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| Hooke's Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance is proportional to that distance. |
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| The negative sign in Hooke's law indicates: |
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| The force a spring provides is always restoring force: The force always points "inward" to the unstretched/uncompressed location. |
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| Always write that the magnitude of the spring force is kx, and then indicate its direction on a free body diagram. Important: Note that the spring constant "k" is always a positive constant for real-life springs. Its units are Newtons per meter (N/m). It determines how much force the spring will provide for a given distortion (stretch or compression). |
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| True or false: A spring that is "soft" has a smaller spring constant than one that is "firm," meaning that the soft spring will stretch or compress more for a given amount of applied force. |
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True
Because: The string stretches or compresses until it is in equilibrium with any applied force (ex. a weight that is hung from it). this force has the magnitude of F, where, F=kx (ignoring the "-" which indicates the force points towards the unstretched end of the spring, aka. is "restorative"). We can rearrange this to solve for the distance of stretch or compression as x = F/k. A soft spring stretches easily (has a large x). To get this, we need a small k for the same (given) F. Or just remember... hard spring, large k... soft spring, small k. |
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| Whenever the net force on an object is zero, the object: |
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Definition
is in translational equilibrium.
Because: This question covers material we had earlier, but is repeated here to note that the spring stretches or compresses until the force it is applying equals any force that is applied to it. Also note that if the spring is oscillating (later) that the force is zero as the object is in translation through this point (but not zero at other points in the oscillation). |
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| You place a watermelon in the basket of a grocery-store spring scale. The spring scale works because: |
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Definition
the stretch of the spring has been calibrated to standardized weights.
Because: Note the many of these choices relate different measurables with very different units... that's a clue that they are the wrong choices. Weight (in N) can't equal length (in m) or energy (in J). Also, if the watermelon stretched the spring to the elastic limit, the reading would be the maximum reading on the scale... not necessarily the true weight, and getting near a range of unreliability. It's DEFINITELY untrue if the scale reading cycles around back to smaller weights! You're therefore left with the correct answer.... the stretch of the spring has been calibrated. |
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You are an interplanetary entrepreneur. The citizens of Planet Y have a heavy demand for chocolate-coated fireflies. Your boxes are sometimes labelled by volume, sometimes by weight, and sometimes by mass. The gravitational acceleration constant on Planet Y is slightly less than that on Earth. When you ship a box of chocolate-coated fireflies, a shipment is stopped in customs on Planet Y for labeling violations. What happened?
1) The boxes that list the volume of the contents are mislabeled.
2) The boxes that list the weight of the contents are mislabeled.
3) The boxes that list the mass of the contents are mislabeled |
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Definition
2 only.
Because: Mass is completely independent of g. Volume of a solid will probably not be changed by a slight decrease in g, but even if it did, it is likely to expand in the case where the gravitational constant is small (because there's probably less atmosphere on the planet, because air is held to a planet through gravity, and less atmospheric pressure.. so if anything your boxes will say they have less volume than they do, an unlikely reason to get stopped in customs (and don't worry about volumes/pressure until late this month!).
On the other hand, the weight of the object (mg) is likely to change in a manner that customs will care about. If you ship items from a planet with a high g to one with a low g, the weight decreases. You'd be stopped in customs for claiming your item weighs more than it does. Be sure you know the units of these measurements! |
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| You drop a bag of apples on a hanging scale at the grocery (it is not digital). It bounces around for a while before reaching equilibrium. What do you see on the scale during the bouncing process? |
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Definition
The reading oscillates, with a higher weight showing when it is lower than the equilibrium point and a lower reading when it is higher than the equilibrium point.
Because: A spring scale reading indicates the force that the scale is providing. When the bouncing motion is below the equilibrium point, the spring provides an extra bit of force trying return it to the middle, so the scale reading is higher than the true weight. When the basket in above the equilibrium point, the spring is not providing as strong a force (instead of supporting the weight it is allowing some of the weight to return the basket back to the middle), so the spring scale reading is lower than the true weight. |
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| You have a spring and a bag of apples. You hang the apples on the spring and measure the stretch of the spring. Then you give the spring and apples to your friend, who is traveling to the Moon. When your friend does the same experiment on the Moon, the stretch of the spring is: |
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Definition
Shorter: The gravitational acceleration constant on the Moon is smaller, so the force on the scale is smaller.
