PUM Physics II - Work & Energy Lesson 3 Solutions Page 1 of 13

Transcription

1 PUM Physics II - Work & Energy Lesson 3 Solutions Page 1 of Represent and Reason a) Charts are a useful way to organize data visually. They allow us to see patterns of data that we might otherwise miss if were just staring at individual data points. From these patterns we can then construct mathematical relationships. b) c) d) Placed side by side the two the two charts show the process of my money going from my bank into my pocket.

2 PUM Physics II - Work & Energy Lesson 3 Solutions Page 2 of Represent Situation Before and After a) You have $15 in your pocket, $60 in your ATM account, and a gift card with $20 on it. You withdraw $20 cash from the ATM. Represent this transaction on the bar chart. Did you earn or spend any money? No. Represent this transaction with a mathematical statement. Bar Chart Representation P+C ATM +C Gift = P+C ATM +C Gift $15+$60+$20 = $35+$40+$20 b) Next, you buy a snow shovel for $10 cash at Jones Hardware. Represent this transaction on the bar chart. Did you earn or spend any money? Yes, I spent $10 from my pocket Represent this transaction with a mathematical statement. P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift $35+$40+$20+(-$10)= $25+$40+$20 c) After returning from the hardware store, you spend three hours shoveling snow for an old lady who gives you $20 cash. Represent this transaction on the bar chart. Did you earn or spend any money? Yes, I earned $20 and put that in my pocket. Represent this transaction with a mathematical statement. P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift $25+$40+$20+($20)= $45+$40+$20

3 PUM Physics II - Work & Energy Lesson 3 Solutions Page 3 of 13 Situation Before and After d) When you are finished shoveling, you spend $20 cash to put gas in your car so you can drive to the Best Buy. Represent this transaction on the bar chart. Did you earn or spend any money? Yes, I spent $20 out of my pocket. Represent this transaction with a mathematical statement. Bar Chart Representation P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift $45+$40+$20+(-$20)= $25+$40+$20 e) At Best Buy, you purchase a "Cher's Greatest Hits" DVD Box Set for $40. You empty out your gift card and use your ATM card to pay for the rest. Represent this transaction on the bar chart. Did you earn or spend any money? Yes, I spent my gift card and $20 on my ATM card Represent this transaction with a mathematical statement. P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift $25+$40+$20+(-$40)= $25+$20+$0 f) What happens next? Continue the story and make a graph to match. I ask my parents for money and they give me my $40 allowance.

4 PUM Physics II - Work & Energy Lesson 3 Solutions Page 4 of 13 Situation Before and After g) Does this graph show something that could happen? If not, explain why not. If so, describe a situation it could match. Bar Chart Representation No, it just doesn t add up. I began with $50 in my pocket, $30 in the ATM, and $10 on my gift card so $90 total. I did not Earn/Spend anything and yet I end up with $30 in my pocket, $20 in the ATM, and $30 on my gift card so $80 total. This means that $10 is not accounted for. h) Draw the missing bar. Write a mathematical statement to match the chart. P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift Describe a story that could match. I got my $60 paycheck for the week and cashed it in at the bank. i) Make a chart to match this mathematical statement: $20 + $0 + $0 + $40 = $20 + $40 + $0 Describe a story that could match. I had $20 in my pocket and no money in my ATM and no gift card. My mom deposted $40 dollars in my bank account. j) P+C ATM +C Gift +Earn/Spend = P+C ATM +C Gift k) In any situation where no money was earned or spent, money was not constant. In all situations however money was conserved. l) Energy also seems to be conserved. It is constant when we choose our system properly and no work is done on our system. Work is like Earning/Spending energy! When positive work is done on the system its like earning money. When negative work is done on the system it is like spending money.

5 PUM Physics II - Work & Energy Lesson 3 Solutions Page 5 of 13 m) Money is conserved and when you do not earn or spend any money it is constant at least for you (the system). n) Momentum and mass are quantities that are also conserved. Quantities like velocity, acceleration, and force are not conserved quantities. 3.3 Represent and Reason a) The system is Jessica and Earth. b) The initial state is on the first floor. The final state is on the 4 th floor. Initial Final System System c) Earth Earth The elevator does positive work on my system to increase the gravitational potential energy.

