Running the Stairs
15
Running the Stairs
Running the Stairs Measuring Work, Energy, and Power OBJECTIVE Students will be timed while running up a flight of stairs to determine the work done against gravity and the power level at which they performed the work. LEVEL Physics
P A G E S
TEKS 1(A), 2(A), 2(B), 2(C), 2(D), 2(F), 5(B), 5(C), 5(D), 6(A)
T E A C H E R
NATIONAL STANDARDS UCP.3, B.4, B.5
TIME FRAME 45 minutes
CONNECTIONS TO AP II. Newtonian mechanics, C. Work, energy, and power
MATERIALS ruler or meter stick string and plumb line tape measure
bathroom scale stopwatch
TEACHER NOTES In this activity students will measure their work done, potential energy and power level as they climb a flight of stairs. First, find a stairway that is at least one flight or higher and open in such a way that you can measure its height with a string or long tape measure. Have each student stand on a bathroom scale and record his or her weight, then calculate his or her mass using the conversion on the student answer page. Take the students to the stairway and choose a few students to measure the height of the stairs. To determine the stair height tie a weight to the string, lower it to the bottom, and measure the length of the string from the bottom of the stairs to the top. Alternatively, you could give each student a centimeter ruler and have them measure the height of each step. They can then add the heights of all of the steps. Be sure and emphasize the use of the proper number of significant digits as discussed in Foundation Lesson II: Using Numbers in Science. Then, stand at the top of the stairs with a stopwatch to time each student as he or she climbs the stairs. Start the clock when the student’s foot touches the first step. Tell the students they must touch each step as they climb. After the students have received their climb time they should perform the calculations on the student answer page and answer the conclusion questions.
454
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Running the Stairs
15
POSSIBLE ANSWERS TO THE CONCLUSION QUESTIONS AND SAMPLE DATA DATA AND OBSERVATIONS •
Mass and weight conversion: 2.2 lbs = 1 kg 100 lbs ×
1 kg = 45.5 kg 2.2 lbs
•
height of stairs h = 5.6 m
•
time to climb stairs t = 6.7 s
ANALYSIS T E A C H E R
Equations and constants: Work = mgh
P =
Work t m s2
1. Calculate the work you performed on your mass against gravity as you climbed the stairs. Show your work and include units. m⎞ kg m 2 ⎛ • W = mgh = ( 45.5 kg ) ⎜ 9.8 2 ⎟ ( 5.6 m ) = 2497.0 = 2497.0 J = 2.5 × 103 J 2 s ⎠ s ⎝
•
A Joule (J) is the product of the units (Newton) × (meters), and is the product of force and displacement.
2. Calculate the power level at which you performed the work. Show your work and include units. •
P =
W 2497.0 J = = 372.7 watts = 370 watts t 6.7 s
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455
P A G E S
g = 9.8
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Running the Stairs
CONCLUSION QUESTIONS 1. If your potential energy is zero when you are on the ground level, what is your potential energy when you reach the top of the stairs? • PE = Work done in climbing the stairs to the top = 2.50 × 103 J 2. How would the work done against gravity change if you ran up the stairs in a. half the time? Justify your answer. • The work done in climbing the stairs does not depend on the time.
T E A C H E R
P A G E S
b. twice the time? Justify your answer. • The work done in climbing the stairs does not depend on the time. 3. How would your power level change if you ran up the stairs in a. half the time? Justify your answer. W 2W = , which gives twice the power. • Power = t ⎛1 ⎞ ⎜ t⎟ ⎝2 ⎠ b. twice the time? Justify your answer. W • Power = , which gives half the power. ( 2t )
4. Brutus the football player has twice as much mass as you do, but takes twice as much time as you to run to the top of the stairs. a. Calculate Brutus’s potential energy at the top of the stairs. m⎞ ⎛ • PE = Work done = mgh = 2 ( 45.5 kg ) ⎜ 9.8 2 ⎟ ( 5.6 m ) = 4994.0 J = 5.0 × 103 J s ⎠ ⎝ b. How does Brutus’s power compare with yours? Justify your answer. W 4994.0 J = = 372.7 watts = 370 watts • P = t 2 ( 6.7 s ) Thus, Brutus operates at the same power level as the student, since he does twice the work in twice the time.
