Speed (cm/s) Practice Final Exam (Answers keys) 1. A group of students arrange two level tracks side-by-side so they can have a race between two carts. They mount identical fan units (each with two real batteries) on two identical carts. When the two carts, with fans turned on, are released simultaneously from the end of the tracks they speed up at the same rate, traveling side-by-side, and so the race ends in a tie (Experiment 1). The students then add extra mass to one of the carts and repeat the experiment (using the same fan units), and record speed-time data for both carts (Experiment 2). a. The next week, when they look at the speed-time data they graphed (shown below), there are two lines (labeled A and B), and they are not sure which is which. Can you help by identifying which line represents the motion of the cart with the added mass? Justify your choice. 60 50 40 30 20 10 A B 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Time (s)
Line B represents the motion of the cart with added mass. Since the fan units were identical they would have provided the same strength force on each cart. However, the cart with the added mass would have sped-up more slowly than the one without the extra mass. The line that represents a lower rate of speeding up is B. However, one of the students remembers that they also attempted to break the tie in Experiment 1 by adding a additional battery to one of the fan units without adding extra mass to either cart (Experiment 3). Could the speed-time data shown in the graph on the previous page be from Experiment 3? Yes or No. Justify your answer. Yes, the data could be from Experiment 3. In this experiment two different strength forces were applied to identical carts. This would mean that the cart with the stronger fan force acting on it would speed up at a higher rate than the other cart this would correspond to line A, with line B being the cart with the weaker fan force acting on it. 2. In one of your experiments you used a friction cart with a fan mounted on it. You carefully adjusted the friction pad so that, with the fan running, the cart still did not move. However, you then made it move by giving it a push with your hand and found that the cart moved at a constant speed after the push. Using ideas about forces, write your own explanation for why the speed of the cart was constant after the push. Explanation: Why does the cart move at a constant speed after it is given a quick push? Draw the Force Diagram Force exerted on cart by fan unit Frictional force exerted on cart by track Write the explanation: When a balanced combination of forces acts on an object at rest it will remain at rest. With the fan running the cart did not move. This tells us the force that the fan unit exerted on the cart and the frictional force opposing motion were balanced. After being given a quick shove to get it started the force of the push was gone and so the only remaining forces acting on the cart were that of the fan unit and the frictional force opposing its motion, and we know
from before we know that these two forces are balanced. When balanced forces act on a moving object it will continue to move at a constant speed, so with these balanced forces acting on it the cart moves at a constant speed. 3. A child playing with a toy car gives it a quick shove on a smooth level floor. (The car does not have any type of motor inside it.) After his push, the car very gradually slows down and stops. Four students are discussing why the car very gradually slows down and stops, after the shove. The car slows down because the force pushing it forward is getting weaker and weaker. It slows because, after the shove, there is no more force to keep it moving. Kristen It slows down because the forces acting on it are balanced, and balanced forces make a moving object come to rest. Daryl The car slows down because there is a force acting on it in the opposite direction to its motion. Samantha Victor Which student do you agree with (if any)? Please explain your reasoning.
I agree with Victor. He has an idea that is consistent with those we developed in class; that objects slow and stop because a force (or unbalanced combination of forces) on them in a direction opposite to their motion. Kristen s idea is not consistent with our class ideas. She seems to be saying that there is still a force pushing the car forward after the initial shove, but our idea was that the force of the shove is gone as soon as the hand loses contact. Her idea that the car slows down because the forward force gets weaker is also inconsistent with our class ideas. We said objects slow down because stop because a force (or unbalanced combination of forces) on them in a direction opposite to their motion. Daryl s idea might be OK, but without more information it is impossible to tell. He implies that for the car to keep moving a force is needed in the direction of motion. If he is accounting for the effects of the friction force that slows the car down, he is correct, but he doesn t say that. On the other hand his thinking could be something like Kristen s, in that he thinks that for any motion to continue a continuous forward force is needed, even in the absence of friction, and without such a forward force it is just natural for the car to stop. This is not consistent with our class ideas. Samantha thinks that if balanced forces act on a moving object, then it will slow and stop. However, in class we found out that when balanced forces act on an object its speed will remain constant. So if balanced forces acted on the car after the initial shove then it would not slow down, but continue at a constant speed. Energy Description of Gravitational Interactions 4. An archer uses a bow to shoot an arrow straight up into the air on a still, calm day. The arrow rises to a certain height and then falls straight back down, sticking in the ground. The speed time graph for the arrow shown below is for the period starting just after it leaves the bow to just before it sticks in the ground.