6 PUM Physics II - Work & Energy Lesson 3 Solutions Page 6 of Represent and Reason a) Initial State Final State Construct the Work-Energy Bar Chart The bob has no velocity and is at the highest point of the swing. The bob is at the bottom of the swing and is going really fast. System: The system is the bob, Earth, and the rope. Equation: U g,i = K f Initial State Final State Construct the Work-Energy Bar Chart The bob is at the bottom of the swing moving really fast. The bob gets to the top of the swing and slows down. System: The system is the bob, Earth, Equation: K f = U g,i and the rope. Initial State Final State Construct the Work-Energy Bar Chart The bob has no velocity and is at the highest point of the swing. The bob is at the bottom of the swing and is going really fast backwards.

7 PUM Physics II - Work & Energy Lesson 3 Solutions Page 7 of 13 System: The system is the bob, Earth, Equation: U g,i = K f and the rope. Initial State Final State Construct the Work-Energy Bar Chart The bob has come to a stop at the top of the swing s motion and begins to swing forward. After a few swings the bob eventually comes to a stop at the center of the swing. System: The system is the bob, Earth, and the rope. Equation: U g,i = ΔU int b) The total energy of the system was conserved and constant. This assumes that no work was done on the system by an external force due to another object, for instance very little air resistance. c) If the rope is not included in the system then it does a negative amount of work to reduce the gravitational potential energy of the system, slowing the pendulum to a stop. 3.5 Reason If Theo and the cannon are the system then: (4) Earth does negative work on the system to decrease the total amount of energy so that U s,i > K f

8 PUM Physics II - Work & Energy Lesson 3 Solutions Page 8 of 13 a) If Theo and Earth are the system then: (2) b) Energy is constant in (1) because no work is done on the system so the total amount of energy in the system remains the same. c) In (1), (2) and (4) energy is conserved because the total amount of energy before and after, when considering the work done by an external object exerting an unbalanced force on the system, is equal. In (3) there is an additional 2 units of energy after considering the before state and the work done in between, so energy was not conserved in this bar chart. 3.6 Bar Chart Jeopardy Homework Bar chart for a process. before after K i + U g,i + U s,i + W = K f + U g,f + U s,f + U int State what is in your system. Describe in words one possible consistent process. I drop a water balloon off the side of a cliff onto my unsuspecting friend. Sketch the process just described. Initial Final Relate these quantities mathematically: U g,i = K f + U g,f The system is the water balloon and Earth. The initial state is the water balloon in my hand. The final stage is somewhere* in between my hand and my friend below. * Somewhere is before the half way point where there is still more gravitational potential energy than kinetic energy.

9 PUM Physics II - Work & Energy Lesson 3 Solutions Page 9 of 13 Bar chart for a process. before after K i + U g,i + U s,i + W = K f + U g,f + U s,f + U int + 0 State what is in your system. Describe in words one possible consistent process. A car screeches to a halt, the tires of the car start smoking. The system is the car (including the tires) and ground. Sketch the process just described. v Initial - The initial state is the car speeding along. v = 0 Final The final state is after it has applied the brakes and come to a stop with the tires smoking. Relate these quantities mathematically: K i = ΔU int 3.7 Reason a) My answer is similar to Alan s. See 3.3 Represent and Reason. b) The bar chart was very useful for Alan. It allowed him to see what his energies were and keep track of the changes. He realized that he needed to include the work done by the elevator because his before and after states didn t match up. c) They represent the amount of that type of energy or work. d) The length of the bars does not matter so long as Alan keeps the relative lengths the same. If the bars representing work and gravitational potential energy were not the same then the bar chart would not have made sense. e) Self evaluation. Students may have difficulty choosing a system or defining an initial and final state. For instance if Earth was not included in the system then there would be nothing on the bar chart. The work done by the elevator and Earth would cancel out. If students also included the elevator in the system then the change in gravitational potential energy would have to come from a negative ΔU int in the elevator. Students may also be tempted to say that there is kinetic energy in the system. This all depends on the choice of initial and final states. In between the first and fourth floor there is both kinetic and gravitational potential energy.

