1. Sample answer: A simple machine is useful because it can provide mechanical advantage by multiplying force or distance. For example, levers are useful because you can arrange the fulcrum and the input and output arms to adjust the mechanical advantage of the lever. 2. Part A: input force; Part B: fulcrum; Part C: output force 3. The mechanical advantage of a machine is defined as the ratio of output force to input force. However, arriving at the mechanical advantage of a machine can be done using a variety of methods depending on the machine (such as using the ratio of the output lever arm length to the input lever arm length). 4. A broom is a third class lever. The fulcrum is at one end of the lever (where you hold one hand) and the input force is applied between the fulcrum and the output force (whisks of broom). This means the output arm is always longer than the input arm, which is a characteristic of third-class levers (mechanical advantage, then, is always less than 1.) 5. The answer is c. 6. Work accomplished is 2.5 joules. 7. The force was applied for 4 meters. 8. The work was accomplished with a force of 40 newtons (40 N 1,000 m = 40,000 joules). 9. The waiter is doing work in Situation 2 because he is applying a force to the cart in the direction that the cart is moving. In Situation 1, the waiter is applying force to the tray in the upward direction, but the tray is only moving forward as it is being carried. Therefore the waiter s upward force does no work on the tray. (Work is being done by friction in this case.) 1. The chemical energy from the food is transformed into kinetic energy as Martha rides her bike. As she moves uphill, some of her kinetic energy is changed into potential energy. Some of her kinetic energy is also changed into electrical energy by the generator and then into light energy by the light bulb. 2. Sample answer: Running out of energy just means that we are running out of certain forms of energy. Once we use fossil fuels for transportation by car or plane, for example, that fuel is used up because it has been converted to motion and heat. However, it has not been destroyed, just converted to forms that not longer give us the form of energy we need to keep our cars and planes moving. 3. Sample answer: Some of the car s fuel energy is converted to kinetic energy or electrical energy to keep the car s engine functioning. Because a car is not 100% efficient, some of the energy is lost as heat energy. This is why a car s engine and other mechanical devices get hot when they are working. 4. The ball has a kinetic energy of 2.25 J, so it will have a potential energy of 2.25 J when it stops. It must therefore have a height of 0.459 m. 5. Sample answer: Energy is like nature s money because you need energy to complete a task the way you need money to buy something. You cannot accomplish a task without energy. And sometimes you need to save or accumulate energy in order to be able to accomplish something. For example, if I wanted to run a marathon, I would need to make sure that my body has enough chemical energy to accomplish the task. Similarly, I would need to fill my car with gas in order to drive it. After I have spent my gas energy it is gone in the sense that it has been converted to heat or motion energy. I need to buy more gas to fill up my car! Because Venus is closer to the Sun, it should be warmer than Earth, and it is. The average temperature on Venus is 461.85 C, and it is constant both day and night. Venus has a thick atmosphere which helps keep it so hot day and night and a desert-like surface. 1. No, this example was not realistic because friction was ignored. However, for this machine input work and output work can be very similar as friction forces are small. 2. You need to divide output work by input work and multiply by 100 to get a percentage.