456
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Running the Stairs
15
5. A calorie (cal) is another unit of energy which is commonly associated with heat in the United States. A kilocalorie (Cal) is 1000 calories. The conversion between kilocalories and joules is 1 kilocalorie = 4184 J a. How many kilocalories did you burn in climbing the stairs? Show your work. ⎛ 1 kilocalorie ⎞ • 2500 J ⎜ ⎟ = 0.60 kilocalories (2 sig. figs.) ⎝ 4184.0 J ⎠
b. If you ate an energy bar consisting of 50.0 kilocalories, what percentage of the energy bar did you use to climb the stairs? 0.60 kilocalories • % of the energy bar used = × 100 = 1.2% 50.0 kilocalories
7. Utility companies often use kilowatt-hours. What physical quantity is expressed in kilowatt-hours? Use dimensional analysis to verify your answer. N ⋅ m h 3600 s • kwh = × × = N ⋅ m = Energy s h
b. How much force is exerted on the trunk? F µ = f Fw •
0.20 =
Ff
740 N F f = 148 N
Expressed to 2 sig. figs. = 150 N
c. How much work is done to move the trunk? • W = (150 N )(12 m ) = 1800 N ⋅ m = 1800 J
d. What is the power exerted? W 1800 J = = 140 watts • P = 13 s t Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
457
P A G E S
8. Joe and Bob needed to move a trunk with a mass of 75 kg to a truck that is to take the trunk away. The trunk is too heavy to lift, so the boys slide it 12 meters to the waiting truck. The coefficient of sliding friction between the trunk and the floor is 0.20. The entire task is accomplished in 13 seconds. a. What is the weight of the trunk? 75 kg 9.8 m 735 kg m × 2 = Expressed to 2 sig. figs. = 740 N • s s2
T E A C H E R
6. Express watts in MKS (meters, kilograms, seconds) units. Nm kg m kg m 2 • watt = N = ∴ watt = s s2 s3
15
Running the Stairs
9. A motor is rated to deliver 10.0 kW. At what speed in m/min can this motor raise a mass of 2.75 × 104 kg? Hint: Refer to question 6 and use dimensional analysis. 4 2 1000 W 1.0 ×10 kg m s2 60 s/ 2.2 m • 10. kW × = × × × = 4 3 1 kW 2.75 ×10 kg 9.8 m min min s/
10. The escalator at Woodley Park Metro Station in Washington D.C. is the longest escalator in the world. It is 65 m long and has a 30° inclination. Phil Physics, who is riding the escalator to see the zoo at the top, weighs 150 lb. How much work does the escalator do on Phil? height sin 30o = 65 m • height = 65 m sin 30o = 33 m
T E A C H E R
P A G E S
• •
150 lb
×
kg 9.8 N × = 670 N 2.2 lb kg
W = ( 670 N )( 33 m ) = 22000 N ⋅ m = 22 kJ
11. Discuss two reasonable sources of error in determining your power to climb the stairs, and explain how each error increased or decreased your value for the power. • If the height of the stairs was measured higher than its actual value, the power would appear to be higher than it actually was. If the height was measured lower than its actual value, the power would appear to be lower than it actually was.
458
•
If the stopwatch was started too late, the power would appear to be higher than its actual value. If the stopwatch was started too early, the power would appear to be lower than its actual value.