Because: The spring constant and mass are unchanged when you move to another planet (or moon). The spring constant is determined by what material the spring is made of and the dimensions of its coils (especially their thickness). However, the spring stretches according to the force that is pulling on it. This is the object's weight. Since weight is a product of mass and local gravitational acceleration (mg), and g is only 1.63 m/s2 on the Moon instead of 9.8 m/s2 as on Earth, the force the spring experiences is less... so its stretch is shorter. |
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| You and your identical twin (who weighs the same as you) hang some bungee cords from the ceiling of your room and add a board to make a seat. You sit in it and observe that while it stretches some length, you are still well above the floor. When your identical twin joins you in the seat,the bungee cords stretch: |
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Definition
twice as much.
Because: This is a direct application of Hooke's law. If you put twice the force (in this case the weight, in N) on, it will stretch twice as much, as long as you are within the elastic limit. A bungee cord is rated to behave elastically for a wide range of forces (so that it can withstand a large force when you jump off a cliff and it must decelerate your downward motion!). |
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| A sumo-wrestler decides to go bungee-jumping. After his jump, you notice that the bungee cord's equilibrium length is now longer than the original unstretched length. What likely happened to the bungee cord? |
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The cord was stretched past its elastic limit.
Because: The force needed to stop the downward motion of the sumo-wrestler stretched the bungee cord past its elastic limit, permanently deforming the cord. If you bungee jump or rock-climb, you are advised to routinely check the length of
your cords to examine their structural integrity. Once they stretch past the elastic limit they are structurally weakened. |
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You are standing in a elevator on a spring scale. When does the scale report an accurate reading of your weight?
1) When the elevator is moving up at constant speed.
2) When the elevator is moving down at constant speed.
3) When the elevator is stationary. |
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Definition
1, 2, and 3
Because: The scale reads accurate measurement of weight as long as the elevator is not accelerating or decelerating. In this case, all the motions are constant velocity, so the normal force from the scale equals your weight. The scale reads the normal force it is providing. Note, if you were accelerating upwards, your net force is up... so the scale force exceeds your weight and the scale would read high. If the elevator were accelerating down, the scale force is smaller than your weight (some of your weight is being allowed to accelerate you down)... so the scale reading would be low. |
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| True or False: You are dropping an object to see how well it bounces. The likelihood and quality of a bounce depends on the composition of both the object being dropped and the characteristics of the surface onto which you are dropping the object. |
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You drop a ball vertically. The ball would experience an ideally elastic bounce if:
1) no energy was dispersed into other forms in the bounce.
2) the coefficient of restitution was equal to 1.
3) the ball bounced back to its original height. |
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| A coefficient of restitution equal to zero would mean that: |
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| The object does not bounce back at all after impact. |
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| You are dropping several objects (described below) on a tile floor. Which ball do you expect to have the lowest coefficient of restitution? |
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| You have two identical hollow plastic balls. You break one open, fill it halfway with plastic beads, then seal it. When you drop it on the floor, you notice that it does not bounce back as well as the unfilled ball. Why? |
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| The beads can shift in the balls, so the kinetic energy is lost to heating by internal friction. |
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| You are swinging a bat at a ball and hit a home run. In order to determine the quality of the bounce with the fewest measurements, you need to measure: |
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| The speeds of the ball and the bat, both before and after the hit. (4 measurements) |
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| Perfectly elastic collisions are: |
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| common only in atomic-scale collisions (ex. between particles in the air). |
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Why are cars bumpers designed to collapse?
1) The bumpers collapse so energy is lost to thermal processes, so the cars will not bounce off each other with high speeds (especially with reversals of momentum).
2) The bumpers collapse to extend the time of the collision; as a result, the forces between the cars involved in the collision will be decreased.
3) The bumpers collapse so damage will be more likely restricted to the replaceable bumper, rather than a more vital area of the car such as the vehicle frame. |
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| You are bouncing a small rubber ball in the music room of your younger brother's high school. You decide it will be fun to try to use the ball to play a song on the xylophone. You notice that the ball doesn't bounce well on the xylophone when you drop it in the middle of the bar (where you would normally hit the bar with a mallet). Instead, you notice it bounces well where the bar is attached to the instrument (and where it won't make a sound). This place where it bounces well (and where the bar doesn't vibrate) is known as |
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| Why are composite baseball bats better than solid wood bats? |
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| The surfaces of composite bats work like small trampolines, temporarily distorting to store the kinetic energy as elastic energy, eventually releasing it back into to the ball as kinetic energy towards the end of the impact. |
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You are in a car, going over a high hill at a high speed. What makes you feel like you are getting thrown from your seat?
