Formula for Work Done
| Work Done | W = F × d |
W = Work Done (J) | F = Force (N) | d = Distance/Displacement (m)
Figure: Formula for work done
The standard unit for work is the Joule (J). One Joule is defined as the amount of work done when a force of one Newton (N) moves an object through a distance of one metre (m) in the direction of the force.WORK DONE BY A FORCE |
Solution
| Given: | F = 50 N, d = 3 m |
| Find: | W = ? |
| Formula: | W = F × d |
| Substitute: | W = 50 N × 3 m |
| Answer: | W = 150 J |
Worked Example: Calculating work done
ENERGY Energy is defined as the capacity or ability to do work. An object possesses energy if it can exert a force over a distance. Energy exists in many forms, such as mechanical, thermal, chemical, electrical, nuclear, and radiant energy. Energy is a scalar quantity. The standard unit for energy is also the Joule (J), just like work. This highlights the close relationship between work and energy: work is the process of transferring energy. For Grade 10, we primarily focus on mechanical energy, which is the sum of kinetic and potential energy. 1. Kinetic Energy (KE) Kinetic energy is the energy possessed by an object due to its motion. The faster an object moves, and the greater its mass, the more kinetic energy it has.Formula for Kinetic Energy
| Kinetic Energy | KE = 12 × m × v2 |
KE = Kinetic Energy (J) | m = mass (kg) | v = velocity (m/s)
Figure: Formula for kinetic energy
KINETIC ENERGY |
Solution
| Given: | m = 2 kg, v = 10 m/s |
| Find: | KE = ? |
| Formula: | KE = 12 × m × v2 |
| Substitute: | KE = 12 × 2 kg × (10 m/s)2 |
| Answer: | KE = 100 J |
Worked Example: Calculating kinetic energy
2. Gravitational Potential Energy (GPE) Gravitational potential energy is the energy an object possesses due to its position or height above a reference point (usually the ground). The higher an object is, and the greater its mass, the more gravitational potential energy it has.Formula for Gravitational Potential Energy
| GPE | GPE = m × g × h |
GPE = Gravitational Potential Energy (J) | m = mass (kg) | g = acceleration due to gravity (≈ 9.8 m/s2 or 10 m/s2) | h = height (m)
Figure: Formula for gravitational potential energy
GRAVITATIONAL POTENTIAL ENERGY |
Solution
| Given: | m = 5 kg, h = 2 m, g = 10 m/s2 |
| Find: | GPE = ? |
| Formula: | GPE = m × g × h |
| Substitute: | GPE = 5 kg × 10 m/s2 × 2 m |
| Answer: | GPE = 100 J |
Worked Example: Calculating gravitational potential energy
POWER Power is the rate at which work is done or the rate at which energy is transferred or transformed. It tells us how quickly work is being performed or how quickly energy is being used. Power is a scalar quantity.Formula for Power
| Power | P = Wt or P = Et |
P = Power (W) | W = Work Done (J) | E = Energy (J) | t = time taken (s)
Figure: Formula for power
The standard unit for power is the Watt (W). One Watt is defined as the rate of doing one Joule of work per second (1 W = 1 J/s).POWER: RATE OF DOING WORK |
Solution
| Given: | W = 600 J, t = 10 s |
| Find: | P = ? |
| Formula: | P = Wt |
| Substitute: | P = 600 J10 s |
| Answer: | P = 60 W |
Worked Example: Calculating power
SUMMARYSummary of Work, Energy, and Power
| Term | Definition | Unit | Formula |
|---|---|---|---|
| Work (W) | Force applied over a distance in the direction of the force. | Joule (J) | F × d |
| Energy (E) | The capacity to do work. | Joule (J) | Various (e.g., KE, GPE) |
| Kinetic Energy (KE) | Energy due to motion. | Joule (J) | 12 × m × v2 |
| Gravitational Potential Energy (GPE) | Energy due to position/height. | Joule (J) | m × g × h |
| Power (P) | Rate at which work is done or energy is transferred. | Watt (W) | Wt |
Figure: Summary of key concepts, units, and formulas
ASSESSMENT QUESTIONS 1. Define the term "work" as used in physics. State its SI unit. 2. What is energy? Name its SI unit. 3. Explain the difference between kinetic energy and gravitational potential energy. 4. A 0.5 kg football is kicked with a velocity of 20 m/s. Calculate its kinetic energy. 5. A builder lifts a 20 kg bag of cement onto a platform 1.5 m high. a) Calculate the work done by the builder. (Take g = 10 m/s2). b) If the builder takes 5 seconds to lift the bag, what is his power output? 6. An electric motor has a power rating of 200 W. How much work can it do in 30 seconds? COMMON DIFFICULTIES & MISCONCEPTIONS • Work vs. Effort: Students often confuse "work" in physics with "effort" in everyday language. If you push a wall for hours and it doesn't move, you've expended effort but done no physical work. • Direction of Force and Displacement: Work is only done when the force has a component in the direction of the displacement. Carrying a heavy bag horizontally at a constant velocity does no work on the bag by the carrier's lifting force, as the force is vertical and displacement is horizontal. • Energy vs. Power: While related, energy is the ability to do work, and power is the rate at which work is done. A small engine can do the same amount of work as a large engine, but the large engine will do it faster (more power). • Units: Students might mix up Joules and Watts, or incorrectly apply units in calculations. Emphasize that work and all forms of energy are measured in Joules, while power is measured in Watts. • "g" value: Sometimes students forget to use the acceleration due to gravity (g ≈ 9.8 m/s2 or 10 m/s2) when calculating gravitational potential energy. QUICK REFERENCE SUMMARY • Work (W): Force × Distance (W = F × d). Unit: Joule (J). • Energy (E): Capacity to do work. Unit: Joule (J). • Kinetic Energy (KE): Energy of motion (KE = 12 × m × v2). • Gravitational Potential Energy (GPE): Energy of height (GPE = m × g × h). • Power (P): Rate of doing work or transferring energy (P = Wt or P = Et). Unit: Watt (W). [END OF TEACHING NOTES]