•
If several steps were measured and an average step height was used to find the height of the stairway, the power may be higher if a large number of the steps were shorter than the average, or the power may be lower if a large number of the steps were taller than the average.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
Running the Stairs Measuring Work, Energy, and Power Any time work is done on an object the energy of that object is changed. When you climb stairs you do work on your mass and increase your potential energy. The amount of work you do is equal to the change in your potential energy. Power is the rate at which work is done. If you climb the stairs quickly, you operate at a high power level. If you climb the stairs slowly, your power level is low. Work and energy are measured in joules (J), and power is measured in watts. The equation for the work done in lifting a mass from the ground level to a height h is Work = mgh
where m is the mass of the object in kg, g is the acceleration due to gravity (9.8 m/s2), and h is the height to which the mass is lifted. The equation for power, P, is the work done divided by time t: P =
Work t
PURPOSE You will be timed while running up a flight of stairs and will determine the work done against gravity and the power level at which you performed the work. MATERIALS ruler or meter stick string and plumb line tape measure
bathroom scale stopwatch
Safety Alert 1. Use caution when running up the stairs. 2. Do not skip any steps. Step on each one as you climb the stairs. 3. Be sure your shoestrings are securely tied.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
459
15
Running the Stairs
PROCEDURE 1. Stand on a bathroom scale to find your weight. Find the mass that corresponds to your weight by using the conversion relationship given on your student answer page. 2. Find a stairway that has a vertical height of at least one floor. 3. Measure the height of the stairway in meters by attaching a weight to a string and lowering it from the top of the stairs to the bottom. Measure the length of the string with the tape measure or several meter sticks. Alternatively, measure the height of each step, and find the sum of the heights of all the steps. Record the height of the stairs in the appropriate space on your student answer page. When using a ruler, meter stick, or tape measure, remember to make your measurements to the correct number of significant digits and estimate between marks. 4. Have your teacher or a student stand at the top of the stairs with a stopwatch to measure the time it takes you to climb the stairs from the bottom to the top. Timing should begin the moment your foot touches the first step. Use caution while climbing the steps, and be sure to step on each step as you travel up the stairs. 5. Record the time it takes for you to run from the bottom of the stairs to the top in the appropriate space on your student answer page. Record your measurement to the correct number of significant digits.
460
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Running the Stairs
15
Name _____________________________________ Period ____________________________________
Running the Stairs Measuring Work, Energy, and Power DATA AND OBSERVATIONS •
Mass and weight conversion: 2.2 lbs = 1 kilogram
•
height of stairs h = ________________ m
•
time to climb stairs t = _____________ s
ANALYSIS Equations and constants: Remember to report the answers to all calculations to the proper number of significant figures. Work = mgh
P =
Work t
g = 9.8
m s2
1. Calculate the work you performed on your mass against gravity as you climbed the stairs. Show your work and include units.
2. Calculate the power level at which you performed the work. Show your work and include units.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
461
15
Running the Stairs
CONCLUSION QUESTIONS 1. If your potential energy is zero when you are on the ground level, what is your potential energy when you reach the top of the stairs?
2. How would the work done against gravity change if you ran up the stairs in a. half the time? Justify your answer. b. twice the time? Justify your answer.
3. How would your power level change if you ran up the stairs in a. half the time? Justify your answer.
b. twice the time? Justify your answer.
4. Brutus the football player has twice as much mass as you do, but takes twice as much time as you to run to the top of the stairs. a. Calculate Brutus’s potential energy at the top of the stairs.
b. How does Brutus’s power compare with yours? Justify your answer.
5. A calorie (cal) is another unit of energy which is commonly associated with heat in the United States. A kilocalorie (Cal) is 1000 calories. The conversion between kilocalories and joules is 1 kilocalorie = 4184 J a. How many kilocalories did you burn in climbing the stairs? Show your work.
b. If you ate an energy bar consisting of 50.0 kilocalories, what percentage of the energy bar did you use to climb the stairs?
462
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Running the Stairs
15
6. Express watts in MKS (meters, kilograms, seconds) units.
7. Utility companies often use kilowatt-hours. What physical quantity is expressed in kilowatt-hours? Use dimensional analysis to verify your answer.
8. Joe and Bob needed to move a trunk with a mass of 75 kg to a truck that is to take the trunk away. The trunk is too heavy to lift, so the boys slide it 12 meters to the waiting truck. The coefficient of sliding friction between the trunk and the floor is 0.20. The entire task is accomplished in 13 seconds. a. What is the weight of the trunk?
b. How much force is exerted on the trunk?
c. How much work is done to move the trunk?
d. What is the power exerted?
9. A motor is rated to deliver 10.0 kW. At what speed in m/min can this motor raise a mass of 2.75 × 104 kg? Hint: Refer to question 6 and use dimensional analysis.
10. The escalator at Woodley Park Metro Station in Washington D.C. is the longest escalator in the world. It is 65 m long and has a 30º inclination. Phil Physics, who is riding the escalator to see the zoo at the top, weighs 150 lbs. How much work does the escalator do on Phil?
