POWER

• power is the rate of doing work, or the rate at which energy is transferred.
• P = W / t
  

  Where, P is power (watts), W is work (joules), t is time (seconds)

• 1 watt is approximately equal to lifting a glass of water half a meter in one second.
• Power is often measured in Kilowatts (kW) ie. 1000 W

Example #1 :

An electric motor lifts an elevator that weighs 1.20 x 10⁴ N a distance of 9.00 m in 15.0 s, what is the power of the motor in watts and in kilowatts?

P = W / t and W = F d , so P = F d / t

P = (1.20 x 10⁴ N)(9.00 m) / 15.0 s

P = 7.20 x 10³ W = 7.20 kW

Example #2 :

How much time does it take to do 5.5 x 10⁴ J of work using 5.0 x 10⁴ Watts of power?

t = W / P = 5.5 x 10⁴ / 5.0 x 10⁴ J = 1.1 seconds

---

Do questions 1 - 3 page 129 of Heath (Rainbow Book)

Do questions 9 - 12 page 203 of red book

Do Investigation : Power Running Up Stairs Lab - See Lab Sheet

---

Power Running Up Stairs Example :

How much power is developed by a 60 Kg boy running up a 4.5 m high flight of stairs in 3.0 s?

F = mg = (60 Kg)(9.8 N/Kg) = 588 N

W = Fd = (588 N)(4.5m) = 2646 J

P = W / t = 2646 J / 3.0 s = 8.8 x 10² W

---

Do practice questions 1 - 3 page 130 of Heath

---

Power Questions

Use your understanding of work and power to answer the following questions. When finished, depress the mouse on the "pop-up menu" to view the answers.

1. Two physics students, Will N. Andable and Chris Pumpiniron, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Chris lifts the 100-pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power? Explain your answers.

   Depress mouse to view answers. Chris and Will do the same amount of work; they apply the same force to lift the same barbell the same distance above their heads. Yet, Chris is the most "power-full" since he does the same work in less time. Power and time are inversely proportional.

    

    

    

2. During the Personal Power lab, Zoe and Liz (piggy backing Sara) ran up the stairs. Liz (and Sara) are a total of twice as massive as Zoe; yet Zoe ascended the same distance in half the time. Who did the most work? Who delivered the most power? Explain your answers.

   Depress mouse to view answers. Liz does more work than Zoe. Liz must apply twice the force to lift her and Sara's bodies up the same flight of stairs. Yet, Zoe is just as "power-full" as Liz. Zoe does one-half the work yet does it one-half the time. The reduction in work done is compensated for by the reduction in time.

    

    

    

3. Cassie the squirrel (mass of 1.0 kg) does push-ups by applying a force to elevate her center-of-mass. If Cassie the squirrel does 1.0 J of work work in 4.0 seconds, then determine her power.

   Depress mouse to view answers. Cassie the squirrel does 1 Joule of work The power rating of this squirrel is found by P = W/t = (1.0 J / 4.0 s) = 0.25 Watts

    

    

    

4. If Alana Newton lifts her 40-kg body a distance of 0.25 meters in 2 seconds, then what is the power delivered by Alana's biceps?

   Depress mouse to view answers. The work done to lift her body is      W = F d = (400 N)(0.25 m)      W = 100 J The power is the      P = work/time      P = (100 J) / (2 s) = 50 Watts.

    

    

    

5. An escalator is used to move 20 physics students every minute from the first floor of a building to the second, (where they jump out a window to calculate the acceleration of gravity). The second floor is located 5-meters above the first floor. The average physics student's mass is 60 kg. Determine the power requirement of the escalator in order to move this number of students in this amount of time.

   Depress mouse to view answers. The work done to lift one physics student is      W = F d      W = (600 N)(5 m) = 3000 J. The work done to lift twenty physics students is      20*3000 J = 60 000 Joules The power is P = W / t      P = (60 000 J) / (60 seconds)      P = 1000 Watts.

---

Conversion Factor :

Because the joule is a very small quantity of work, we often use a kilowatt hour. It is the amount of work done by a machine with a power of 1 kW in 1 hour

(a small fan can do several million joules of work in a day)

When amounts of work are calculated in kilowatt hours, we can convert to Joules

W = P t (using Kwatts and Hours)

1 kWh = 3 600 000 J = 3.6 MJ

units for work would then be kW instead of watts and hours instead of seconds

Example :

How much work is done by a 25 W water pump running steadily for a week, in Kilowatt hours?

W = P t = (25 kW)(7 x 24 h) = 4.2 x 10³ kWh

---

Do practice questions 1 - 3 page 131

---

EFFICIENCY

• efficiency is the ratio of output work to input work
  
  
• an ideal machine has an output equal to input and an efficiency of 100%
• all real machines have efficiencies less than 100%

Example :

A 1500 W kettle heats 1.5 kg of water from 18 to 59 °C in 3.0 min.

1. How much electrical energy was used by the kettle? (Hint : Electrical energy is Work)

   E = P t = (1500 W)(180 s) = 2.7 x 10⁵ J

   
   
2. How much heat energy was delivered to the water? (Hint : Use the equation for 'q' that we learned last day)

   q = m c DT = (1.5 kg)(4200 J/Kg°C)(59 - 18°C)

   q = 2.6 x 10⁵ J

   
   
3. What is the efficiency of the kettle?
   

   Efficiency = 2.6 x 10⁵ J / 2.7 x 10⁵ J x 100 = 96%

Do question 1 - 3, page 149 Heath,

Do Investigation : Efficiency of a Kettle

UNIT REVIEW : REVIEW 8.11 QUESTIONS 1 - 32, PAGES 150 - 152 HEATH