Energy ~ Learning Guide Name:

Transcription

1 Energy ~ Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the assignment is marked, based on effort, completeness, neatness, and accuracy. Every time you see a bold word, make sure you refer back to your "Submission Requirements." Do your best! Pre-Unit Thoughts: Why do you think it has been said that "all modern political decisions are related to energy?" Work and Energy: 1. Potential energy can be viewed as stored energy. This type of energy becomes able to do work most commonly when it changes forms. For example, gravitational potential energy means that an object s position in a gravitational field wants to fall. Once it falls it can do work as its potential energy is converted into kinetic. This is how hydro-electric dams work. They transfer the potential energy of water into kinetic energy as it falls. Then the kinetic energy is transformed into electric energy as the moving water turns the turbines and create electricity. Examine the list of energies presented in the notes. Pick out the energies that you would consider to be potential energies. Beside each choice briefly describe how this energy is stored and must be transformed to do work (you may use an example). Type of Potential Energy Why it is Potential Page 1 of 11

2 2. Work is a scalar quantity. However it is acceptable in physics to have negative work. What would this mean? Provide an example of negative work. 3. A car of mass 800kg is moving with a speed of 15m/s. a. Calculate its kinetic energy. (ans: 9 x 10 4 J) b. Calculate its kinetic energy if the speed of the car doubles. How does this compare to the original kinetic energy? (ans: 3.6 x 10 5 J, four times bigger) c. Calculate its velocity if its initial kinetic energy is doubled. (ans: 21.2 m/s) d. Examine your answer above and compare it to your original velocity. Use the equation to explain why doubling the original kinetic energy does not double your velocity? What, exactly, is the relationship between speed and kinetic energy? Page 2 of 11

3 4. If you push a 75 N block along a floor a distance of 4.2 m at a steady speed, and the coefficient of kinetic friction is 0.40, how much work will you do on the block? Show all work. (ans. 130 J). 5. The observation platform at the top of the Eiffel tower is 290m above the ground. a. How much work must the average person perform to climb to this level? Assume that an average person has a mass of 70 kg. (ans: 2.0 x 10 5 J) b. Would the amount of work done above be different if you stopped for a rest from time to time? Explain your answer. c. Would the amount of work change if you ran up some stairs and walked up others? Explain your answer. d. Repeat (b) and (c) above by replacing the word work with power. Question (b): Question (c): Page 3 of 11

4 6. A car of 1200 kg is travelling at 20 m/s when it slams on the brakes. a. How much kinetic energy does the car have before it hits the brakes? (ans: 2.4 x 10 5 J) b. Where does this energy go when the driver brakes to a stop? c. What is the work done by the car s brakes? (ans: -2.4 x 10 5 J) d. If the car brakes over a distance of 50 m before coming to rest, what is the force of friction provided by the brakes on the car? (ans: 4800 N) Power: 1. An express lift (elevator) takes a 70 kg passenger from street level to the top of a 400 m skyscraper in 4 minutes. The mass of the elevator itself is 500 kg. a. How much gravitational potential energy does the passenger gain on the way up? (ans: 2.74 x 10 5 J) b. At what rate (energy per second) is the passenger gaining potential energy? (ans: 1140 J/s) c. At what rate is the lift plus the passenger gaining potential energy? (ans: 9310 J/s) d. What power is the lift plus the passenger experiencing as it climbs? (ans: 9310 W) e. The motor driving the lift has an efficiency of only 25%. At what rate is the motor working as the lift is going up? (ans: 3.72 x 10 4 W) Page 4 of 11

5 2. How much work will a 4.0 HP (3 kw) motor do in half an hour? Show all work. (ans. 5.4 x 10 6 J ). Conservation of Energy: 1. The figure below shows a roller coaster. The 500 kg carriage is pulled up the first incline from ground level at A to the first peak at B. From here it then rolls freely from rest under the influence of gravity. a. Describe the energy transformations involved when the cart travels from B to C i. If track is frictionless: A to B: B to C: C to D: ii. If we include friction: A to B: B to C: C to D: b. If no friction forces are present, how fast will the cart be moving at location C? (ans: 26.2 m/s) c. Upon reaching location C the cart continues to roll freely to location D. How much gravitational potential energy does the cart gain from C to D? (ans: 9.8 x 10 4 J) Page 5 of 11

