0.22 Phy1200: energy -- power  (Page 3/3)

1 watt = 1 kg*(m^2)*(s^(-3)), or

1 watt = 1 N*m/s

Another viewpoint

As explained above,

Power = force*distance/time

We learned in earlier modules that velocity is equal to the ratio of displacement and time. Therefore,

Power = force * velocity

Therefore, power is proportional to both force and velocity. A truck in a load-pulling contest that moves rather slowly but with great force is powerful.

Similarly, a racing motorcycle that moves very fast with relatively little force is also powerful.

And the great granddaddy of them all, a huge boulder that plows through a house at great speed during a landslide is very powerful.

Sample calculations

A story of two cranes

One crane named A lifts a 1000 kg object to a height of 100 meters in 10 seconds. Another crane named B requires 100 seconds to do the same thing.

Which crane does the most work?

Which crane delivers the most power?

Solution:

Both cranes do the same amount of work by displacing the same object the same distance against the force of gravity. The work done is equal to

(1000kg*9.8m/s^2)*100m = 980000 joules

Crane A delivers 980000 joules in 10 seconds. Therefore, crane A delivers

(980000 joules) / (10 seconds) = 98000 watts

Crane B delivers

(980000 joules) / (100 seconds) = 9800 watts

Therefore, crane A delivers the most power.

Another story about cranes

One crane named A lifts a 1000 kg object to a height of 100 meters in 10 seconds. Another crane named B lifts a 500 kg object to a height of 100 metersin 5 seconds.

Which crane does the most work?

Which crane delivers the most power?

Solution:

The work done by crane A is

(1000 kg) * (9.8 (m / (s^2))) * (100 m) = 980000 joules

The work done by crane B is

(500 kg) * (9.8 (m / (s^2))) * (100 m) = 490000 joules

Therefore crane A does the most work.

Crane A delivers 980000 joules in 10 seconds. Therefore, crane A delivers

(980000 joules) / (10 seconds) = 98000 watts

Crane B delivers

(490000 joules) / (5 seconds) = 98000 watts

Therefore, both cranes deliver the same amount of power.

Your electric bill

An electric bill is often expressed in terms of kilowatt-hours (kwh). One kilowatt-hour represents a power expenditure of 1000 watts in one hour.

How many joules of energy are represented by 100 kwh?

Solution:

1 kwh = 1000 watt * 1 hour * 3600 s/hour, or

1 kwh = 3.6*10^6 watt*s

1 watt = 1 N*m/s, therefore

1 kwh = 3.6*10^6 *(N*m/s) * s = 3.6*10^6 N*m

1 joule = 1 N*m, therefore

1 kwh = 3.6*10^6 joules, and

100 kwh = 3.6*10^8 joules

Do the Calculations

I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment with the scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

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