1. Power pg. 37

2. Objectives Physics terms
Calculate the power generated within a physical system when given the energy and time.
Calculate the energy used or given off within a physical system when given the power and the time.
Calculate power in units of watts, kilowatts, and horsepower.
power
work
energy
watt
kilowatt
kilowatt-hour
Horsepower

3. Brainstorm
A 1200 kg sports car accelerates from 0 to 60 mph (27 m/s) in 5.0 seconds.
An typical car of equal mass takes 8.0 seconds to do the same thing.
So what’s the difference between the two cars? ? vs

4. Power The difference is power.
Both cars convert their gasoline (i.e.chemical energy) into the same amount of kinetic energy when they’re moving, BUT the sports car converts the energy faster than the regular car. It converts more energy every second which means the sports car has greater power.

5. Power is a rate
Power is the rate at which work is done or the rate at which energy is transformed.
This means power looks at how quickly the work is happening (or how quickly energy is being transformed)
Example Lifting a ball quickly requires more power than lifting it slowly.
Power is typically measured in watts.

6. Equations
𝑃= ∆𝐸 𝑡
The power of a system is equal to the energy transformed (change in Energy) divided by the time it takes to happen.
Change in energy
𝑃= 𝑊 𝑡
The power of a system is equal to the work done divided by the time it takes to do the work.
Power
Work
Power
time
time

7. Rearranging Equations
Base equation: 𝑃= ∆𝐸 𝑡
Solve for change in energy:
Solve for time:
Base Equation: 𝑃= 𝑊 𝑡
Solve for work:
Solve for time:

8. An elephant vs. an ant
An elephant lifts a 300 kg log to a height of 3.0 meters in a time of four seconds.
An ant can lift several times its own body weight (~3x10-6 kg) in a time of two seconds.
Which one is more powerful?
The elephant is more powerful, of course!
The elephant transforms more chemical energy every second than the ant.

9. Math Practice & what power means
A ball gains one joule of potential energy in one second. How much power does this require (in watts)?
𝑷= ∆𝑬 𝒕 =
𝟏 𝑱 𝟏 𝒔 =
1 watt
One watt of power means that one joule of energy is transformed in one second.
One watt of power ALSO means that one joule of work is done in one second.
Point out that when they press [Run], the ball takes one second to rise one meter.

10. Math Practice
1- A forklift raises a crate in 5.0 seconds, giving the crate 5000 joules of potential energy. What is the power of the forklift? G U E S
2- What is the power of the forklift if it does this job in half the time?
2000 W; twice as much power!
1000 W

11. Math Practice
A runner might burn Calories (4,180,000 J) in an hour. How much power does that correspond to? G U E S
1160 watts

12. Test your knowledge
Nala does twice as much work as Mateo in the same amount of time. How much power does she have, compared to Mateo?
Alonzo and Irina do the same amount of work, but Irina takes twice as long. How much power does Alonzo have, compared to Irina?
Nala has twice as much power.
Alonzo has twice as much power.

13. Power of a sports car
A 1200 kg sports car transforms 437,400J of energy to be able to accelerate from 0 to 60 mph (27.0m/s) in 5.20 seconds. What is the average power developed? G U E S
84,100 watts

14. Units for power
There are 3 ways to express Power values. Use the Power value from the previous problem to show the 3 ways to express Power:
In Watts: 84,100 watts
In kilowatts:
(or just shift the decimal)
3) In horsepower:

15. More Math Practice
A toaster oven operating at 800 watts takes one and a half minutes to toast a bagel. How much energy is this? G U E S
72,000 joules

16. More Math Practice
A toaster oven operating at 800 watts takes 60 minutes to bake a potato. How much energy is this in joules & in kWh? G U E S
2,880,000 joules
0.80 kilowatt-hours

17. Homework What do each of the symbols mean in this equation?
Translate the equation E = PΔt into a sentence with the same meaning.
An engine has an output energy of 2,400 J in 10 seconds. What is its average power in watts?

18. Homework
An appliance uses 1,400 watts of power. How much energy does this appliance use if it is turned on for 30 minutes, in joules?

19. Homework
A stonemason lifts a small boulder weighing 80 newtons from the ground onto a 1.50 meter wall in 2.0 seconds.
a. How much work does he do?
b. What power does he develop, in watts? in kilowatts? in horsepower?