1) You no longer feel as strong of a normal force from the seat because your inertia keeps you moving up as the car drops beneath you.
2) There is a force throwing you up from your seat. |
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Definition
1 only.
Because:
The feeling of weightlessness is often a result of not having the upward normal force that you are accustomed to feeling. This is true especially when you are doing an activity like sky-diving... but it's also true in simple cases, like when you go over a hill in your car at high speeds. There is no force actually throwing you out of your seat. Rather, the inertia of your motion keeps you going forward (until gravity pulls you down or until you hit your head on the roof of the car). You might, however, feel more pressure from your shoulder strap (because he car is slowing down while you are not, causing you to collide into it)... which would also contribute to your false feeling of getting "thrown" upward or forward. Your car drops quicker beneath you because of other forces on it that you are less likely to experience because you are inside the car (like air resistance, etc.). |
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| Which car in a rollercoaster offers the most excitement due to increased feelings of weightlessness? |
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The last car.
Because: Since more of the set of the train is over the hill, its now has more force down the slope. The downward acceleration is greater, so the car's seat drops beneath you faster... makes you feel more weightless (because the downward pressure from the upper part of your restraint system is greater, while the normal force from the seat is less). |
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| You are riding in a car. It is braking. The direction of the acceleration is in what direction? |
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Backwards.
Because: We had this question before (with a bike). This is one of the reappearing themes in the text/course (even exams!). You might feel "thrown forward" when you brake, but it's because you aren't directing experiencing the backwards force caused by the brakes. Instead, your backward force is caused by the seatbelt.
Note: when you're accelerating, you also aren't thrown backward... the force on you is actually a force normal force caused by your set. |
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| You are riding in a car. It is turning left. The direction of the force on the car AND everything in it is: |
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Left (into the turn)
Because: You're right... A leftward force causes the car to no longer go straight ahead, but to turn left. A leftward force causes the car to no longer go straight ahead, but to turn left. This force is caused by a static friction force between the wheels and the ground (or, if you're squealing your tires and sliding a bit outward AS you turn, a sliding friction force). Don't allow your "feeling" of forward or outward motion confuse you about the real forces.
Extra addition: Usually on the test, I tend to make it a bit more difficult: say you are riding in a bus and it's turning left, what direction is the force on you as you feel yourself shifting towards the passenger to your right?.... The force is actually left. Inertia keeps your "eardrum motion sensors" feeling like you should be moving forward (or tangential, and possibly even radially outward), but the passenger to the right is actually providing a normal force pushing you left. Don't trust your feelings when you are in a non-inertial reference frame (i.e. when your motion is changing)! |
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| You are in a car and it is turning left. You notice the fuzzy dice hanging from the dash of the car are swinging right. What causes this? |
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The inertia of the dice keeps them moving forward as the car (and you) turn left underneath the dice.
Because: This concept of forces and inertia comes up many times in class. In the case of the car, you're hopefully buckled in, therefore turning and experiencing an acceleration (and thereby in a non-inertial reference frame). That means your observations about motion can't be trusted. |
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Why is a bank on a race-car track useful to help the cars make fast, sharp turns?
1) The normal force from the bank is now directed partially inward, and this support force then is able to help the car turn.
2) The static friction force from the wheels alone cannot provide enough inward-directed force to cause the fast-moving car to turn. |
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Both 1 and 2.
Because: On page 88. |
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| A bug is sitting on a spinning record. What provides the centripetal acceleration force that keeps the bug on the record? |
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A static friction force.
Because: Static friction forces are mentioned often in your text as forces that can cause circular motion. All real forces can cause centripetal accelerations. In the case of carousel swings at a fair (or the "Down Draft", the force is a tension force (in the ropes or beams). In the case of the space-station circling earth or Earth circling the sun, the force is a gravitational force. In the rudimentary model of the atom (the "Bohr" model), the electrostatic force between the electron and the proton keep the electron in orbit. Electrical forces and magnetic forces can keep charges circling in large particle accelerators. There is no fundamental/special "centripetal force" that itself causes only circular motion. Additionally, there is no centrifugal force that throws you outward (see the misconception on page 88). |
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Which of the following contribute to whether or not the bug in the above problem will be able to sit on a fixed position on a spinning record?
1) The radius where the bug sits.