a) At what time does the arrow reach its highest point? Briefly justify how you know. The arrow reaches its highest point at 5 seconds. We can tell this from the graph because it is at this time that it stops slowing down as it rises, stops for an instant at its highest point, and then begins to speed up again as it falls. b) Indicate on the graph the entire region during which the arrow was an energy receiver. Briefly justify how you know. The arrow was an energy receiver from 5 seconds to 10 seconds. You can tell this because it was during this period that it was speeding up, hence its kinetic energy was increasing, indicating it must be receiving mechanical energy in an interaction. c) During the entire time that the arrow was an energy receiver, what was the energy source? During this time the energy source was the gravitational field of the Earth and the arrow. 5. Imagine holding a small ball at arms length and then releasing it, so that it falls to the ground. (Assume air resistance is negligible.) a) Is the ball involved in an interaction as it falls? What evidence supports your answer? Yes, the ball is involved in an interaction as it falls, because it speeds up as it does so. b) Is the falling ball an energy source or an energy receiver? How do you know? The falling ball is an energy receiver. Since its kinetic energy is increasing as it falls it must be receiving mechanical energy in an interaction. c) What other object does the ball interact with while it is falling? Why does the interaction have only an imperceptible effect on this other object? The ball is interacting with the Earth as it falls. This interaction has only an imperceptible effect on the Earth because its mass is very much larger than the ball. d) Draw an energy diagram for the interaction that makes the ball fall.
Gravitational Interaction Energy Source Gravitational Field of Earth and Ball Mechanical Energy Energy Receiver Earth And Ball Decrease in stored gravitational field energy Increase in kinetic energy of ball (There is also an imperceptible increase in the kinetic energy of the Earth that may be omitted from the energy diagram.) 6. A small child attempts to push a box full of toys across the floor in his playroom. However, despite pushing as hard as he can, the box does not move. Which one of the following statements best describes the reason the box does not move while he is pushing it. a. The force resisting moving the box is greater in strength than the child s push. The child weighs less than the box does. b. The force resisting moving the box is equal in strength to the child s push. c. The strength of the child s push is greater than the strength of the force resisting moving the box, but not great enough to move it. Please explain your reasoning If an object is at rest and remains at rest, then the forces acting on it must be balanced. This means the force of the boy and the force resisting him must be equal. 7. The child in the previous question calls for help and his mother comes and helps him push the box, in the same direction. Which one of the following statements best describes why the box now begins to move. a. The combined push of the mother and child is equal in strength to the force resisting the movement of the box. b. The mother weighs more than the box does.
c. The combined push of the mother and child is greater in strength than the force resisting the movement of the box. d. The strength of the mother s push alone is greater in strength than the force resisting the movement of the box. Please explain your reasoning 8. Consider the following three arrangements of battery, bulb and wire(s). Circle the arrangement(s) where you predict the bulb would glow. In the space below the pictures, explain why you think so. If you do not think any of the bulbs would glow, explain why not. A. B. C. The tip of the bulb touches the positive end of the battery, on the knob. A wire touches the negative end of the battery and the flat part of the positive end of the battery. The screwy side of the bulb touches the negative end of the battery. A wire touches the bottom tip of the bulb and the flat part of the positive end of the battery. The bottom tip of the bulb touches the negative end of the battery. There are two wires. One wire touches the screwy side of the bulb and the negative end of the battery. The other wire touches the negative end of the battery and the knob on the positive end of the battery. In order for the bulb to light both its metal tip and the metal side need to be connected, one to each end of the battery. When this is done a complete circuit is established from one end of the battery, through the bulb, and then to the other end of the battery. Then electric current can flow round the circuit, through the bulb, thus making it light.
