WORK, ENERGY, AND POWER

 WORK, ENERGY, AND POWER

Definitions

1. Work (W): Work is said to be done when a force is applied to an object and the object moves in the direction of the applied force. Mathematically, work is given by: $W = F \times d \times \cos \theta$ where:

   • $W$ = Work done (Joules, J)
   • $F$ = Force applied (Newtons, N)
   • $d$ = Displacement (meters, m)
   • $\theta$ = Angle between the force and displacement

2. Energy (E): Energy is the capacity to do work. It exists in different forms such as kinetic energy, potential energy, thermal energy, and chemical energy.

   • Kinetic Energy (KE): Energy possessed by a moving object. $KE = \frac{1}{2} m v^2$
   • Potential Energy (PE): Energy stored in an object due to its position. $PE = mgh$ where:
   • $m$ = Mass (kg)
   • $v$ = Velocity (m/s)
   • $g$ = Acceleration due to gravity (9.8 m/s²)
   • $h$ = Height (m)

3. Power (P): Power is the rate at which work is done or energy is transferred. It is given by: $P = \frac{W}{t}$ where:

   • $P$ = Power (Watts, W)
   • $W$ = Work done (Joules, J)
   • $t$ = Time taken (seconds, s)

JAMB Exam Worked Examples

Work Examples

1. A force of 10 N is applied to move an object by 5 m in the direction of the force. Calculate the work done. $W = F \times d$ $W = 10 \times 5 = 50 J$ Answer: 50 J

2. A 20 N force is applied at an angle of 60° to move a box 4 m. Find the work done. $W = 20 \times 4 \times \cos 60°$ $W = 20 \times 4 \times 0.5$ $W = 40 J$ Answer: 40 J

3. If no displacement occurs when a force of 50 N is applied to a wall, what is the work done? $W = 50 \times 0 = 0 J$ Answer: 0 J (No work is done)

Energy Examples

1. A car of mass 800 kg moves at 20 m/s. Find its kinetic energy. $KE = \frac{1}{2} m v^2$ $KE = \frac{1}{2} \times 800 \times 20^2$ $KE = 160,000 J$ Answer: 160,000 J

2. A 10 kg object is lifted to a height of 5 m. Calculate its potential energy. $PE = mgh$ $PE = 10 \times 9.8 \times 5$ $PE = 490 J$ Answer: 490 J

3. A 2 kg ball is dropped from a height of 10 m. What is its kinetic energy just before it hits the ground? Since total energy is conserved, $KE_{final} = PE_{initial}$ $KE = mgh = 2 \times 9.8 \times 10$ $KE = 196 J$ Answer: 196 J

Power Examples

1. A machine does 600 J of work in 3 seconds. Find its power. $P = \frac{W}{t} = \frac{600}{3} = 200 W$ Answer: 200 W

2. A pump lifts 200 kg of water to a height of 10 m in 5 s. Find its power. Work done = PE = $mgh$ $W = 200 \times 9.8 \times 10$ $W = 19600 J$ $P = \frac{W}{t} = \frac{19600}{5} = 3920 W$ Answer: 3920 W

3. A person lifts a 50 kg box to a height of 2 m in 4 s. Calculate the power. $W = mgh = 50 \times 9.8 \times 2$ $W = 980 J$ $P = \frac{W}{t} = \frac{980}{4} = 245 W$ Answer: 245 W

JAMB Exam Practice Questions

1. A force of 25 N moves an object by 6 m in the direction of the force. Find the work done.
2. A 5 kg ball moving at 10 m/s has a kinetic energy of ____?
3. A 15 kg mass is lifted to a height of 8 m. Calculate its potential energy.
4. A car of mass 1000 kg moves at 30 m/s. Find its kinetic energy.
5. A force of 50 N is applied at 30° to move a box by 3 m. Find the work done.
6. A 500 W motor lifts a 50 kg object in 4 seconds. How high is it lifted?
7. A generator produces 1500 W of power in 5 minutes. How much work is done?
8. A 20 kg mass is dropped from a 10 m building. What is its kinetic energy just before impact?
9. A machine does 10,000 J of work in 20 seconds. Calculate its power.
10. A force of 100 N moves an object by 2 m in the direction of the force. What is the work done?

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This document provides a thorough understanding of Work, Energy, and Power with detailed explanations, formulas, worked examples, and JAMB-style practice questions.