Physics 115
Two forces, F⃗ 1 and F⃗ 2, act at a point, as shown in the picture. (Figure 1) F⃗ 1 has a magnitude of 8.60 N and is directed at an angle of α = 57.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 5.20 N and is directed at an angle of β = 54.1 ∘ below the negative x axis in the third quadrant. What is the x component Fx of the resultant force?
-7.733 FX=(-cos(57)*8.60)+(-cos(54.1)*5.20)
What does Prof. Purcell estimate the efficiency of the propulsive motion of E. coli to be?
1%
What is the angle γ that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.
-21.20, but since its counterclockwise, its positive= 21.20 tan^-1( 3.00/-7.73)=tan^-1 (Fy/Fx)
What is the correct answer to Stop to Think 13.8?
A ( the greater pressure difference is because the tube is the smallest on that end and then goes to the largest section to the pressure gradient is the greatest there.
Now please download studio 3 from Sakai and answer the following questions. What is the principal focus of part A of this studio?
Analyze and determine the buoyant forces exerted on different objects.
What is the correct answer to Stop to Think 20.4?
B > A > D > C
Why does an object falling in a fluid have a terminal speed?
Because the drag force depends on the object's speed and the other forces do not.
What is the y component Fy of the resultant force?
Fy=3.00 FY=(sin(57)*8.60)-(-sin(54.1)*5.20)
Consider the portion of a flow tube shown in the figure. (Figure 1) Point 1 and point 2 are at the same height. An ideal fluid enters the flow tube at point 1 and moves steadily toward point 2. If the cross section of the flow tube at point 1 is greater than that at point 2, what can you say about the pressure at point 2?
-lower than the pressure at point 1. ***Thus, by combining the continuity equation and Bernoulli's equation, one can characterize the flow of an ideal fluid.When the cross section of the flow tube decreases, the flow speed increases, and therefore the pressure decreases. In other words, if A2<A1, then v2>v1 and p2<p1.
What is the volume flow rate through the pipe?
.31 L/s
According to Prof. Purcell, if a microorganism (size about 1 µm) is swimming in water at a speed of 30 µm/s and suddenly stops making swimming motions, how far will it travel before it comes to a stop?
0.1 Å = 0.01 nm
Suppose that in response to some stimulus a small blood vessel narrows to 90 % its original diameter. If there is no change in the pressure across the vessel, what is the ratio of the new volume flow rate to the original flow rate?
0.66
A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 4.0m/s. What is the speed in the second segment?
1.0m/s
What does the top pressure gauge in (Figure 1) read?
110kPa --check mastering for the actual problem
What is the speed in the third segment?
16 m/s
A loudspeaker of mass 24.0 kg is suspended a distance of h = 2.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.70 m . (Figure 1)
218N mg=2*T*sin(theta)
The locations of the two caps at equilibrium are now as given in this figure. (Figure 4) The dashed line represents the level of the water in the left arm. What is the mass of the water located in the right arm between the dashed line and the right cap?
3.0kg
What is the height h of the standing column of water?
4.6m
At what value of the hematocrit is the viscosity of blood approximately 5 x 10-3 Pa-s?
47%
Because the flow speed in your capillaries is much less than in the aorta, the total cross-section area of the capillaries considered together must be much larger than that of the aorta. Given the flow speeds noted, the total area of the capillaries considered together is equivalent to the cross-section area of a single vessel of approximately what diameter?
75 cm
Assume patmos=1.00atm. What is the gas pressure pgas?
8.63×104 Pa
Ice at 0.0∘C has a density of 917 kg/m3. A 3.00 cm3 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, ρoil?
917 kg/m3
From a physical point of view, how do you explain the fact that the pressure drop at the ends of the elevated flow tube from Part C is larger than the pressure drop occurring in the similar but purely horizontal flow from Part A?
A greater amount of work is needed to balance the increase in potential energy from the elevation change. ***In the case of purely horizontal flow, the difference in pressure between the two ends of the flow tube had to balance only the increase in kinetic energy resulting from the acceleration of the fluid. In an elevated flow tube, the difference in pressure must also balance the increase in potential energy of the fluid; therefore a higher pressure is needed for the flow to occur.