3. Answers: a. The output work would be 26 joules. b. Sample answer: Car manufacturers work on streamlining the car to reduce air friction that occurs when the car is moving. Manufacturers also reduce the weight of the car to reduce its inertia and make it more fuel efficient. Ball bearings and oil in the engine parts reduce friction in the engine and also make it more efficient. 4. (25 joules 50 joules) 100 = 50% 5. Power is work divided by the time it takes to accomplish the work. 6. Knowing this information, you can calculate the amount of work accomplished. Power time = work. 7. One horsepower equals 746 watts. 8. $0.08 36 kilowatts = $2.88. A two dollar gallon of gasoline would be less expensive. 9. (100 N 100 m) 100 seconds = 100 watts of power 10. The answer is: b 11. 100 horsepower 746 watts/horsepower = 74,600 watts 100 watts per light bulb = 746 light bulbs 12. 200 Calories 4,187 J/Calorie = 837,400 J 837,400 J/600 seconds = 1,396 watts or 1.87 horsepower 1. work 8. potential energy 2. lever 9. kinetic energy 3. mechanical advantage 10. joule 4. gear 11. chemical energy 5. simple machine 12. mechanical energy 6. machine 13. radiant energy, 7. input, output nuclear energy 14. law of conservation of energy 15. energy 16. power 17. horsepower 18. watt 19. efficiency, work output 20. work input 1. Answers: a. Correct. The formula for mechanical advantage using lever arm lengths is: input arm output arm. b. Correct. You can use the lever arm lengths to calculate the mechanical advantage. Then, using mechanical advantage and the value for input force, you can determine the output force. 2. Answers: Force Work done? Motion of the block A No No motion B Some Some motion C Yes Yes, in the direction of force C 3. Answers: a. You do work when you lift the boxes up off the floor. b. You don t do work when you stand and take a break on the landing between the two floors, even if you continue to hold the box. c. Yes, the elevator exerts an upward force on the boxes and moves them upward. d. It requires more work to lift the boxes up to the 5th floor because a force must be applied against gravity, and the boxes have an increase in height. e. The work would be the same because the force and distance would be the same in each case.
4. Sample answer: The design of a bicycle includes wheel and axle systems and gears. The gear shifters and brake calipers are levers. 5. The mechanical advantage for a second class lever is always greater than 1 because the input arm length is always longer than the output arm length. The mechanical advantage for a third class lever is always less than 1 because the input arm length is always shorter than the output arm length. 6. Answers: a. The wave has energy because it has enough force to move the sand of the sand castle. b. The houseplant grows better in the sunlight because the plant uses the Sun s energy to make food. Changes take place in the plant when it is exposed to sunlight. c. The plate has potential energy before it is dropped since it is off the ground. Then, the plate gains kinetic energy when it is dropped. When it hits the floor, the kinetic energy is converted to energy and forces that result in the plate breaking. d. Electricity is produced in our cities and towns by burning fossil fuels. This energy source is then used to work the motors of appliances like hair dryers so that we can move air around and cause water to evaporate off of our hair. 7. Answers: Potential energy Kinetic energy E p E k What happens to energy when the mass of an object increases? What happens when the object is lifted to a higher height (without a change in speed)? What happens when the speed of an object increases (without a change in height)? E p increases E p increases E p stays constant E k increases E k stays constant E k increases 8. Answers: a. The first hill is the largest so that the car has the most potential energy at the beginning of the roller coaster ride. This energy is then used to get the car moving all along the track. b. To create all the stored energy of the car on the top of the first hill, a motor is needed to pull the car up the hill. Once the car has potential energy in this position, a motor is no longer needed. The potential energy is then converted to kinetic energy to move along the track. c. Toward the bottom of hills, most of the potential energy is converted to kinetic energy and the car is moving really fast. When the car then goes up a hill, the kinetic energy is re-converted into potential energy. 9. Sample answer: I would say that the data does not look correct because you cannot have more output work accomplished than input work. The values can only be equal or nearly equal (in the event that there is no friction or very little friction) or output work is less (in the event of a lower efficiency machine). This data seems to indicate that there is error in the experiment or a mistake was made in recording the data. 10. Answers: a. Neither. Both boys do the same amount of work since they are both applying 500 newtons of force over 2 meters or 1,000 joules of work. b. Mikhail uses greater power in his lift since he accomplishes the lift in less time. Mikhail uses 500 watts of power whereas Tobias uses 250 watts of power. c. (1,000 joules work input) 100 = 8% 1,000 joules 0.08 = work input 12,500 joules = work input