6 d. Based on your answer above, how much kinetic energy does the cart lose from C to D? Where did the kinetic energy go? (ans: x 10 4 J) e. What is the final speed of the cart at location D? (ans: 17.1 m/s) f. In reality we will always have friction. The final speed of the cart at location D is found to be only 13 m/s. What is the total amount of mechanical energy (both potential and kinetic) at location D? (ans: J) g. How much energy was lost overall from location B to D? (ans: J) h. Efficiency is a percentage that describes how much energy was conserved as useful energy between B and D. What is the efficiency of this coaster? (ans: 82 % efficient) 2. A pole-vaulter of mass 75 kg reaches a maximum speed of 7 m/s just before he jams his pole into the notch to launch himself over the bar. Assuming that his pole is only 80% efficient, what is the maximum height that the pole-vaulter can reach? (ans: 2.0 m) Page 6 of 11

7 3. Two rocks are thrown off of a cliff with the same initial speed, v. The first rock is launched with at an angle Ө directed below the horizontal as shown below as 1, while the second rock is launched above at the same angle. a. Predict how the final speeds of each rock compare just before they strike the water. Provide a brief explanation justifying your prediction. b. Measurements are taken and it turns out that both rocks strike the water below at precisely the identical speed. Justify using a conservation of energy argument. Use equations to aid your explanation. c. Justify using a kinematics argument (projectile motion). The diagram below might help your explanation. Page 7 of 11

8 d. Both arguments above assume that we are ignoring air resistance. Which rock would strike the water with a larger final velocity if we include air resistance? Use a conservation of energy argument to help with your solution. 4. A pendulum bob is moving 1.8 m/s at the bottom of its swing. To what height above the bottom of the swing will the bob travel? Show all work (ans m). 5. Tarzan grabs a vine 12 m long and swings on the end of it, like a pendulum. His starting point is 5.0 m above the lowest point in his swing. How fast is Tarzan moving as he passes through the bottom of the swing? Show all work (ans. 9.9 m/s). Thermal Energy: 1. You have six Styrofoam cups containing the same amount of water at 20 C. You also have six copper blocks whose masses and initial temperatures vary as shown below. One block goes into each cup. (Assume the mass of the water is 1000g.) a. The specific heat of copper is 385 J/(kgC) while that for water is 4180 J/(kgC). Based on these two numbers, which mass, copper or water, will undergo the greatest change in temperature? Use these specific heats to help explain why. Page 8 of 11

9 b. Based on your answer above estimate the final temperature of the system. A. B. C. D. E. F. c. What is providing the heat flow into the water? How can you calculate the approximate amount of heat available for the water? Show the equation and describe the variables specifically. 2. Considering the previous questions, rank these cups according to the maximum temperature of the water after the block is added. Focus on the heat added to the system by the copper. Background Knowledge: Criteria: Conclusion: Lowest (any calculations can be shown beside the corresponding situations above) Page 9 of 11

10 3. A kg block of iron is heated from 295 K to 325 K. How much heat is absorbed by the iron? Show all work. (ans. 5.4 x 10 3 J) 4. Phileas Fogg, the character who went around the world in 80 days, was very fussy about his bathwater temperature. It had to be exactly 38.0 o C. You are his butler, and one morning while checking his bath temperature, you notice that it s 42.0 o C. You plan to cool the kg of water to the desired temperature by adding an aluminum-duckie originally at freezer temperature ( o C). Of what mass should the Al-duckie be? [Specific heat of Al = 900 J/(kg o C)]. Assume that no heat is lost to the air. (ans: 30 kg) Page 10 of 11

11 5. Shown below are eight cars that are moving along horizontal roads at specified speeds. Also given are the masses of the cars. All of the cars are the same size and shape, but they are carrying loads with different masses. All of these cars are going to be stopped by plowing into identical barriers. All of the cars are going to be stopped by the same constant force by the barrier. Rank these situations from greatest to least on the basis of the stopping distance that will be needed to stop the cars with the same force. That is, put first the car that requires the longest stopping distance and put last the car that requires the shortest distance to stop the car with the same force. Background Knowledge: Criteria: Conclusion: Shortest (any calculations can be shown beside the corresponding situations above) Page 11 of 11