If the blocks were released while submerged, which, if any, would sink to the bottom of the flask?
ACEF, based on high mass in small volume to produce high density
How much force is exerted on the roof? Express your answer to two significant figures and include the appropriate units.
F = 9.29×104 N
What real world application of Archimedes's principle is addressed in part C of the activity?
Fish swim bladders
What behavior of DNA will you be able to explain as a result of your experiments?
Its ability to fold up despite being charged.
Water flows from the pipe shown in (Figure 1) with a speed of 4.0 m/s . What is the water pressure as it exits into the air?
P = 101.3 kPa
The figure shows a syringe with a 4.0-cm-long needle, filled with water at 20∘C. (Figure 1) --What is the gauge pressure of the water right at the point P, where the needle meets the wider chamber of the syringe? Neglect the pressure difference caused by the radius change. Express your answer using two significant figures.
P = 3200 Pa
Which software application do you need to use in part B?
PhET simulation
What happens if some ethyl alcohol of density 790 kg/m3 is poured into the container after the ice cube has melted?
The layer of ethyl alcohol forms on the surface.
When a muscle cell (such as in the heart) is resting, which statement is correct about the charge on the membrane that encloses it?
The outside is positive and the inside is negative.
If the roof cannot withstand this much force, will it "blow in" or "blow out"?
The roof will blow outward (up), because pressure inside the house is greater than pressure on the top of the roof.
What behavior of phospholipids will you use electric forces to explain?
Their ability to form clusters.
Which of the following comes from the conservation of mass?
continuity equation
Now assume that point 2 is at height h with respect to point 1, as shown in the figure. (Figure 2) The ends of the flow tube have the same areas as the ends of the horizontal flow tube shown in Part A. Since the cross section of the flow tube is decreasing, Bernoulli's equation tells us that a fluid element flowing toward point 2 from point 1 moves toward a region of lower pressure. In this case, what is the pressure drop experienced by the fluid element?
larger than the pressure drop occurring in a purely horizontal flow.
Who can help you figure out the answers to the questions in part D? Select all that apply.
other students in your group
You can assume that all fluids you will reason about in this course are incompressible. What does incompressible mean?
the fluid's density is constant
An object in a fluid experiences a buoyant force from the fluid. What is the direction of that force?
up
Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 30 cm. The two liquids do not mix. **What is the difference in height between the top surface of the glycerin and the top surface of the alcohol? Suppose that the density of glycerin is 1260 kg/m3 and the density of alcohol is 790 kg/m3.
Δh = 11.2 cm
Water flows into a horizontal, cylindrical pipe at 1.6 m/s. The pipe then narrows until its diameter is halved. What is the pressure difference between the wide and narrow ends of the pipe?
Δp = 1.9×104 Pa
What is the pressure difference Δp=pinside−poutside? Use 1.28 kg/m3 for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation. Express your answer using two significant figures.
Δp = 970 Pa
Compared to the speed of the heavier block, what is the speed of the light block after both blocks move the same distance d?
twice as fast
What types of forces acting on an object in a fluid determine its Reynolds number?
-Drag forces -Inertial forces
What forces must be considered to determine the motion of a sphere falling in a fluid?
-The buoyant force. -The drag force. -The gravitational force.
An object in a fluid experiences a buoyant force from the fluid. If the object is completely immersed, which of the following does the magnitude of this force depend on? Select all that apply.
-density of the fluid -total volume of the object
Which is the larger viscosity: 1 Pa-s or 100 centipoise?
1 Pa-s is a larger viscosity than 100 centipoise.
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. (Figure 1) 1.What is the buoyant force acting on the block? 2.The density of water is 1.00 g/cm3. What is the density of the block? 3. Masses are stacked on top of the block until the top of the block is level with the waterline. This requires 20 g of mass. What is the mass of the wooden block? 4. The wooden block is removed from the water bath and placed in an unknown liquid. In this liquid, only one-third of the wooden block is submerged. Is the unknown liquid more or less dense than water? 5. What is the density of the unknown liquid ρunknown?