1. Work done by the jack = 5,000 N 0.25 m = 1,250 joules 2. 40 joules of work = 50 N distance 40 J/50 N = 0.8 m Isabella lifts the box 0.8 meter. 3. In this case, the mechanical advantage is 0.7 (2 m 3 m). This lever does not multiply force as determined by the mechanical advantage of less than 1. This lever would, however, be able to multiply speed with which the work was being done. 4. Answers: a. The work is stored for a time in the bottle in the form of air pressure. When the bottle rocket is launched the air then does work on the bottle as it is released. b. The maximum kinetic energy that the rocket can have would be 2,000 joules. c. No, the rocket would have less than this amount of energy. Some of the work done to pump air into the bottle is lost as heat (due to friction between the parts of the pump) and some air might not efficiently push the bottle upward. Finally, the bottle will encounter air resistance that it has to push against. So some of its energy will be used to overcome air resistance. 5. 4,000 joules 6. The object could be moved over a distance of four meters. 7. = (0.1 kg)(9.8 m/s2)(5 m) = 4.9 joules 8. The time to life the object decreases. 9. (2,000 50 m)/5 s = 20,000 watts or 20 kilowatts or 26.8 horsepower 10. (1,000 N 20 m)/time = 8,000 watts time = 2.5 seconds 1. Sample answers: a. The machine I picked was an elevator. I can either use the elevator to get from the fourth floor to the first in my apartment building, or I can take the stairs. The same amount of work is done in both cases since the distance is the same and the amount of force (my weight and the weight of my things) is the same. However, in one case, I am using my own energy and I can feel that. That s how I know that work is being done. With the elevator, I don t have to expend my own energy to do the work. b. The power output was greater with the elevator because the elevator takes less time that I would spend taking the stairs. c. I think it is important to have machines because having certain machines is time-saving. However, if I rely on machines too much I might get out of shape. So, I would rather take the stairs than the elevator so that I am exercising and using my own energy. However, I would rather use a washing machine to wash my clothes than wash them by hand! 2. No, mechanical advantage is a value that does not have units. This is because the units cancel when doing the calculation (force units, for example, cancel when you divide output force by input force). 3. Solar energy is energy obtained from radiant energy. Photovoltaic cells can be used to convert this energy into electrical energy. Alternatively, radiant energy can be used to heat liquid so that steam is produce to turn a turbine and run a generator. Resources to research: U.S. Department of Energy (www.energy.gov), Energy Information Administration (www.eia.doe.gov), and American Solar Energy Society (www.ases.org). An excellent cover article on solar energy s potential for the future is in, January 2008, Volume 298, Number 1. Hydroelectric energy is energy obtained from water that is falling. The kinetic energy from the falling water is converted to electricity. Resources: U.S. Department of Energy (www.energy.gov) and the Energy Information Administration (www.eia.doe.gov). A table of the Net Generation from Hydroelectric (Conventional) Power by State by Sector, Year-to-Date through September 2007 and 2006 is at http:// www.eia.doe.gov/cneaf/solar.renewables/page/hydroelec/hydroelec.html).
4. Sample answer: Pros to using nuclear energy: Nuclear energy is one energy source that does not produce pollution or emissions that contribute to global warming. Nuclear energy is a non-polluting, large-scale producer of hydrogen fuel from water for cars should the country move toward this cleaner (less greenhouse gases emitted) fuel for cars and other forms of transportation. Cons to using nuclear energy: Nuclear energy production by nuclear plants does need water to cool down. Sometimes the heated water affects neighboring ecosystems. But, the main issue with nuclear energy is the fact that nuclear waste is produced that does not go away for thousands to millions of years. Nuclear waste is radioactive and very harmful to people. Resource: American Nuclear Society (www.ans.org). 5. The graph and answers: a. The mass of the object is 10 kilograms. b. Graph: The kinetic energy of the object is 4,500 joules. c. The relationship between kinetic energy and speed is exponential. 6. Answers: a. Potential energy = (100 kg)(9.8 m/s2)(20 m) = 19,600 joules b. 19,600 joules/s = 19,600 watts c. Modern water-powered turbines are very efficient at 90% efficiency or greater.