11. Discuss two reasonable sources of error in determining your power to climb the stairs, and explain how each error increased or decreased your value for the power.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
463
Running the Stairs
Running the Stairs Measuring Work, Energy, and Power OBJECTIVE Students will be timed while running up a flight of stairs to determine the work done against gravity and the power level at which they performed the work. LEVEL Physics
P A G E S
TEKS 1(A), 2(A), 2(B), 2(C), 2(D), 2(F), 5(B), 5(C), 5(D), 6(A)
T E A C H E R
NATIONAL STANDARDS UCP.3, B.4, B.5
TIME FRAME 45 minutes
CONNECTIONS TO AP II. Newtonian mechanics, C. Work, energy, and power
MATERIALS ruler or meter stick string and plumb line tape measure
bathroom scale stopwatch
TEACHER NOTES In this activity students will measure their work done, potential energy and power level as they climb a flight of stairs. First, find a stairway that is at least one flight or higher and open in such a way that you can measure its height with a string or long tape measure. Have each student stand on a bathroom scale and record his or her weight, then calculate his or her mass using the conversion on the student answer page. Take the students to the stairway and choose a few students to measure the height of the stairs. To determine the stair height tie a weight to the string, lower it to the bottom, and measure the length of the string from the bottom of the stairs to the top. Alternatively, you could give each student a centimeter ruler and have them measure the height of each step. They can then add the heights of all of the steps. Be sure and emphasize the use of the proper number of significant digits as discussed in Foundation Lesson II: Using Numbers in Science. Then, stand at the top of the stairs with a stopwatch to time each student as he or she climbs the stairs. Start the clock when the student’s foot touches the first step. Tell the students they must touch each step as they climb. After the students have received their climb time they should perform the calculations on the student answer page and answer the conclusion questions.
454
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
POSSIBLE ANSWERS TO THE CONCLUSION QUESTIONS AND SAMPLE DATA DATA AND OBSERVATIONS •
Mass and weight conversion: 2.2 lbs = 1 kg 100 lbs ×
1 kg = 45.5 kg 2.2 lbs
•
height of stairs h = 5.6 m
•
time to climb stairs t = 6.7 s
ANALYSIS T E A C H E R
Equations and constants: Work = mgh
P =
Work t m s2
1. Calculate the work you performed on your mass against gravity as you climbed the stairs. Show your work and include units. m⎞ kg m 2 ⎛ • W = mgh = ( 45.5 kg ) ⎜ 9.8 2 ⎟ ( 5.6 m ) = 2497.0 = 2497.0 J = 2.5 × 103 J 2 s ⎠ s ⎝
•
A Joule (J) is the product of the units (Newton) × (meters), and is the product of force and displacement.
2. Calculate the power level at which you performed the work. Show your work and include units. •
P =
W 2497.0 J = = 372.7 watts = 370 watts t 6.7 s
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
455
P A G E S
g = 9.8
15
Running the Stairs
CONCLUSION QUESTIONS 1. If your potential energy is zero when you are on the ground level, what is your potential energy when you reach the top of the stairs? • PE = Work done in climbing the stairs to the top = 2.50 × 103 J 2. How would the work done against gravity change if you ran up the stairs in a. half the time? Justify your answer. • The work done in climbing the stairs does not depend on the time.
T E A C H E R
P A G E S
b. twice the time? Justify your answer. • The work done in climbing the stairs does not depend on the time. 3. How would your power level change if you ran up the stairs in a. half the time? Justify your answer. W 2W = , which gives twice the power. • Power = t ⎛1 ⎞ ⎜ t⎟ ⎝2 ⎠ b. twice the time? Justify your answer. W • Power = , which gives half the power. ( 2t )
4. Brutus the football player has twice as much mass as you do, but takes twice as much time as you to run to the top of the stairs. a. Calculate Brutus’s potential energy at the top of the stairs. m⎞ ⎛ • PE = Work done = mgh = 2 ( 45.5 kg ) ⎜ 9.8 2 ⎟ ( 5.6 m ) = 4994.0 J = 5.0 × 103 J s ⎠ ⎝ b. How does Brutus’s power compare with yours? Justify your answer. W 4994.0 J = = 372.7 watts = 370 watts • P = t 2 ( 6.7 s ) Thus, Brutus operates at the same power level as the student, since he does twice the work in twice the time.