2) The coefficient of static friction between the bugs feet and the record's surface.
3) The speed at which the record is played. |
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Definition
1, 2, and 3.
The dependence of the bug's ability to sit on the record as a function of these variables. Interestingly... it does NOT depend on the mass. The acceleration required to stay on is determined by the speed of the record and the radius at which the bug sits, and this must be provided by static friction (so the bug doesn't slide off). A larger bug needs a larger friction force (but the same centripetal acceleration) to keep turning with the record... so the mass is not a factor (it balances out). This is similar to projectile motion, where larger balls required a greater force, but the same acceleration (g) to turn their paths. |
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| You are spinning a toy yo-yo in a vertical loop, with the yo-yo moving at constant speed. When is the tension force on the yo-yo's string the least? |
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Definition
When the yo-yo is at the top of the loop.
Because: At the top of the loop, the tension force can be smaller because the gravitational force downward provides some of the centripetal acceleration. If it isn't moving in a circle fast enough (requiring a large force), the gravitational force will exceed the required centirpetal acceleration, and the yo-yo will start to drop (and not move in a circle). |
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| You are swinging in a set of spinning swings at the fair in the image below. You are in the middle of the ride. What is the direction of your velocity (in your frame of reference)? |
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Forwards.
The velocity is tangent to the circle (in the forward direction). Because that direction is changing as you go around the circle, the velocity is changing. An acceleration must be present... and it's an inward "centripetal" acceleration caused by the force from the tension in the swings chains. If you slid off the swing somehow, you wouldn't be thrown "out"... you'd be thrown forward! This is pictured on page 87 with a boy on a turning carousel (since he is facing outwards his velocity is to his left). It is static friction in this case that keeps him on the ride. If he was thrown off the ride (say if static friction was reduced by making the surface of the ride a slick plastic) he'd land on his left side, not his face. |
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| When a force is distributed over a surface, the average force per unit area is known as: |
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| Pressure Definition and Units: |
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| The average force per unit area. Surprisingly, a woman putting all her weight on one high heel exerts more pressure on the ground than an elephant standing on one foot. Fluids and gases, which have free-moving particles whose energy depends on their temperature, also bump around and exert pressure on surfaces. In Pascals, with 1 Pa = 1N/m |
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| Density Definition and Units: |
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| Is mass per unit volume (in kg/m3). An important concept with density involves objects settling into vertical positions with the least dense object on the top. This occurs in fluids as well. Rocks sink in water because they are more dense, while oils float because their density is less than water. |
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| Temperature Definition and Units: |
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| Is a measure of the average kinetic energy of the molecules of a particular object (or in a collection of gases). The molecules in solid still vibrate, but they are bonded to each other. In fluids, the interactions between molecules are weaker, so they move over each other. and in gases, the particles are more free to float around and fill up a volume. |
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| Buoyancy Definition and Units |
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Definition
| Is an upward directed force that exists when an object is submerged in a sample of fluid or gas. In a gas, because of gravity, more particles are at the bottom of the sample than the top. But if the temperature is the same, the KE of the particles is the same. The extra collisions (from extra particles with the same KE) means that there is a greater pressure at the bottom of the submerged object than the top. This means that there will be an upward force. Bouyancy also occurs in non-compressible fluids, whose density does not vary. The weight of any layer of fluid or air (even when its density does not vary) above an object creatser a pressure in the fluid that pushes down on the top layer of the object. At the bottom of the object deeper down in the fluid, the pressure in the fluid is greater, because of the larger mass of fluid above it. But here, the molecules in the fluid are freely moving, and they exert an upward force on the bottom of the object. Because the pressure is greater at the bottom than the top, the net force is upward. Interestingly, the force can be shown to be equal to the density of the fluid (of gas) that the object is submerged in times the objects volume. This is also equal to the weight of the "displaced" fluid. |
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| The absolute zero SI temperature scale is the: |
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Kelvin Scale.
Because: The Celcius scale is water-based: it has water's freezing point as 0 degrees C, and water's boiling point as 100 degrees C.
The Kelvin scale has the same degree sizes, but shifts so that it's zero is "absolute zero", the a theoretical, calculated temperature at which all KE of particles stops and they shrink to zero volume. Experimentally, there have been samples coolled to a few hundred picokelvin (~500 pK = 500x10-12 K = 0.0000000005 K). 0K is equal to -273.5 degrees C.