A WILL NOT LIGHT. The tip of the bulb is connected to the + end of the battery, but the side of bulb is not connected to anything. Electric current cannot flow through the bulb.. B WILL LIGHT. The metal tip of the bulb is connected to the + end of the battery by the wire (Note: the wire does not need to touch the knob on the end.) and the side of the bulb is connected to the end of the battery by touching it directly. Thus current can flow through the bulb and it will light. C WILL NOT LIGHT. Both the tip and the side of the bulb are connected to the end of the battery, the tip by touching it directly and the side by the wire. Neither part of the bulb is connected to the + end of the battery. Thus current cannot flow through the bulb and it will not light. (Note: the extra wire is actually a short circuit that connects the + and ends of the battery directly a high current will flow through this wire and it will get hot.) 9. Students in a class were trying to decide which was a better model for how electric current flowed in a circuit: the two flow model, in which current flows out of both the positive and negative ends of the battery and meets at the bulb; or the one flow model, in which current flows out of one end of the battery and travels all around the circuit, through the bulb, and into the other end of the battery. Below are representations of the two models. TWO FLOW MODEL ONE FLOW MODEL a) Describe one good example of evidence from an experiment you did in class that would support either the two flow or the one flow model, but not both.
In a regular circuit connected like this, with the two sides of the bulb holder connected to the + and ends of the same battery, the bulb lights We did an experiment in class where we connected the two sides of a bulb holder to the + and ends of two separate batteries, like this: In this set-up the bulb did not light! b) State which model, the two flow or the one flow, is supported by your evidence. This evidence supports the one flow model c) Carefully explain why your evidence supports the model you chose and not the other model. (In so doing it would be best to also describe what would have happened if the other model were a better model.) This evidence supports the one flow model because in the regular circuit the electric charges can flow out of one end of the battery, through the bulb, and back to the battery, through battery, and then back out into the circuit again. This could not happen in the second circuit since the charges flowing into the battery could not flow through it and back out into the circuit. The evidence does not support the two-flow model because it says electricity flow out from both ends of the battery and meets in the bulb, making it light. If this were the case the second circuit should still work since there are connections that would still allow this to happen from the two ends of the different batteries.
10. How did the blowing-through-straws analogy help you understand the idea that thinner bulb filaments have more resistance to the flow of electricity than thicker bulb filaments (of the same length)? In answering this question, make sure you refer specifically to what was done in the experiments you did in class and how that helped you change or enhance your own model or idea. Note: Acceptable student responses to this question will vary depending on what model or ideas they had before being introduced to the blowing-through-straws analogy, and how they interpreted the analogy itself. Given below is an example of students using the analogy to move from an idea of the independence of resistance to variations in thickness, to a definite dependence. When thinking about resistance of bulb filaments we first though that they would all be the same, since we thought that the battery supplied the same current to all bulbs and so the resistance to current flow in all circuits would be the same. We then blew through a thin straw and a thicker straw of the same length and made two observations: i. It was easier to blow through the thicker straw ii. For the same strength blow, more air flowed through the thicker straw than the thinner straw This meant the thinner straw had more resistance to air flow through it than the thicker straw. This made us think that perhaps in a bulb it is easier to push the charges through a thicker filament than a thinner filament. Therefore, for the same push from a battery, there would be more current flowing through a thicker filament than a thinner filament. This would then also mean that the thicker filament must have less resistance to the flow of electricity than the thinner filament. Since more current also means a brighter bulb, this would mean that when connected to the same battery (or other power source) a bulb with a thicker filament would glow brighter than a bulb with a thinner filament of the same length. We confirmed these ideas in two ways. Firstly we used the simulator and saw that as we increased the resistance of the bulb in a circuit the current in then circuit decreased and the brightness of the bulb decreased also. For an object at rest to start moving, the forces acting on it must be unbalanced. This means the combined forces of the boy and the mother must be greater than the force resisting them.
11. Below is a circuit with three batteries, an ammeter and three bulbs. The ammeter reads 337.3 ma, and all three bulbs glow equally bright. Imagine that the bulb on the left is removed from its socket; everything else remains the same nothing else is changed. (In the picture below, the ammeter and bulbs are covered so you cannot tell what happens.) a) Would the ammeter reading be higher, lower or remain at 337.3 ma? Briefly explain in terms of electric circuit ideas. This is a PARALLEL circuit. In a parallel circuit each loop is an independent circuit and the current flowing through each loop is determined only by the bulb(s) in it. The battery will supply whatever total amount of current is needed. In the circuit above the ammeter is measuring the total current flowing out of the battery, before it splits and goes into the separate loops. Removing the left bulb means that loop is now open and no current will flow through it. However, this has no affect whatsoever on the current flowing through the other two loops. Since the battery only now needs to supply current to two loops instead of three, the total current it has to supply will decrease. Therefore the reading on the ammeter will DECREASE. b) After the left bulb is removed, would the bulb on the far right get brighter, get dimmer or remain just as it is now? Briefly explain in terms of electric circuit ideas.
