MATH - SCIENCE INTEGRATION

bullet1 POWER AND MECHANICAL ADVANTAGE

bullet2 Calculating Power


bullet3 Steps for Solving Power Equations

Let's look at the steps for solving power problems.  It is always easier to learn the steps as we work through an actual problem.

Problem:
If a swimmer does 3654 joules of work in 65 seconds, what is the swimmer's power output?

Step 1:   Write down the equation needed to solve a power problem.

P =  W
         t


Step 2 :   Place the known measurments into the equation.

P =  3654J  =
         65s


Step 3:   Solve.  Carefully put the numbers into your calculator and divide for the answer.
  • Remember to place SI units next to all numbers.
  • Watch for any numbers that might need converted.  If the known measurements are not in joules and seconds, then you need to do conversions.
  • Recheck your answers!  It is very easy to hit the wrong button on your calculator.

It will help to work through some sample problems.




bullet3 Sample Problems #1

You need to work on these problems using the same step by step procedures as used earlier in the lesson.  So get your paper, pencil, and calculator ready to go.

Sample Problem #1:
A mechanic uses a jack to lift a truck and does 7258J of work.  If he lifts the truck .45m, what was the power output?



  • Equation
    P =   7258J  =
              .45m



     
    • Answer
      16,128.89W

      The mechanic's power output is 16,128.89 watts.



       

bullet3 Sample Problem #2

Sample Problem #2:
How much work is done by a 125 watt blender that is crushing ice for 5 minutes?  
  • Don't forget to check and make sure that all measurements are in the correct SI unit to solve the problem.  If not, you need to convert.  


  • Needed Conversion
    This is the conversion needed to complete your problem.  
    Since power is calculated in seconds, we need to convert the 5 minutes into seconds.

    5 min| 60 s| = 300 = 300s
             | 1min|      1



     
    • Equation
      W = P x t = (125W) (300s) =



       
      • Answer
        W = 37,500J

        The blender does 37,500 joules of work.



         

bullet3 Sample Problem #3

Problem #3:

If a 60 watt light bulb does 216,000 joules of work, how long has it been burning?  


  • Equation
    t =  W  =   216,000J  =
           P            60W



     
    • Answer
      t = 3600s

      The bulb is burning for 3600s.   

      Are you ready to solve on your own?  Then move on to the practice problems!



       

bullet3 Practice Problems

Do you have everything ready to begin?  Then you should have your paper, pencil, and calculator in front of you, so let's go!

PRACTICE PROBLEMS:
1.  A set of pulleys lifts a piano and does 3,356 joulles of work.  If the piano is lifted in 75 seconds, how much power is used?

2.  How much work is done in order to cook a bag of popcorn in a 500 watt microwave oven for 5.5 minutes?

3.  What is the power of an electric toothbrush if it can do 755.8 joulles of work in 75 seconds?

4.  Sara and Josh do the exact same amount of work.  Sara does the work in 2.3 hours and Josh does it in 2.5 hours.  Who is more powerful?  Explain.

5.  A dock worker lifts a 375N crate a distance of 0.5m over his head in 2.3 seconds.  What is his power output?
  • Hint:  You must do a calculation before you can begin to solve for power.  

6.  An athlete is using the row machine in the gym.  She does 3245 joulles of work on the oars in 72 seconds.  What is her power output?

7.  John is walking to class up the front staircase.  He weighs 595N and the stairs are 3.15 meters long.  Calculate his power output if he climbs the stairs in 15.2 seconds.