⚡ Power - Rate of Doing Work

Explore how power measures the speed of energy transfer and discover why some machines and people work faster than others!

Power - Rate of Doing Work
Exploring how power measures the speed of energy transfer in our world
What is Power?
Power is the rate of doing work or the rate of energy transfer. It measures how fast work is done.
P = W/t
Where:
P = Power (Watts), W = Work (Joules), t = Time (Seconds)
🏃
Human
💡
Electrical
🚗
Mechanical
🏃
Human Power
Human power is generated through muscle activity and physical effort. When we climb stairs, lift objects, or exercise, our muscles convert chemical energy from food into mechanical work.

Example:

• A person climbing stairs: 100-200 W
• Professional cyclist: 300-400 W
• Olympic sprinter: 1500-2000 W (peak)
P = mgh/t (for climbing)
💡
Electrical Power
Electrical power is consumed by lights, computers, and appliances. It's the rate at which electrical energy is converted into other forms like light, heat, or motion.

Common Appliances:

• LED bulb: 9-15 W
• Laptop: 50-100 W
• Microwave: 800-1200 W
• Air conditioner: 1500-3000 W
P = VI (Voltage × Current)
🚗
Mechanical Power
Mechanical power is found in cars, motorcycles, and industrial machines. It involves the conversion of fuel energy into motion and work output.

Vehicle Examples:

• Small car: 50-100 kW (67-134 HP)
• Sports car: 200-400 kW (268-536 HP)
• Motorcycle: 15-150 kW (20-200 HP)
• Industrial motor: 1-1000 kW
P = F × v (Force × Velocity)
Height: 8m
🧒
Child A
Time: 15s
Power: 52.3 W
Height: 8m
🧒
Child B
Time: 20s
Power: 39.2 W
Example 10.8: Boy Running Upstairs
🏃
Boy's Mass: 50 kg
Total Steps: 45
Step Height: 15 cm
Total Height: 6.75 m
Time Taken: 9 s
Power: 375 W

Given:

Mass = 50 kg, Steps = 45, Step height = 15 cm
Time = 9 s, g = 10 m/s²

Calculations:

Weight = mg = 50 × 10 = 500 N
Total height = 45 × 0.15 = 6.75 m
Work = mgh = 500 × 6.75 = 3375 J
Power = Work/Time = 3375/9 = 375 W

Power:

P = mgh/t = (500 × 6.75)/9 = 375 W
Power = 375 W
💡
Light Bulb
60 W
Converts electrical energy to light and heat at 60 joules per second
🏍️
Motorcycle
15 kW
Engine converts fuel energy to mechanical work at 15,000 joules per second
🚗
Car Engine
100 kW
High-power engine transfers energy at 100,000 joules per second

Power Formula Derivation

P = W/t
Power is defined as the rate of doing work or the rate of energy transfer. It measures how fast work is done or energy is consumed.

Units of Power

1 Watt = 1 Joule/second
1 W = 1 J s⁻¹
1 kilowatt = 1000 watts
1 kW = 1000 J s⁻¹
Named after James Watt (1736-1819): The unit honors the Scottish inventor who improved the steam engine and contributed significantly to the Industrial Revolution.
Example 10.7: Girls Climbing Rope
Two girls, each of weight 400 N climb up a rope through a height of 8 m. Girl A takes 20 s while Girl B takes 50 s to accomplish this task. What is the power expended by each girl?
Solution:
Given:
Weight of each girl = 400 N
Height climbed = 8 m
Time for Girl A = 20 s
Time for Girl B = 50 s
For Girl A:
Work done = Weight × Height = 400 N × 8 m = 3200 J
Power of Girl A:
P = Work/Time = 3200 J / 20 s = 160 W
For Girl B:
Work done = Weight × Height = 400 N × 8 m = 3200 J
Power of Girl B:
P = Work/Time = 3200 J / 50 s = 64 W
Girl A: 160 W     Girl B: 64 W
Practice Problem 1
A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Solution:
Given:
Energy consumed (Work done) = 1000 J
Time taken = 10 s
Formula:
Power = Work done / Time taken
P = W / t
Calculation:
P = 1000 J / 10 s = 100 W
Power of the lamp = 100 W
Practice Problem 2
A motor pumps 200 kg of water to a height of 10 m in 25 s. Calculate the power of the motor. (Take g = 10 m/s²)
Solution:
Given:
Mass of water = 200 kg
Height = 10 m
Time = 25 s
g = 10 m/s²
Weight of water:
Weight = mg = 200 kg × 10 m/s² = 2000 N
Work done against gravity:
Work = Weight × Height = 2000 N × 10 m = 20000 J
Power calculation:
P = Work / Time = 20000 J / 25 s = 800 W
Power of the motor = 800 W = 0.8 kW
Activity 10.17: Electric Meter Reading
12345
kWh