1. W 2. 0.50 g/cm3 3. 20g 4. more dense 5. 1.5 g/cm3
The highest that George can suck water up a very long straw is 2.0 m . (This is a typical value.) -What is the lowest pressure that he can maintain in his mouth?
82kPa
Postural hypotension is the occurrence of low (systolic) blood pressure when standing up too quickly from a reclined position, causing fainting or lightheadedness. For most people, a systolic pressure less than 90 mm of Hg is considered low. -If the blood pressure in your brain is 120 mm when you are lying down, what would it be when you stand up? Assume that your brain is 40 cm from your heart and that ρ = 1060 kg/m3 for your blood. Note: Normally, your blood vessels constrict and expand to keep your brain blood pressure stable when you change your posture.
89mmHg
For which object, do you need to draw a free-body diagram for in part B of the studio?
A small volume of water within a larger container.
In Conceptual Example 13.13, if instead of narrowing by 8%, a section of the artery increased its diameter by 5% (due to an aneurism), would the pressure difference across that section of artery increase or decrease, and by how much?
Decrease by 18%
A 6-kg bucket of water is being pulled straight up by a string at a constant speed. What is the tension in the rope?
F=ma (6m/s^2)*(9.8m/s^2)=60N
In example 20.4 in the text, if the -50 nC charge (q1) were replaced with a +50 nC charge, what would be the direction of the net force on q3 due to the other two charges?
In the negative y direction.
What does the Venturi meter do?
It uses the difference in pressure between two points in a pipe of varying cross section to measure the flow speed of a fluid.
Which of the answers below best describes the discussion between Maria and Oliver?
Maria and Oliver are discussing how to correctly determine the pressure at a particular depth in a fluid.
Objects A, B, and C in (Figure 1) have the same volume.
Rank in order, from largest to smallest, the sizes of the buoyant forces FA, FB, and FC on A, B, and C. --Archimedes' principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Each object displaces exactly the same amount of fluid since each is the same volume. So the buoyant force on all three objects is the same.
Rank these cars on the basis of their speed a short time (ie. before any car's speed can reach zero) after the forces are applied.
See the homework notes
By how many orders of magnitude (factors of ten) do the viscosities of air and honey (at 40 C) differ?
Six orders of magnitude
At low Reynolds number, which statement is correct about how a microorganism can acquire nutrients?
Stirring the liquid around itself with its flagella doesn't do much of anything, so waiting for molecules to diffuse toward it is just as effective as stirring.
A ball of mass mb and volume V is lowered on a string into a fluid of density ρf. (Figure 1) Assume that the object would sink to the bottom if it were not supported by the string. --What is the tension T in the string when the ball is fully submerged but not touching the bottom, as shown in the figure?
T = (mbg)−(ρfgV)
Which of the following comes from conservation of energy?
The Bernoulli equation.
In figure 13.23b, why does the stream of water get narrower as it flows farther away from the faucet?
The fluid accelerates as if falls, and so its speed is higher farther away from the faucet and so the cross-sectional area must be smaller to maintain the same volume flow rate.
Two points (X and Y) in a fluid are at the same depth in a container. The pressure at X is greater than the pressure at Y. Which of the floowing must be true? Select all that apply.
The fluid cannot be at rest.
Now assume that both blocks have the same speed after being pushed with the same force F⃗ . What can be said about the distances the two blocks are pushed?
The heavy block must be pushed 4 times farther than the light block. --Because the heavier block has four times the mass of the lighter block, when the two blocks travel with the same speed, the heavier block will have four times as much kinetic energy. The work-energy theorem implies that four times more work must be done on the heavier block than on the lighter block. Since the same force is applied to both blocks, the heavier block must be pushed through four times the distance as the lighter block.
Once the ice cube melts, what happens to the liquid water that it produces?
The liquid water sinks to the bottom of the container.
In example 20.3 in the text, the net force on a +1.0 nC charge located between two +10 nC charges is calculated. How would the answer change if the two +10 nC charges were replaced by two -30 nC charges, leaving the +1.0 nC charge the same?