Fahrenheit is the temperature scale used in the US and only a few other countries. It has 32 degeres for waters freezing point and 212 degrees for water's boiling point. Its main strength is its finer scale (a 2 degree change in F is only about a 1 degree change in Celcius).
Rankine (which is not discussed in your text) uses Fahrenheit degree sizes, but is offset to have its zero at absolute zero. |
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| As you cool off a sample of gas in a container, its molecules will: |
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Definition
lose KE, and slow down and eventually clump together as a liquid on the walls or at the bottom of the container.
Because: As you cool a sample of gas (by cooling the sides of the container it is in, for example) molecules lose some of their KE (first by colliding with the container sides, losing some of their energy to the less energetic molecules of the container). The population of particles as a whole has a lower average KE/molecule. A slower moving molecule is less likely to "zoom by" an attractive gravitational force (from the sides of the container or another molecule of gas), and is more likely to be "caught" in these small gravitational fields -- or even by attractive electrostatic forces (that can exist between uncharged molecules as "van der waals forces"). These attractive forces are described more in Section 4.2, pg 109 (which we skipped) and 10.1 (which we'll get to). thus, the particles will clump together, and form a fluid... and even eventually a solid. As the gas clumps together, it will exert less pressure on the walls of the container. If the container is not flexible, the container will just have a lower pressure inside. If the walls are flexible, the outside pressure will shrink down the volume of the container, decreasing the internal surface area until the pressure inside is again equal to that outside. |
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A sample of helium, and a sample of nomal air (a mix of mostly nitrogen but also oxygen, carbon dioxide, water vapor and many other gaseous components) have the same temperature and pressure. What is different about them?
A) The molecules in the helium sample have smaller mass.
B) The helium sample has a smaller particle density.
C) The molecules in the helium sample have a smaller average KE. |
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Definition
A only.
Because: Because they have the same temperature, the average KE/particle in the helium sample is the same as the average KE/particle in the air sample.
Because they have the same pressure and the same KE per particle, the collisions against the container are the same: in terms of the energies involved and the frequency (number per unit time). This requires that the two samples have the same particle density (particles/unit volume).
The molecules in the helium sample, however have smaller mass. Thisleads to helium being 14% the density of normal air (as stated on page 129) How?: Helium is a monoatomic gas... where its particles are just single atoms, of the second lightest atom on the periodic table. Nitrogen, the largest component of air, is diatomic... with 2 atoms of nitrogen in each molecule. A single atom of nitrogen is 3.5 times heavier than a single atom of helium, so a molecule is 7 times heavier. This leads to helium's density being about 14% that of air (100%/7). |
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| You are visiting a pet store and looking at decorations to place in a fish tank. You are concerned that a solid plastic"diver" decoration should need to have its base embedded in the gravel at the bottom of the tank, while a rock of the same volume does not have this concern. Which of the following statements is true, and explains your concern? |
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Definition
The weight of the diver is less than the weight of the rock, EVEN THOUGH the buoyant forces on each object from the water will be about the same.
Because: Your concern is that the NET FORCE on the diver may be upward. The buoyant forces on each ornament from the water are THE SAME... they are mathematically equal to the weight of fluid that is displaced... and since both objects are the same size, they will displace the same amount of water when they are submerged. The concern is that the plastic ornament may be less dense than the water. Its own weight, therefore, may be less than the weigh of the water that is displaced... so the upward buoyant force may exceed the downward gravitational force. The rock, whose density and weight are greater than water, still experiences the same buoyant force... but its weight is larger, so the net force is down. |
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| You stop for a cappuccino at a coffee shop and notice that the tiny white bubbles of steamed milk remain on the surface of the coffee. These air filled bubbles stay where they are instead of descending into the coffee or rising into the air because they are: |
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| Less dense than the coffee but more dense than the air above the coffee. |
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| A log is floating on a lake. What is the direction of the buoyant force, and its relative strength as compared to the weight of the log? |
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The buoyant force is up, and equal to the weight of the log.
Because:The buoyant force is always upwards. But because the log is floating peacefully (not bobbing up and down), the buoyant force is equal to the object's weight (the net force is down).