10 PUM Physics II - Work & Energy Lesson 3 Solutions Page 10 of Reason a) Both the work bar and the final gravitational potential energy bar would be halved. Since there would only be half as much gravitational potential energy in the end and it would have taken half as much work to get there. b) If Jessica was still moving and the initial state was still the same (not moving initially): Work is done by the elevator to increase the kinetic and gravitational potential energy of the system. c) W Elevator = U g,f Jessica-Earth d) The elevator is already initially moving as it comes to the first floor from the basement. The elevator continues to move at constant velocity as it goes to the fourth floor. The final state is somewhere between the third and fourth floor before the elevator starts to slow to a stop. Work is being done by the elevator to increase the gravitational potential energy of the Jessica-Earth system.

11 PUM Physics II - Work & Energy Lesson 3 Solutions Page 11 of Represent and Reason Situation Before and After You have some food in your pantry and refrigerator already. Bar Chart Representation before after buy or F P,i +F R,i + F S,i + discard =F P,f +F R,f +F S,f + U ate You go shopping and come home with bags of groceries. You put some away in the pantry and some away in the refrigerator Represent this on the bar chart. The situation starts from where we left off in the previous question. before buy or F P,i +F R,i + F S,i + discard after =F P,f +F R,f +F S,f + U ate You take some ingredients from the pantry and some from the refrigerator and make a meal on the stove. + 0 Represent this on the bar chart. - You eat half of the food you cooked and store the rest in the refrigerator. before after buy or F P,i +F R,i + F S,i + discard =F P,f +F R,f +F S,f + U ate Represent this on the bar chart.

12 PUM Physics II - Work & Energy Lesson 3 Solutions Page 12 of 13 Situation Before and After The next day you come home with a takeout from White Castle. You eat the stack of White Castles and throw out your leftovers from the day before. + Bar Chart Representation before after buy or F P,i +F R,i + F S,i + discard =F P,f +F R,f +F S,f + U ate 0 - Represent this on the bar chart. e) ΔU ate represents the change in how much U ate before and after. Since before hand you could have already had food in your stomach, it is difficult to keep track of U ate,i and U ate, f. Therefore we talk about ΔU ate, which goes on the right since it represents the change. This is the same with internal energy. There is always some amount of internal energy initially present so we are interested in the change or ΔU int Observe and Reason a) The system is the skateboarder and Earth. b) From the top to the bottom: From the bottom to the top: c) The skater seems to be moving the fastest at the bottom of the track, meaning this is where he has the greatest kinetic energy. d) The system has the highest gravitational potential energy at the ends of the track on either side, when he reaches the highest point.

13 PUM Physics II - Work & Energy Lesson 3 Solutions Page 13 of 13 e) If the skater was the system he could have kinetic energy by himself but not gravitational potential energy by himself without including Earth in the system. f) The two charts are the same in the way they represent energy with bars. It differs in that the PhET bar chart is in real time and shows how the types of energy transform from one to the other. There is no elastic potential energy.there is no negative section of the graph. And there is a total energy and thermal energy bar. g) The total column represents the total amount of energy in the system (kinetic energy + gravitational potential energy) at any given time, which is constant in this system. h) Thermal energy could stand for internal energy. i) When you increase the coefficient of friction the thermal energy bar gets bigger over time until the skater comes to a rest. If we include the track as part of the system then we can explain the increase in thermal energy as a change in internal energy. Kinetic energy is being converted into internal energy as the skater slows down to a stop Reason a) Energy is constant whenever there is no work done on the system. This depends on how we define our system. b) Energy is always conserved so long as we carefully keep track of it with a bar chart. Energy in a system may change, but if we consider the work done on that system then energy is conserved. c) Work changes the energy of a system. Thus when work is done on our system the energy does not remain constant, but it is conserved.