The net force would be the same.
If an ideal fluid element flowing horizontally from left to right slows down at a particular location, is the pressure higher on the left side of the fluid element or the right side at that location?
The pressure is higher on the right side of the fluid element.
Water (which you may consider to be an ideal fluid) is flowing in a horizontal tube. At a certain point the tube's diameter is decreased to half of its original size. What happens to the volume flow rate at that point?
The volume flow rate remains the same.
A non-ideal fluid flows in a tube. If you double the pressure difference between the ends of the tube and increase the tube length by 50%, what will happen to the volume flow rate?
The volume flow rate will increase by a factor of 1.3
a)Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop. b)Rank each pendulum on the basis of the maximum kinetic energy it attains after release. c)Rank each pendulum on the basis of its maximum speed.
a) All based on the PE=mgh formula and rank the energies ( check mastering) b) based on the concept that KE=PE so rankings remain the same c) all based on height, the higher, the faster and the lower, the slower
Which of the topics below will you investigate in part C of the studio?
blood pressure
What is the magnitude F of the resultant force?
make a triangle and apply pythagorean theorem: sqrt( (3)^2+(-7.73)^2)=8.29
Find the pressures pA and pB at surfaces A and B in the tube, respectively. Use patmos to denote atmospheric pressure.
pA, pB = pgas,patmos
Draw a new gravitational potential energy vs. height graph to represent the gravitational potential energy if the ball had a mass of 2.00 kg. The graph for a 1.00-kg ball with an arbitrary initial velocity is provided again as a reference. Take g=10.0m/s2 as the acceleration due to gravity.
pick an exact point and double the slope for double the mass ORIGINAL (5, 50) new: (5, 100) should be a point
which of the following are rules that will help you solve hydrostatic probelms? Select all that apply.
-If two points can be connected by a horizontal line, then they must be at the same pressure as long as they are both in the same connected fluid -If the surface of a fluid is in contact with air, then the pressure at that point is 1 atm.
Which of the following will you do in your experiment?
-Measure the time it takes a sphere to fall through a fluid. -Determine the Reynolds number of a sphere falling in a fluid. -Compare the Reynolds numbers of two different spheres falling in the same fluid.
What does the pressure at a point in a fluid depend on? Select all that apply.
-The depth of that point within the fluid. -The pressure at the fluid's surface.
What is the tension in the string in (Figure 1) ? The volume of plastic ball is 95 cm3 and the density is 840 kg/m3.
.149N
Now download and read studio 2 from Sakai and answer the questions in parts E-I. What is the principal focus of part A of this studio?
By considering the forces on a body of water, determine an expression for hydrostatic pressure.
How does the microorganism E. coli swim?
By rotating its flagellum like a corkscrew.
Which of the following answers best describes the experiment that you wil carry out in part B of the activity?
Estimating the mass of extinct animals.
At a certain point the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now?
T=mg+f =(6kg)*(9.8m/s^2)+(6kg)*(3m/s^2)=76.8= roughly 78N
Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude 3 m/s2. Now what is the tension in the rope?
T=mg+f =(6kg)*(9.8m/s^2)-(6kg)*(m/s^2)=40.8N ROUGHLY 42N ***Note: that the force of tension is not related to the direction or the magnitude of the bucket's velocity: Only the acceleration matters.
Is the Reynolds number a property of a fluid, of an object, or of an object moving in a fluid?
The Reynolds number is a property of an object moving in a fluid; it depends on the dimensions of the object and its motion as well as on the fluid.
If an ideal fluid flows from a region of lower pressure to a region of higher pressure, what will happen to its speed?
The fluid's speed will decrease.
An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe?
The object would float submerged less deeply than in the first container.
A hurricane wind blows across a 8.00m×12.0m flat roof at a speed of 140 km/h . --Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.
The pressure above the roof is lower due to the higher velocity of the air.
If an ideal fluid element moves from a region of lower pressure to a region of higher pressure, is the work done on it by the pressure force positive, negative, or zero?
