work-energy theorem: −50,000d = (50,000d) − 2,000,000
100,000d = 2,000,000 → d = 20 m
• At the top of each hill: maximum PE, minimum KE
• At the bottom of each valley: maximum KE, minimum PE
• Each subsequent hill is lower because some mechanical energy is lost to friction and air resistance at every point. The total energy available decreases, so the ball cannot reach the same height again.
Running up stairs in 1 minute feels very different from walking up in 5 minutes, even though the same work is done. This difference is described by power -- the rate at which work is done.
Requires more power
Also requires more power
Question: A weightlifter lifts 75 kg by 2 m in 5 seconds. How much power?
Answer: W = mgh = 75 × 10 × 2 = 1500 J
P = 1500/5 = 300 W
Question: A car (1000 kg) goes from rest to 72 km/h in 10 s. Calculate engine power.
Answer: v = 20 m/s. Work = ½mv² = ½ × 1000 × 400 = 200,000 J
Power = 200,000/10 = 20,000 W = 20 kW
Although the total work required for a task cannot be reduced, it can be made easier by changing the magnitude or direction of the force. Devices that help us do this are called simple machines.
A pulley is a wheel with a groove that guides a rope. A fixed pulley changes only the direction of force (easier to pull down than lift up), so its MA = 1.
Changes direction of effort only. MA = 1. Example: Raising a flag.
Can have MA > 1, lifting much heavier loads with smaller effort. Used in elevators and cranes.
An inclined plane helps move a heavy load to a higher level using less force over a greater distance. The force decreases as the plank becomes less steep (longer), but the displacement increases.
Question: A ramp raises an object over a 30 cm step. The ramp width is 40 cm. Find MA.
Answer: Ramp length = √(30² + 40²) = √2500 = 50 cm
MA = L/h = 50/30 = 1.67
Enter the mass, ramp height, and ramp length to calculate effort, mechanical advantage, and work done. Watch the block slide up!
A lever is a rigid bar that can rotate about a fixed point. It has three main parts:
The fixed point about which the lever rotates.
The force applied. Distance from fulcrum = effort arm.
The force to be overcome. Distance from fulcrum = load arm.
| Class | Arrangement | Examples |
|---|---|---|
| Class I | Fulcrum in between effort and load | Scissors, seesaw, crowbar, pliers, balance scale |
| Class II | Load in between fulcrum and effort | Lemon squeezer, wheelbarrow, bottle opener |
| Class III | Effort in between fulcrum and load | Tweezers, broom, hammer, oar |
Question: A seesaw has seats at distances 1 m and 2 m from the fulcrum on each side. Where should children of 15 kg and 30 kg sit to balance?
Answer: 15 kg × 2 m = 30 kg × L → L = 1 m
The 15 kg child sits at 2 m from fulcrum, the 30 kg child at 1 m from fulcrum.
Place weights on left and right sides and adjust their distance from the fulcrum. Try to balance the lever!
• Every real machine loses some energy to friction and air resistance.
• This energy converts to heat, which dissipates and cannot be fully recovered.
• Because of these inevitable losses, no machine can run forever without an external energy source.
• This is a consequence of the conservation of energy -- you cannot get more energy out than you put in.
In the Himalayan region, water flowing downhill converts potential energy into kinetic energy. This was traditionally used in the gharat (water mill) to grind grain. Water from the top (PE) flows down a pipe, gaining KE, which drives a wheel connected to a grinding stone.
The same principle is used in modern hydroelectric dams. Water stored at height has PE, which converts to KE as it falls, driving turbines that generate electricity.
Scientists have discovered that the Universe is expanding and this expansion is accelerating. To explain this, a mysterious form of energy called dark energy has been proposed. There is no way to exchange dark energy with other forms of energy, and it may govern the fate of the Universe billions of years into the future!
W = F × s. Work is done when a force displaces an object in its direction. SI unit: joule (J). Work can be positive, negative, or zero.
Work done on an object = Change in its energy. This connects force, displacement, and energy.
KE = ½mv². Energy due to motion. Doubles velocity means 4 times KE!
PE = mgh (gravitational). Energy stored due to position or deformation. Greater height = more PE.
KE + PE = constant (when no external forces). Lost PE converts to KE and vice versa.
P = W/t. Rate of doing work. SI unit: watt (W). 1 hp = 746 W.
Pulley, inclined plane, lever. They change force magnitude or direction. MA = Load/Effort.
Machines do NOT create energy. They only help us use it more effectively. Total work done remains the same.
Consider an object of mass m with initial velocity u that acquires final velocity v under a constant force F, undergoing displacement s.
From kinematics: v² = u² + 2as, so s = (v² - u²)/2a
Work done: W = F × s = ma × (v² - u²)/2a = ½m(v² - u²)
If the object starts from rest (u = 0), all the work done appears as kinetic energy:
K = ½mv²
The work-energy theorem states that work done on an object equals the change in its energy. This is a powerful tool because it works even when forces are complex or vary with time, offering a simpler approach than Newton's laws in many cases.
The conservation of mechanical energy states that when an object moves under gravitational force alone (no external forces like friction), its total mechanical energy (KE + PE) remains constant.
Freely falling object: An object of mass m is dropped from height h.
• At the top (A): PE = mgh, KE = 0. Total energy = mgh
• At point B (after time t): Height h' = h - ½gt². PE = mgh' = mgh - ½mg²t². KE = ½mv² = ½mg²t². Total = mgh
• At the ground (C): PE = 0, KE = mgh. Total energy = mgh
At every point, the decrease in PE exactly equals the increase in KE. The total mechanical energy remains mgh throughout. This demonstrates that potential energy is converted into kinetic energy during free fall while the total is conserved.
A pendulum also demonstrates this -- the bob swings between PE (at extremes) and KE (at the lowest point), reaching almost the same height on both sides.
1. Pulley: A wheel with a groove guiding a rope. A fixed pulley changes the direction of effort (MA = 1). A movable pulley system can have MA > 1, allowing heavier loads to be lifted with smaller effort. Used in cranes and elevators.
2. Inclined Plane: A ramp that allows moving heavy loads to a height with less force. By conservation of energy: F' × L = mgh, so MA = L/h. Since L > h, the effort F' is less than the weight mg. A longer, gentler ramp reduces force further. This is why hill roads wind around in gentle slopes.
3. Lever: A rigid bar rotating about a fulcrum. It has effort arm and load arm. The principle: Effort × Effort arm = Load × Load arm. MA = Effort arm / Load arm. By increasing the effort arm, a smaller force can lift a heavier load. Three classes: Class I (fulcrum in between -- scissors, seesaw), Class II (load in between -- wheelbarrow, bottle opener), Class III (effort in between -- tweezers, broom).
Important: All simple machines conserve energy. They reduce force but increase displacement. Total work done remains the same.
Energy exists in many forms: Mechanical energy (due to motion or position), Chemical energy (stored in bonds -- food, fuels), Electrical energy (motion of charges), Thermal energy (makes things hot), Light energy (allows us to see), Sound energy (vibrations), and Nuclear energy (in atomic nuclei).
Energy transformations:
• A bulb converts electrical → light energy
• A water heater converts electrical → thermal energy
• Food converts chemical → mechanical energy (muscles)
• A bell converts mechanical → sound energy
• A watermill (gharat) converts PE of water → KE → mechanical energy for grinding
• A solar panel converts light → electrical energy
• Photosynthesis converts light → chemical energy
In all transformations, the total energy is conserved -- it changes form but is never created or destroyed.