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โš™๏ธย ap physics c: mech

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๐ŸŽขย Unit 3

ย ย โ€ขย ย โฑ๏ธ2 min read

3.4 Power ๐Ÿ’ก

โฑ๏ธ November 5, 2020

๐Ÿ“…

3.4: Power ๐Ÿ’ก

Power is essentially the rate of change of energy/work in a system. While this key concept is quite brief, power is a topic explored not just in the realm of mechanics. Power is typically used in reference to electricity but it can refer to even the simplest scenarios like walking up the stairs. The units for power are typically Watts or Joules/seconds.

Here are the two main formulas for Power:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-nPUui9lYzKgo.PNG?alt=media&token=5e6377b1-734e-4ad8-8900-15f92417e478

Here you can see above that Power can be the slope in a Work vs Time graph or an Energy vs Time graph, which may be useful for FRQs! Let's take a look at one of those graphs!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-R10tvFIinkLS.png?alt=media&token=6844a641-7cec-4d30-bbde-4f9b7d8e9507

Taken from New York State Library System

Work won't always be a straight line, sometimes it may be a constant horizontal line, and it can also be negative! Just be aware that power is the slope.

It can also be simplified into the equation below:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-7vVgmlT1GMgA.PNG?alt=media&token=a94d3fb8-c198-45af-b087-74e6b3e65827

We must remember our formula from kinematics and simplify

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-rVlJzLjpILKu.PNG?alt=media&token=01126e8f-2a5c-4d5a-80d2-db9a06189daa

Practice Questions

1. A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW ยท h? (Taken from Lumen Learning)

Answer:

Multiply the cost of electricity per hour by the maximum consumption to find the cost per hour

$15 * 0.110 = 1.65$

Then multiply by the amount of usage per day and the amount of days

$1.65 330 = 148.5$

$149

2. Calculate the power output needed for a 950-kg car to climb a 2.00ยบ slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N. (Taken from Lumen Learning)

Answer:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UmlA0WKcxcbe.PNG?alt=media&token=a43e2f29-f8c3-42a9-a6bd-16a50c4c6ac2

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