The work done on the fluid element by the pressure force is zero.
What charged objects will you use in the experiments in part A of this studio?
Transparent tape.
What measurements will each group make in part B of the studio activity?
Volume flow rate as a function of pressure difference and one of the folllowing: tube length, tube diameter, or viscosity.
A cylindrical beaker of height 0.100 m and negligible weight is filled to the brim with a fluid of density ρ = 890 kg/m3 . When the beaker is placed on a scale, its weight is measured to be 1.00 N .(Figure 1) A ball of density ρb = 5000 kg/m3 and volume V = 60.0 cm3 is then submerged in the fluid, so that some of the fluid spills over the side of the beaker. The ball is held in place by a stiff rod of negligible volume and weight. Throughout the problem, assume the acceleration due to gravity is g = 9.81 m/s2 .
What is the weight Wb of the ball? Wb = 2.94 N
The rod is now shortened and attached to the bottom of the beaker. The beaker is again filled with fluid, the ball is submerged and attached to the rod, and the beaker with fluid and submerged ball is placed on the scale.(Figure 2) What weight W3 does the scale now show?
What weight W3 does the scale now show? Note that in this case it is not necessary to know the buoyant force acting on the ball in to answer the question.
Bernoulli's equation is a simple relation that can give useful insight into the balance among fluid pressure, flow speed, and elevation. It applies exclusively to ideal fluids with steady flow, that is, fluids with a constant density and no internal friction forces, whose flow patterns do not change with time. Despite its limitations, however, Bernoulli's equation is an essential tool in understanding the behavior of fluids in many practical applications, from plumbing systems to the flight of airplanes. For a fluid element of density ρ that flows along a streamline, Bernoulli's equation states that p1+ρgh1+12ρv21=p2+ρgh2+12ρv22, where p is the pressure, v is the flow speed, h is the height, g is the acceleration due to gravity, and subscripts 1 and 2 refer to any two points along the streamline. The physical interpretation of Bernoulli's equation becomes clearer if we rearrange the terms of the equation as follows: p1−p2=ρg(h2−h1)+12ρ(v22−v21). The term p1−p2 on the left-hand side represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from point 1 to point 2. The two terms on the right-hand side represent, respectively, the change in potential energy, ρg(h2−h1), and the change in kinetic energy, 12ρ(v22−v21), of the unit volume during its flow from point 1 to point 2. In other words, Bernoulli's equation states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the change in potential and kinetic energy per unit volume that occurs during the flow. This is nothing more than the statement of conservation of mechanical energy for an ideal fluid flowing along a streamline.
XX
an object is placed in a fluid and then released. Assume that the object either floats to the surface (settling so that the object is partly above and partly below the fluid surface) or sinks to the bottom. (Note that for Parts A through D, you should assume that the object has settled in equilibrium.) 1.Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true?
---for every object submerged partially or completely in a fluid
An ideal fluid is flowing in a horizontal tube. What quantity or quantities must be the same at every point in the tube?
-The volume flow rate of the fluid. - The time it takes a particular volume of fluid to flow past a specific location.
Which of these statements is correct about the experiment you will perform in part C of the activity in studio 4?
-We will measure the kinetic energy/volume of the water at the top and the bottom of the container. -We will use Bernoulli's equation to determine the amount of kinetic + potential energy lost as the water flows downward. -We will measure the potential energy/volume of the water at the top and bottom of the container.
Which of the following is a correct unit for viscosity?
-kg-m-1s-1 -Pa-s -centipoise -poise
Which of the following differ between system A and system AE in part C? Select all that apply.
-the change in the gravitational potential energy -the forces external to the system
As stated in rule 3 in the Tactics Box, it is always convenient to use horizontal lines in hydrostatic problems. In each one of the following sketches, a different horizontal line is considered. Which sketch would be more useful in solving the problem of finding the gas pressure?
