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Power

Table of Contents
Introduction
Problems
Answers

  

Introduction

          Work                                             Joules
Power = ---------                            Units      ----------- = Watt = W
                time                                              second
   

1 horsepower = 550 ft . lbs/s = 746 Watts

When you buy electricity, you pay for kilowatt . hours.  Since this is Power . time, you are paying for the work that is being done by the electricity.

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Problems

1.     What is the power rating of a fireman, 90.0 kg, who can climb stairs rising 30.0 m in 25.0 seconds while carrying 50.0 kg of equipment? 
   
2. A 1500. kg car requires a 40.0 hp motor to maintain 100.0 km/h.  What is the force of air friction on the car at this speed?
    
3. The express elevator at the Empire State Building can lift the elevator and 20 passengers for a total mass of 3500. kg at a rate of 8.00 m/s.  What is the minimum power rating of the elevator?
  
4. A crane with a 37.3 kilowatt motor is lifting a 3000. kg load to a height of 50.0 m.  How long does it take the crane to lift the load?

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Answers

1.     What is the power rating of a fireman, 90.0 kg, who can climb stairs rising 30.0 m in 25.0 seconds while carrying 50.0 kg of equipment? 
   
    
                 Work      Fd      140.0 kg x 9.80 m s -2 x 30.0 m
Power  = ---------- = ---- = ------------------------------------------- = 1560 W
                 time          t                      25.0 s
   

                    1 hp
1569 W x ----------- = 2.10 hp
                  746 W
   
   

   
2. A 1500. kg car requires a 40.0 hp motor to maintain 100.0 km/h.  What is the force of air friction on the car at this speed?
    
    
100.0 km         1 h         1000 m
------------- x ---------- x ------------- = 27.8 m/s
    1 h            3600 s         1 km
    

                 746 W
40.0 hp x ----------- = 29,800 W = 29,800 J/s = 29,800 Nm/s
                    1 hp
   

Set up the Problem to cancel m and s.
   

29,800 Nm         1 s
--------------- x ------------ = 1070 N
     1 s              27.8 m
    
   

   
3. The express elevator at the Empire State Building can lift the elevator and 20 passengers for a total mass of 3500. kg at a rate of 8.00 m/s.  What is the minimum power rating of the elevator?
  
   
Set up the Problem to get units of Nm/s
   

3500. kg x 9.80 m s -2      8.00 m
                                     x  ---------- = 274,000 Nm/s = 274 kW motor        
                                             1 s
      

                        1 hp
274,000 W x ----------- = 367 hp
                       746 W
    
   

   
4. A crane with a 37.3 kilowatt motor is lifting a 3000. kg load to a height of 50.0 m.  How long does it take the crane to lift the load?
   
   
                 Work      Fd                    Power                  37,300 Nm s -1 
Power  = ---------- = ----    =>    t = ---------- = ------------------------------------------ = 2.54 seconds
                 time          t                        Fd         3000. kg x 9.80 m s -2 x 50.0 m
   

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