As stated above, in a parallel circuit all of the loops are independent of each other. Therefore, removing the left bulb will not affect the current flowing through the other loops and the bulb on the right will REMAIN JUST AS BRIGHT IT IS. 12. To the right is a circuit with one battery and one bulb. The bulb glows with a certain brightness. In the space below, draw two different circuits. One must be a parallel circuit and one must be a series circuit. Each circuit must include two bulbs and any number of batteries that you need. However, all the bulbs in the two circuits must glow with the same brightness as the bulb to the right. Make sure you draw your circuit diagrams carefully so it is clear how bulbs and batteries are connected to each other. For each circuit, briefly explain (in terms of electric circuit ideas) why all the bulbs glow with the same brightness as the one above. Series Circuit Parallel Circuit In this series circuit there are two identical bulbs in a single loop. This means there is more resistance in the loop than if only one bulb were present and so, with only a single battery a smaller current would flow, making the bulbs dimmer. However, by adding a second battery the push of the batteries is doubled and so the current flowing will be doubled also. This will mean the current flowing will now be the same as in a one-battery, one-bulb circuit, so the two bulbs will glow with the same brightness as the single bulb in the circuit above. In this parallel circuit there are two identical bulbs connected to a single battery, each in their own loop. In a parallel circuit each loop behaves independently, as if it were the only loop connected to the battery. This mean the current flowing in each loop in this parallel circuit will be the same as in a one-battery, one-bulb circuit. Therefore each bulb will glow with the same brightness as the single bulb in the circuit above.
13. Students in a class were trying to decide which was a better model for how electric current flowed in a circuit: the two flow model, in which current flows out of both the positive and negative ends of the battery and meets at the bulb; or the one flow model, in which current flows out of one end of the battery and travels all around the circuit, through the bulb, and into the other end of the battery. Below are representations of the two models. TWO FLOW MODEL ONE FLOW MODEL d) Describe one good example of evidence from an experiment you did in class that would support either the two flow or the one flow model, but not both. In a regular circuit connected like this, with the two sides of the bulb holder connected to the + and ends of the same battery, the bulb lights We did an experiment in class where we connected the two sides of a bulb holder to the + and ends of two separate batteries, like this: In this set-up the bulb did not light! e) State which model, the two flow or the one flow, is supported by your evidence.
This evidence supports the one flow model f) Carefully explain why your evidence supports the model you chose and not the other model. (In so doing it would be best to also describe what would have happened if the other model were a better model.) This evidence supports the one flow model because in the regular circuit the electric charges can flow out of one end of the battery, through the bulb, and back to the battery, through battery, and then back out into the circuit again. This could not happen in the second circuit since the charges flowing into the battery could not flow through it and back out into the circuit. The evidence does not support the two-flow model because it says electricity flow out from both ends of the battery and meets in the bulb, making it light. If this were the case the second circuit should still work since there are connections that would still allow this to happen from the two ends of the different batteries. 14. Below are four pictures from the Electricity and Magnetism Field Patterns Simulator, showing different arrangements of magnets with a nearby Magnetic Field Meter. Identify the two arrangements that would produce the highest and lowest readings on the Field Meter. A. B. C. D. Lowest Highest Briefly justify your answers. We learned from the simulator homework that strong magnetic fields are produced when many small magnets are aligned in the same direction and weak fields are produced when equal numbers are aligned in opposite directions. In D there are three small magnets, all in the same direction, so this will produce a strong field. In C the four magnets are aligned in opposite directions, so they cancel each other out to a large degree. 15. A student did an experiment to determine whether the size of a nail makes a difference in how strong it can be magnetically. She used two nails, one large, one small.