Learning Objectives:

  • Observe your home's electric meter features closely
  • Take readings at 6:30 AM and 6:30 PM daily for a week
  • Calculate units consumed during day and night
  • Tabulate observations and draw inferences
  • Compare with monthly electricity bill
  • Estimate consumption by specific appliances based on their wattage
Types of Power Sources
🏃
Human
Generated through muscle activity and physical effort
💡
Electrical
Consumed by lights, computers, and appliances
🚗
Mechanical
In cars, motorcycles, and industrial machines

All these power sources follow the same fundamental principle:

P = W/t
Power = Work done ÷ Time taken
Week-long Data Collection
Day 6:30 AM Reading 6:30 PM Reading Day Units Night Units
Monday 12345 12365 20 15
Tuesday 12360 12382 22 16
Wednesday 12376 12396 20 14
Thursday 12390 12412 22 17
Friday 12407 12430 23 18
Saturday 12425 12448 23 19
Sunday 12444 12466 22 16

Total Week Consumption: 152 units (Day: 152, Night: 115)

Appliance Power Consumption
💡
LED Bulb
9W
💡
CFL Bulb
15W
🌀
Ceiling Fan
75W
📺
LED TV
120W
❄️
Refrigerator
300W
🌀
Air Conditioner
1500W
🔥
Water Heater
2000W
👔
Iron
1200W

Formula: Energy (kWh) = Power (kW) × Time (hours)

Key Concepts
1. Average Power: Total energy consumed divided by total time taken
2. Power varies with time: An agent may work at different rates at different times
3. Higher power = faster work: More powerful machines complete tasks quicker

Observations:

  • Day consumption is generally higher than night
  • Weekends show different patterns due to lifestyle changes
  • High-power appliances significantly impact consumption
  • Energy-efficient appliances reduce overall consumption
  • Peak hours (evening) show maximum usage
⚡ Power Calculator
Enter work and time values to calculate power
Explore Power and Energy Transfer Rate
What is Power?
Power is the rate of doing work or the rate of energy transfer. It measures how quickly work is done or how fast energy is consumed or converted from one form to another. A more powerful agent can do the same amount of work in less time.
P = W/t
Where:
P = Power (Watts, W)
W = Work done (Joules, J)
t = Time taken (Seconds, s)
Activity 10.16: Climbing Comparison
  • Two children A and B of same weight climb a rope to 8m height
  • Child A takes 15 seconds, Child B takes 20 seconds
  • Both do the same work (W = mgh), but at different rates
  • Child A has higher power as they complete work faster
  • Power shows who does more work per unit time
Example 10.7: Two Girls Climbing
Problem: Two girls, each weighing 400 N, climb 8m high. Girl A takes 20s, Girl B takes 50s. Find the power expended by each.
Given:
Weight = 400 N, Height = 8 m
Time A = 20 s, Time B = 50 s
Girl A's Power:
P = mgh/t = (400 × 8)/20 = 160 W
Girl B's Power:
P = mgh/t = (400 × 8)/50 = 64 W
Girl A: 160 W, Girl B: 64 W
Example 10.8: Boy Running Upstairs
Problem: A 50 kg boy runs up 45 steps in 9s. Each step is 15 cm high. Find his power. (g = 10 m/s²)
Given:
Mass = 50 kg, Steps = 45, Step height = 15 cm
Time = 9 s, g = 10 m/s²
Calculations:
Weight = mg = 50 × 10 = 500 N
Total height = 45 × 0.15 = 6.75 m
Power:
P = mgh/t = (500 × 6.75)/9 = 375 W
Power = 375 W
Activity 10.17: Electric Meter Reading
  • Observe your home's electric meter features closely
  • Take readings at 6:30 AM and 6:30 PM daily for a week
  • Calculate units consumed during day and night
  • Tabulate observations and draw inferences
  • Compare with monthly electricity bill
  • Estimate consumption by specific appliances based on their wattage
Key Concepts
1. Average Power: Total energy consumed divided by total time taken

2. Power varies with time: An agent may work at different rates at different times

3. Higher power = faster work: More powerful machines complete tasks quicker

4. Applications: Power ratings help classify vehicles, appliances, and machines