Note: If you submerged the log, the volume of fluid the log displaced would be larger, causing the buoyant force to be larger... so the net force would be upward... pushing the log up until it is only partly submerged. |
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| A small rolled-up ball of aluminum will float... but a larger bar of aluminum will not. What statement explains this? |
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Due to the air trapped inside the ball, the average density of the ball is less than water's density (while the bar's density is higher)
Because: Note: a larger ball of rolled up aluminum (with air pockets) COULD be made with an equal mass / weight of aluminum as the bar... and it would still float. The average density of the ball is less than the density of water. It is only partly submerged, so that the buoyant force (the weight of the displaced water) balances the ball's weight.
The large bar is fully submerged. The buoyant force on the bar is therefore bigger than the force on the small ball (NOT smaller). However, the bar's density is greater than water, so its weight is greater than the weight of water displaced (the buoyant force). |
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| You and your friend are on a trip to the local museum and you notice that in the aquarium there are four fish: Fish 1 is floating, Fish 2 is stationary 2m below the water’s surface, Fish 3 is stationary 4 m below the water’s surface and Fish 5 is on the sand at bottom of the tank. (Note: things don’t look good for Fish 1 and Fish 4 but that’s beside the point here.) Your friend says that she’ll buy you lunch if you rank the densities of the fish in order of increasing density, including the density of water in your ranking. Please select your ranking below. |
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Definition
1<(2=3=water)<4
Because: Healthy fish are neutrally buoyant (their average density is about that of the surrounding water). They have an organ called an air bladder that contains some air to make their average density that of water, since some body parts such as the bones, are more dense. Fishes 2 and 3 are both healthy (they're stationary, but probably upright, with fins and gills still slightly moving). Fish 1 is floating, so its density is less (Maybe its gills are not functioning properly and it rose to the surface to gasp for air, getting extra gases into its stomach decreasing its density)... and fish 4 is sinking (maybe some fluid accumulated in the air bladder). Things are probably NOT going well for it. |
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| You crack open a can of "The Fizzicist" (a soda sold at Dillon's that is similar to Dr. Pepper). After you pour it into a glass, you notice some bubbles of carbon dioxide (CO2) are rising within the fluid. Which statement is true? |
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Definition
| The weight of the fluid displaced is greater than the weight of the bubble of CO2 |
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| You work with a catering firm and have been given a challenge. There are several identical liquid beverage dispensers sitting on a table, and they have horizontally directed spouts. You have been asked to have to rank the dispensers in order of their contents (which one is fullest, next fullest, etc.) Having had a physics class, you decide to open the spouts and compare where the streams land on the ground below. In terms of how far each stream lands from the jug, which of the following statements is correct: |
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Definition
The pressure (and hence water level) is lower when the speed is lower. Lower speeds result in smaller ranges and the streams will land closer to the jug.
Because: The pressure is greater at the bottom of the dispenser with the highest beverage-level. It has more fluid above the spout, creating a greater pressure (atmospheric pressure, plus additional pressure due to the weight of the fluid above the spout). When you open the spout, the pressure potential energy is converted to gravitational potential energy and the water flow will be faster. If it is directed horizontally, it will travel out to a further distance (via our projectile motion in Ch 1). |
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| You are trying to deliver water to a sink in the tree house in your backyard. You run an old hose from the spigot behind your home, across your yard, and up the tree to a sink inside the tree house. You let water fill the hose all the way to the tree house sink and then leave the hose pressurized overnight, with no water flowing in it (there is a valve at the open end which you have shut). Unfortunately, the hose cannot tolerate high pressure anymore and it springs a leak around midnight. By morning your whole backyard is a swamp. The most likely site for the leak is: |
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Definition
| on the ground—the lowest point on the hose. |
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| The brake system in most cars makes use of a hydraulic system. This system consists of a fluid filled tube connected at each end to a piston. Assume that the piston attached to the brake pedal has a cross sectional area of one half a square inch and the piston attached to the brake pad has a larger cross section area (say two square inches). According to Pascal's principle, when you apply a force of 10 pounds (~45 N) to the piston attached to the brake pedal, the force at the brake pad will be: |
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Definition
larger than 45N.
Because: Pascal's principle states that any change in water pressure induced in one region of an enclosed fluid sample, within the fluid or at a surface (in this case by pressing on one region of the surface, the "entrance" piston at the pedal) will be conveyed equally within the entire fluid including at other regions of the surface, (which in this case is the "exit" piston at the brake pad). Because the pressure is the same (Force / Area) a larger area will have a greater force. This same phenomena is used in barber chairs (at your local haircut shop), hydraulic lifts (at your local auto-repair), and Hoyer lifts (used to lift disabled persons in/out of seating). |
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| Suppose you had a very long (and flexible) straw that could reach from a cup of water on the ground level to the top of a very tall building (say One Kansas City Place, shown below, which has a 42nd floor at ~600m above ground level). When you suck on the straw in order to bring water up: |
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You could bring the water up to only a certain height in the straw because the atmosphere pushes down on the surface of the water by a given amount.