S N S N S N S N S N S N S N S N S N S N S N S N S N S N S N S N S N S N She rubbed the two nails identically with a bar magnet (rubbing the south pole of the magnet from tip to head of each nail). To determine the strength of the magnetic field produced by each rubbed nail, she placed a magnetic field meter (similar to the one used in the simulator) equal distances from the tip of each nail. Which nail do you think produced the higher reading on the magnetic field meter? Explain your thinking in terms of the domain model. (Write some sentences and draw some pictures. You do not need to identify the interacting objects, nor draw force or energy diagrams.) The larger nail will produce the higher reading on the magnetic field meter. There are more magnetic domains in a large nail than in a small nail. We know from the simulator homework that when a large number of domains is aligned in the same direction it produces a stronger magnetic field than when a smaller number is aligned. Thus when the two nails are rubbed, the larger one has more aligned domains, making it a stronger magnet. 16. Imagine taking an elevator ride from the1 st floor to the 10 th floor of a building. While moving between the 1 st and 2 nd floors the elevator speeds up, but then moves at a constant speed between the 2 nd and 9 th floors. Which one of the following statements about the elevator best describes the forces acting on it, as it moves upward at a constant speed? (Assume any frictional forces can be neglected.) Circle your choice. The upward pull of the cable is stronger than the downward gravitational pull of the Earth. g) The upward pull of the cable is equal in strength to the downward gravitational pull of the Earth. h) The upward pull of the cable is weaker than the downward gravitational pull of the Earth.
Explain your reasoning When an object moves at a constant speed the forces acting on it must be balanced. In this case the only two forces involved are the downward gravitational pull of the Earth and the upward pull of the cable. For the forces to be balanced these two must be equal in strength. (If one of the forces was stronger than the other, the forces would be unbalanced and the speed of the elevator would be changing.) 17. You have observed that mercury rises in a thermometer when placed in hot water. Carefully draw two particle-level (microscopic) models of the mercury one at 32 C and 87 C. Describe how your drawings account for the observed thermal expansion of mercury in the closed system of the thermometer. As the mercury warms up the mercury particles move further away from each other, so there are fewer in the microscopic window as shown above. Since each of the particles moves further away, the mercury liquid takes up more volume, that is, it expands. (Note: it would be wrong to show each particle growing in size when heated.)
The density of the mercury changes during thermal expansion? Does it increase or decrease? Describe how your drawings account for this change in density. The density of the mercury decreases as it expands. We know this because the same amount of mercury is taking up more volume. Since density is mass/volume this ratio decreases. The drawings show this because fewer particles are visible in the ultrascope window, meaning there is less mass in the same volume. 18. A scientist collected the following data for ethanol: i. The melting point of ethanol is -114 C; the boiling point of ethanol is 78 C. ii. The specific heat of solid and gaseous ethanol are ~ 0.3 cal/g C; the specific heat of liquid ethanol is ~0.6 cal/g C. iii. Boiling liquid ethanol requires twice as much heat energy than melting the same mass of solid ethanol. Select the graph that best represents the heating curve for ethanol given the data above.
In the space below, explain why you chose the graph that you did. For maximum credit, be sure that your explanation describes how the graph addresses data i, ii, and iii. Graph A is the correct graph. (i) the melting point is the short horizontal line at -114 C and the boiling point is the longer horizontal line at 78 C. (ii) the specific heat of solid and gaseous ethanol is twice that as liquid ethanol; specific heat is the amount of heat energy (related to the amount of time required at constant heating) required to raise the temperature of one gram by 1 C. On the heating curve, the greater the slope, the lower the specific heat. On graph A, the slope for the warming liquid is less than the slope for the warming solid or gas, implying the specific heat for the liquid is greater than the specific heat for the solid or gas. (iii) On the heating curve, the length of the horizontal segments are related to the amount of heat energy required for all the material to change phase. Since the horizontal line for boiling is about twice that for melting, it would take twice as much heat energy to boil the liquid ethanol than to melt an equal mass of solid ethanol. At room temperature both water and ethanol are liquids, but at 90 C, water is still liquid and ethanol is a gas. What does this suggest about the attractive forces between particles of ethanol in comparison to those of water? 19. Rocky grabs a cold can of soda from the refrigerator and sits down on his soft chair to watch some TV. He falls asleep almost immediately, while still holding the can. After about ten minutes he wakes up and, to his disappointment, the can of soda is no longer cold. Explain why the can warms up by filling in the following steps. What is the type of interaction that causes the soda can to become warmer and what are the interacting objects? The main interaction that causes the soda can to become warmer is the heat conduction interaction between Rocky s hand and the can. a) Draw a Source/Receiver energy diagram to describe the interaction. Include the interacting objects, and label the interaction type, energy transfer and the energy changes within the interacting objects.