456
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
5. A calorie (cal) is another unit of energy which is commonly associated with heat in the United States. A kilocalorie (Cal) is 1000 calories. The conversion between kilocalories and joules is 1 kilocalorie = 4184 J a. How many kilocalories did you burn in climbing the stairs? Show your work. ⎛ 1 kilocalorie ⎞ • 2500 J ⎜ ⎟ = 0.60 kilocalories (2 sig. figs.) ⎝ 4184.0 J ⎠
b. If you ate an energy bar consisting of 50.0 kilocalories, what percentage of the energy bar did you use to climb the stairs? 0.60 kilocalories • % of the energy bar used = × 100 = 1.2% 50.0 kilocalories
7. Utility companies often use kilowatt-hours. What physical quantity is expressed in kilowatt-hours? Use dimensional analysis to verify your answer. N ⋅ m h 3600 s • kwh = × × = N ⋅ m = Energy s h
b. How much force is exerted on the trunk? F µ = f Fw •
0.20 =
Ff
740 N F f = 148 N
Expressed to 2 sig. figs. = 150 N
c. How much work is done to move the trunk? • W = (150 N )(12 m ) = 1800 N ⋅ m = 1800 J
d. What is the power exerted? W 1800 J = = 140 watts • P = 13 s t Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
457
P A G E S
8. Joe and Bob needed to move a trunk with a mass of 75 kg to a truck that is to take the trunk away. The trunk is too heavy to lift, so the boys slide it 12 meters to the waiting truck. The coefficient of sliding friction between the trunk and the floor is 0.20. The entire task is accomplished in 13 seconds. a. What is the weight of the trunk? 75 kg 9.8 m 735 kg m × 2 = Expressed to 2 sig. figs. = 740 N • s s2
T E A C H E R
6. Express watts in MKS (meters, kilograms, seconds) units. Nm kg m kg m 2 • watt = N = ∴ watt = s s2 s3
15
Running the Stairs
9. A motor is rated to deliver 10.0 kW. At what speed in m/min can this motor raise a mass of 2.75 × 104 kg? Hint: Refer to question 6 and use dimensional analysis. 4 2 1000 W 1.0 ×10 kg m s2 60 s/ 2.2 m • 10. kW × = × × × = 4 3 1 kW 2.75 ×10 kg 9.8 m min min s/
10. The escalator at Woodley Park Metro Station in Washington D.C. is the longest escalator in the world. It is 65 m long and has a 30° inclination. Phil Physics, who is riding the escalator to see the zoo at the top, weighs 150 lb. How much work does the escalator do on Phil? height sin 30o = 65 m • height = 65 m sin 30o = 33 m
T E A C H E R
P A G E S
• •
150 lb
×
kg 9.8 N × = 670 N 2.2 lb kg
W = ( 670 N )( 33 m ) = 22000 N ⋅ m = 22 kJ
11. Discuss two reasonable sources of error in determining your power to climb the stairs, and explain how each error increased or decreased your value for the power. • If the height of the stairs was measured higher than its actual value, the power would appear to be higher than it actually was. If the height was measured lower than its actual value, the power would appear to be lower than it actually was.
458
•
If the stopwatch was started too late, the power would appear to be higher than its actual value. If the stopwatch was started too early, the power would appear to be lower than its actual value.
