Work, Power, and Energy problems and calculations Honors Physics Name__________________________ Work 1. A child pulls her sled across the snow with a horizontal force of 50 N for 30 m at a constant velocity. How much work did she do on the sled? 2. An adult reaches down and pulls the sled with a force of 50 N at an angle of 30⁰ above the horizontal for 30 m at a constant velocity. How much work did the adult do on the sled? 3. How much work would an 80 kg person have to do in order to lift his/her own body weight up the entire flight of stairs of the Empire State building (FYI: 1576 stairs!) , which is 320 meters high? 4. How much work does a football player do in the weight room when he squats 150 kg up a distance of 1 meter? How much work does he do if he does 3 sets of 10 squats in a row? Power 5. Calculate the power output of a motor that is able to do 1500 Joules of work in 30 seconds. Then, calculate and compare that power rating to another motor that does 1500 Joules of work in 15 seconds. 6. If a lawn mower engine is rated as a 1 Horsepower motor, its power rating is 746 Watts. Calculate how long it would take a 746 Watt motor to do 2000 Joules of work. 7. If the same 746 Watt motor were hooked up to a winch, how long would it take the motor to lift a 60 kg student up to the top of the Empire State building, which is 443 meters high? 8. How many Joules of energy are used by a 1119 Watt motor that is left running for 30 minutes? Potential Energy 9. How much potential energy does a 1500 kg roller coaster have when it is at the top of a 20 meter hill? 10. Calculate the potential energy of 4.3 x 106 kg of water at the top of Niagara Falls, which is 22 m high. 11. The energy content of 1 gallon of gasoline is 132,000,000 Joules per gallon. How high could you lift a 50 kg student into the air if all of this energy could be transferred? 12. Calculate the height of stairs a 60 kg student would have to run in order to burn off 1 Calorie of food energy, which is the equivalent of 4190 Joules. 13. Consider the combined mass of the cyclist and bike to be 80 kg. How much energy does a cyclist use in climbing Mount Ventoux in the Tour de France, which has a height of 1912 meters? Kinetic Energy 14. Calculate the kinetic energy of a car that has a mass of 1950 kg that is traveling 27 m/s. 15. Calculate the kinetic energy of a 0.050 kg bullet that is traveling 400 m/s. 16. How fast would a 60 kg student have to run in order to have a kinetic energy of 2000 Joules? 17. Calculate the kinetic energy of a 1000 kg car is traveling at 10 m/s, and then calculate and compare that energy to the kinetic energy the same car would have if it were going 20 m/s. (Note: the velocity doubled. What happened to the KE?) Elastic potential energy 18. A mass of 0.44 kg is placed on a spring and it stretches 0.051 m. Calculate the spring constant of the spring using Hooke’s law (F =kx). 19. Calculate the energy stored in a spring with a spring constant of 12 N/m when it is stretched out 0.35 meters. 20. How far does a spring with a spring constant of 15 N/m need to be compressed in order to store 20 J of energy? Conservation of Energy 21. An archer puts a 0.150-­‐kg arrow to the bowstring. An average force of 200 N is exerted to draw the string back a distance of 1.0 m. a)
b)
c)
d)
e)
How much work did the archer do to draw the arrow back? All of the work is stored in the bowstring as what form of energy? Just as the arrow leaves the bowstring, what form of energy does the arrow have? Assuming no frictional loss, with what speed does the arrow leave the bow? If the arrow were shot straight up, how high would it rise? PE = __________ PE = __________ PE = __________ KE = __________ Total=__________ KE = __________ Total=__________ KE = __________ Total=__________ 22. A 1000 kg roller coaster is moving slowly at 5 m/s at the top of a 20 meter hill. Assume that there is no air resistance or friction. a)
b)
c)
d)
e)
What is the potential energy at the top of the hill? What is the kinetic energy at the top of the hill? What is the total energy at the top of the hill? What is the speed of the roller coaster at the bottom of the hill? What is the speed of the roller coaster when it is up at the top of the second hill, which is 14 meters tall? 23. A pendulum with a mass of 2 kg is raised up to a height of 1 meter from the bottom of its swing. (a) Calculate the velocity of the pendulum at the very bottom of its swing. (b) If you replace the pendulum with a 4 kg mass and raise it to the same height of 1 meter, what will be its velocity at the bottom of the swing? (c) Explain how the answers to parts (a) and (b) make sense? 24. A Nerf dart with a mass of 0.020 kg is placed on a spring loaded gun. The spring constant is 112 N/m and the spring is compressed 0.12 meters. a) Calculate the energy stored in the spring. b) If there are no energy losses, how much kinetic energy should the dart have after it’s launched? c) What is the velocity of the dart immediately after launch? Answers 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
1500 J 1300 J 251,000 J 1470 J ; 44,100 J 50 W ; 100 W 2.7 s 350 s 2,014,200 J 294,000 J 8
9.3 x 10 J 270,000 m 7.1 m 6
1.5 x 10 J 711,000 J 4000 J 8.2 m/s 50,000 J ; 200,000 J k =85 N/m PE = 0.735 J 1.63 m (a) 200 J (d) 52 m/s (e) 136 m (a) 196,000 J (b) 12,500 J (c) 208,500 J (d) 20.4 m/s (e) 11.9 m/s 23. 4.4 m/s 24. (a) .806 J (b) same (c) 8.98 m/s