Heat Conduction Interaction Hand Heat Energy Can Decrease in thermal energy Increase in thermal energy b) Write a few sentences to explain why the can becomes warmer. While Rocky is holding the can there is a Heat Conduction Interaction between his warm hand and the cold soda can, during which there is a transfer of heat energy from the hand to the can. This input of heat energy to the soda can means that its thermal energy increases. This increase in thermal energy means of the soda can means that its temperature rises and so it becomes warmer. 20 (5 points) A boy has a ball in his hand. He then tosses the ball straight upward. The ball rises to a certain height and then falls back down, and is caught by the boy again. Below, sketch a speed-time graph for the entire history of the ball s motion. Use the following labels to show on the graph each separate part of the ball s motion. TOSSES RISES FALLS CAUGHT
Rises Falls Caught Tosses i) Draw a force diagram for the ball for the part of the motion where it is being tossed upwards. Make sure you label the force(s), pay attention to the length(s), and also include a motion arrow. Force exerted on ball by the Gravitational force exerted on ball by the j) Draw an energy diagram for the part of the motion where the ball is falling back down, but before it is caught. Consider the ball and earth as a single system. Earth And Ball Increase in kinetic energy Decrease in gravitational potential energy
21) Imagine you are standing waist deep in water in a lake at night. You have a flashlight in your hand. A friend who is under the water wants you to shine your light on a non-shiny white object at the bottom of the lake, so he can see it. Below is a side view diagram of your eye, your friend s eye and your flashlight. Also shown is the surface of the lake, the bottom of the lake, and the object. Carefully draw a light ray diagram, showing how light goes from your flashlight to the object, and how your friend can see it. (You may re-aim the flashlight in any direction you think is necessary.) You do not need to write an explanation. 22) After performing some experiments with magnet-rubbed and un-rubbed nails, students were asked to propose a model to describe the difference. Some students came up with the following model:
Before Rubbing After Rubbing a. What magnetism behavior can this model account for quite well? There are a few behaviors that this model can account for quite well. For example: the observation that when a nail is rubbed with a magnet its ends behave differently, with like ends attracting and unlike ends repelling. It would account for this by saying that N and S entities attract each other, but N and N, or S and S, entities repel each other. (It could also account for the observation that when a rubbed nail is hammered it becomes un-rubbed, by saying that hammering the nail mixes up the N and S entities again.) b. What magnetism behavior can this model not account for at all? This model cannot account for what is observed when a rubbed nail is cut in half. According to this model when a rubbed nail is cut, the tip half will have all the S entities at the tip end (making a South pole) and nothing at the cut end (making No pole). Meanwhile the head half will have all N entities at the head end (making a North pole) and nothing at the cut end (making No pole). However, we know from observation that when a rubbed nail is cut in half, each half will have both a North and South pole. N NoP S NoP N S N S Model Prediction Observation 23) If you hold the head of an unrubbed nail near the North Pole of a magnet, the nail becomes magnetized with its head acting like a South Pole. Suppose you then turned the magnet around, as shown to the right. What do you predict will happen to the nail? (Circle one of the following choices.) c. the nail is magnetized, with its head a north pole d. the nail is magnetized, with its head a south pole e. the nail becomes un-magnetized Justify your prediction in terms of the domain model of magnetism.
When the head of the un-rubbed nail is brought close to the North Pole of the magnet the south end of all the domains in the nail are attracted to the magnet and the north ends of the domains are repelled. This means that the domains will line themselves up with all the south ends pointing toward the magnet, making the head end a South Pole. N S N S N S N S N S N S N S Now, when the head of the un-rubbed nail is brought close to the South Pole of the magnet the north end of all the domains in the nail will be attracted to the magnet and the south ends of the domains will repelled. This means that the domains will flip over and line themselves up with all the north ends pointing toward the magnet, making the head end North Pole. S N S N S N S N S N S N S N