Because: The pressure at the bottom of the cup is atmospheric pressure, plus just a bit more (due to the depth of the fluid) in the cup. Even if you suck ALL the air from the straw, the water would rise only about 10m (34 feet) above the surface of the fluid in the cup, because the top, open to the air, can only push down on the outside, exposed surface with that pressure. The air pressure potential energy is equal to the gravitational potential energy at the top of the fluid level in the straw. If the straw was thin plastic, its sides would collapse inward... the water wouldn't rise higher.
Two ways you can still drink from a cup at the top floor.
1) Carry the cup up with you (or at least to the floor below you). There the pressure at the outside surface is still about atmospheric pressure (just a bit less than before, but air pressure doesn't vary much with these small changes in height). Your straw could still work to a height of about 10 m.
2) Get a really tall cup and fill it. If your cup is at ground-level and filled to 590 m, you can still drink at 600m. |
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| Cities and towns choose to use water towers to supply water to because: |
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Water pressure at the bottom of the tower is much higher than at the top.
Because: Air pressure changes with altitude (with higher altitudes having lower pressures). There is a gradient that is non-uniform (the pressures increases are greater near the surface, due to the greater density of air.
Similarly, the deeper down you go into water, the greater the pressure. Here, the pressure gradient is uniform (the pressure increases linearly with depth). But because of the greater density of water, these pressure changes are greater. If you can pump water to a high level in a tank (or water tower), the pressure at the bottom will be very large. Cities and towns need these high pressures distribute water to surrounding suburbs or to large populations. |
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| The pressure gradient set up in water standing is a glass is an example of ________ ________ , while variations in pressure due to water flowing faster in the smaller parts of a pipe are a type of ________ ________ . |
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| static variation; dynamic variation |
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| In order for a fluid flow to be well-modeled by Bernouli's equation (which asserts that energy per unit volume (in terms of pressure potential energy, kinetic energy, and gravitational potential energy) is constant within a flow, which of the following is not true? |
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Definition
The fluid must be moving in a closed pipe with no bends or curves.
Because: This is discussed on pages 135 and 138. Pipes are allowed to have curves and bends, changing in altitude or diameter, and Bernoulli's equation is still useful. The equation is less likely to model the flow well when the flow is not steady (you might be changing the energy as you open or close a value), or when the flow has energy losses (due to visocity) or if the fluid is compressible (i.e. a gas). |
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| You are using a hand-pump to pump up a bicycle tire. Even though air is compressible, it is still a fluid and your text's discussion on pg 134 about water pumps is still valid (hint, hint). In the process of pumping up the tire, you pull a piston outward (when you draw the handle up) and push it inward (when you push the handle down). Which of the following statements is true: |
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| You do more work when you push the handle down than when you pull it up. |
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Some European toilets have a small, wall-mounted tank high above the toilet, instead of a larger tank low down. True or false:
The water in a wall-mounted tank has additional gravitational potential energy that can be converted to kinetic energy when the tank valve is opened to flush the toilet. This allows an effective flush, even though less water is used. |
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In a closed pipe with a uniform diameter (that makes many twists and turns, including changes in height), which of the following is constant?
A) the water pressure (pressure potential energy).
B) the water's gravitational potential energy.
C) the flow speed (kinetic energy). |
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Definition
C only.
This is on page 139. In closed pipes, the water flow must be a constant speed unless the diameter of the pipe changes or if the flow opens to air as in the next section, section 6.1 on Garden Watering (where there is no restriction to a set diameter). This is known as the "continuity equation" in other text books... and is basically about conservation of mass. Because the speed is constant, the kinetic energy in the flow is constant throughout the pipe.
In a uniform diameter-closed pipe with an established flow, the energy exchange is then between gravitational potential energy and pressure potential energy. In closed pipes, as the pipe become vertical, the water pressure decreases (because some of the water's energy is now gravitational potential energy). In lower sections, the pressure is higher. The pipe is more likely to burst at lower locations, whether the pipe has an established flow, or has been blocked (has zero-flow) and is pressurized (like the question about the garden hose and the tree-house!). |
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| Which of the following terms best describes when a flow has eddies, vortices and churning...as opposed to smooth streamlines? |
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| Which of the following will INCREASE the flow rate of fluid through a pipe? |
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Increasing the pressure difference between one end of the pipe and another.