•
If several steps were measured and an average step height was used to find the height of the stairway, the power may be higher if a large number of the steps were shorter than the average, or the power may be lower if a large number of the steps were taller than the average.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
Running the Stairs Measuring Work, Energy, and Power Any time work is done on an object the energy of that object is changed. When you climb stairs you do work on your mass and increase your potential energy. The amount of work you do is equal to the change in your potential energy. Power is the rate at which work is done. If you climb the stairs quickly, you operate at a high power level. If you climb the stairs slowly, your power level is low. Work and energy are measured in joules (J), and power is measured in watts. The equation for the work done in lifting a mass from the ground level to a height h is Work = mgh
where m is the mass of the object in kg, g is the acceleration due to gravity (9.8 m/s2), and h is the height to which the mass is lifted. The equation for power, P, is the work done divided by time t: P =
Work t
PURPOSE You will be timed while running up a flight of stairs and will determine the work done against gravity and the power level at which you performed the work. MATERIALS ruler or meter stick string and plumb line tape measure
bathroom scale stopwatch
Safety Alert 1. Use caution when running up the stairs. 2. Do not skip any steps. Step on each one as you climb the stairs. 3. Be sure your shoestrings are securely tied.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
459
15
Running the Stairs
PROCEDURE 1. Stand on a bathroom scale to find your weight. Find the mass that corresponds to your weight by using the conversion relationship given on your student answer page. 2. Find a stairway that has a vertical height of at least one floor. 3. Measure the height of the stairway in meters by attaching a weight to a string and lowering it from the top of the stairs to the bottom. Measure the length of the string with the tape measure or several meter sticks. Alternatively, measure the height of each step, and find the sum of the heights of all the steps. Record the height of the stairs in the appropriate space on your student answer page. When using a ruler, meter stick, or tape measure, remember to make your measurements to the correct number of significant digits and estimate between marks. 4. Have your teacher or a student stand at the top of the stairs with a stopwatch to measure the time it takes you to climb the stairs from the bottom to the top. Timing should begin the moment your foot touches the first step. Use caution while climbing the steps, and be sure to step on each step as you travel up the stairs. 5. Record the time it takes for you to run from the bottom of the stairs to the top in the appropriate space on your student answer page. Record your measurement to the correct number of significant digits.
460
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
Name _____________________________________ Period ____________________________________
Running the Stairs Measuring Work, Energy, and Power DATA AND OBSERVATIONS •
Mass and weight conversion: 2.2 lbs = 1 kilogram
•
height of stairs h = ________________ m
•
time to climb stairs t = _____________ s
ANALYSIS Equations and constants: Remember to report the answers to all calculations to the proper number of significant figures. Work = mgh
P =
Work t
g = 9.8
m s2
1. Calculate the work you performed on your mass against gravity as you climbed the stairs. Show your work and include units.
2. Calculate the power level at which you performed the work. Show your work and include units.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
461
15
Running the Stairs
CONCLUSION QUESTIONS 1. If your potential energy is zero when you are on the ground level, what is your potential energy when you reach the top of the stairs?
2. How would the work done against gravity change if you ran up the stairs in a. half the time? Justify your answer. b. twice the time? Justify your answer.
3. How would your power level change if you ran up the stairs in a. half the time? Justify your answer.
b. twice the time? Justify your answer.
4. Brutus the football player has twice as much mass as you do, but takes twice as much time as you to run to the top of the stairs. a. Calculate Brutus’s potential energy at the top of the stairs.
b. How does Brutus’s power compare with yours? Justify your answer.
5. A calorie (cal) is another unit of energy which is commonly associated with heat in the United States. A kilocalorie (Cal) is 1000 calories. The conversion between kilocalories and joules is 1 kilocalorie = 4184 J a. How many kilocalories did you burn in climbing the stairs? Show your work.
b. If you ate an energy bar consisting of 50.0 kilocalories, what percentage of the energy bar did you use to climb the stairs?
462
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Running the Stairs
15
6. Express watts in MKS (meters, kilograms, seconds) units.
7. Utility companies often use kilowatt-hours. What physical quantity is expressed in kilowatt-hours? Use dimensional analysis to verify your answer.
8. Joe and Bob needed to move a trunk with a mass of 75 kg to a truck that is to take the trunk away. The trunk is too heavy to lift, so the boys slide it 12 meters to the waiting truck. The coefficient of sliding friction between the trunk and the floor is 0.20. The entire task is accomplished in 13 seconds. a. What is the weight of the trunk?
b. How much force is exerted on the trunk?
c. How much work is done to move the trunk?
d. What is the power exerted?
9. A motor is rated to deliver 10.0 kW. At what speed in m/min can this motor raise a mass of 2.75 × 104 kg? Hint: Refer to question 6 and use dimensional analysis.
10. The escalator at Woodley Park Metro Station in Washington D.C. is the longest escalator in the world. It is 65 m long and has a 30º inclination. Phil Physics, who is riding the escalator to see the zoo at the top, weighs 150 lbs. How much work does the escalator do on Phil?
11. Discuss two reasonable sources of error in determining your power to climb the stairs, and explain how each error increased or decreased your value for the power.
Laying the Foundation in Physics ©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
463