Because: Flow rates are increased by decreasing the viscosity of the fluid (ex. by heating it)... and by decreasing the overall length of the pipe. Both of these will reduce frictional effects (both within the fluid and between the fluids and the walls of the pipe. On the other hand, flow crate can be increased by increasing the pressure difference between the ends, and by increasing the diameter of the pipe. All four of these factors are summed up in a relationship called "Poiseuille's Law". |
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| Which of the following will INCREASE the likelihood that a flow around an obstacle is laminar (low Reynold's number)? |
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Definition
Decreasing the fluid's speed.
Because: Decreasing a fluid's speed will increase the likelihood that a flow is laminar, while increasing it will make it more likely that the flow becomes turbulent. Laminar flow is also more likely with more dense and viscous fluids (honey versus water)... and is more likely with small obstacles (little rocks in a stream vs. large boulders). |
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| What is the advantage of adding fuzz to a tennis ball? |
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The fuzz triggers turbulence layers that decrease the size of the turbulent wake that can create drag.
Because: The fuzz triggers turbulent boundary layers that actually keep the rest of the airstream from "stalling" or breaking away until a point further back on the ball. This increases viscous drag losses... but often this is made up by reduced drag forces created by the wake... a region of roughly atmospheric pressure behind the ball. When no wake is present, there are regions of air both in front and behind the ball with pressure that is greater than atmospheric... but when the wake is behind the call, there is greater pressure in front than in back, which means there is a net drag force against the ball's motion. The larger the wake region, the more drag.... so reduces this region helps reduce drag. (note: unfortunately the fuzz on a tennis ball actually creates more viscous drag than the amount of drag it prevents by reducing the wake). |
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| Which of the following describes a side-to-side force on a curveball, caused by a greater path-length and airflow speed on one side of the ball versus the other? |
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| At a critical point during lift-off, a vortex is shed off the wing, that establishes a longer and faster airflow over the top surface than the bottom. When this flow is established, what can be said about the relative pressures above and below the wing? |
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| The pressure above the wing is less than atmospheric pressure and then pressure below is more.The pressure above the wing is smaller than the pressure below the wing. |
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| One reason many propeller planes have two propellers is: |
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Definition
spin the propellers in opposite directions so that trque on the plane (makiing it flip) is not of a threat.
Because: On a plane with two propellers, the second propeller does spin in the opposite direction to eliminate net torque on the plane. Helicopters also have a small side mounted propeller that can do this. Many helicopters are now being built with two, or even 4 propellers (like drones). This increases the stability, as well as the thrust (which in the case of a helicopter is in the upward direction). |
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| The ball that is shown in the image is moving to the right. As seen from above, the spin is clockwise. This spin will influence the ball's motion. How? |
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Definition
The ball will have a deflection out of the screen (towards you).
Because: The motion of the ball pulls the airstream with it, so the path of air is longer and the speed of flow greater on the side of the ball that is facing you. This creates a lower pressure region, while the side way from you is a higher pressure region. The net force is then towards the low pressure side, towards you. If the airflow separated (due to high speed, etc), the direction of the wake deflection would also be towards you. |
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| Which of the following actions or design features will help prevent stalling? |
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Definition
Having structures that trigger turbulent boundary layers on the surface of the wing (similar to the fuzz on tennis balls).
Because: Stalling occurs when the streamline separates from the wing (or propeller) and a large region of turbulence is created on one side of the wing (or propeller blade). This can greatly increase drag... and slow the plane down so much that perhaps enough lift is not generated... and the plane could start to drop from the sky. This can be created by trying to force the airflow on one side to its limit... which can happen by tilting the structure too much or by demanding too much of the airstream -- by increasing the speed either directly, or by forcing higher speeds over the structure by increasing the structure's curvature. But in section 6.2 we learned that by triggering a turbulent boundary layer, we actually allow the airstream to smoothly flow near the surface of the structure for a longer time. This was also found in a note on page 166. |
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| For an object falling through air (or another fluid), there is a point where the drag forces (through viscous drag or through a turbulent wake) will balance the gravitational force. At this point, the object will stop accelerating downward and have a constant speed. This speed is known as the: |
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