-use C and B, because they are at the same level so the same pressure and add the ( density*g*v) to get the addition above this pressure to find pGAS. **It is useful to draw a horizontal line as in this sketch because it allows you to relate pressure in the mercury at critical points in the tube. For example, even though you are not given the pressure at point C, you know that pC=patmos, because point C is at the same height as any point on surface B. At the same time, you can also use the hydrostatic pressure equation to relate the pressure at point C to that at surface A, where pressure is determined by the gas pressure in the box.
Which of the following topics from PHYS 114 will we use in PHYS 115? Select all that apply.
-work and energy principles -mathematical modeling -Newton's laws
The container shown in (Figure 1) is filled with oil. It is open to the atmosphere on the left. 1.What is the pressure at point A? 2.What is the pressure difference between points A and B? 3.What is the pressure difference between points A and C?
1. 1.1×105 Pa 2. pB−pA = 4400 Pa 3.pC−pA = 4400 Pa
A U-tube is filled with water, and the two arms are capped.(Figure 1) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. ** one-inch depth of sand is poured onto the cap on each arm. (Figure 2) After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap?
1. The same height **Although one inch of sand on the right cap is much heavier than one inch of sand on the left cap, the pressures exerted by the sand are the same on both caps. Since the pressures exerted by the sand are equal, the pressures at the base of each arm due to the water must be equal. This requires equal heights of water in the two arms.
The sand is removed and a 1.0-kg-mass block is placed on each cap. (Figure 3) After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap?
1. higher ***Although the masses of the blocks are equal, the pressures exerted by them on the caps are not equal. There is a greater pressure on the left cap, which results in a greater pressure at the base of the left arm. To compensate for this increased pressure, the height of the water column in the right arm will have to be greater than in the left arm.
What is the reading W2 of the scale when the ball is held in this submerged position? Assume that none of the water that spills over stays on the scale. Calculate your answer from the quantities given in the problem and express it numerically in newtons.
1.00 N The "extra force" that the ball exerts on the water is equal to the force that the water exerts on the ball, that is, the weight of the displaced water. Therefore, the reading does not change.
The blood pressure at your heart is approximately 100 mm of Hg. As blood is pumped from the left ventricle of your heart, it flows through the aorta, a single large blood vessel with a diameter of about 2.5 cm. The speed of blood flow in the aorta is about 60 cm/s. Any change in pressure as blood flows in the aorta is due to the change in height: the vessel is large enough that viscous drag is not a major factor. As the blood moves through the circulatory system, it flows into successively smaller and smaller blood vessels until it reaches the capillaries. Blood flows in the capillaries at the much lower speed of approximately 0.7 mm/s. The diameter of capillaries and other small blood vessels is so small that viscous drag is a major factor. --There is a limit to how long your neck can be. If your neck were too long, no blood would reach your brain! What is the maximum height a person's brain could be above his heart, given the noted pressure and assuming that there are no valves or supplementary pumping mechanisms in the neck? The density of blood is 1060 kg/m3 .
1.3 m
What is the force Fr applied to the ball by the rod? Take upward forces to be positive (e.g., if the force on the ball is downward, your answer should be negative).
2.42 N The force does act upward as one would expect because the ball is denser than the fluid and would have sunk if it weren't for the rod.
If a 1.0-kg-mass block is on the left cap, how much total mass must be placed on the right cap so that the caps equilibrate at equal height?
4.0kg
To understand the applications of Archimedes' principle. Archimedes' principle is a powerful tool for solving many problems involving equilibrium in fluids. It states the following: When a body is partially or completely submerged in a fluid (either a liquid or a gas), the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. As a result of the upward Archimedes force (often called the buoyant force), some objects may float in a fluid, and all of them appear to weigh less. This is the familiar phenomenon of buoyancy. Quantitatively, the buoyant force can be found as Fbuoyant=ρfluidgV, where Fbuoyant is the force, ρfluid is the density of the fluid, g is the magnitude of the acceleration due to gravity, and V is the volume of the displaced fluid. In this problem, you will be asked several qualitative questions that should help you develop a feel for Archimedes' principle.
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Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true?
for an object completely submerged in a fluid
Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true?
for an object that floats
Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true?
for an object that sinks
A flask of water rests on a scale that reads 100 N. Then, a small block of unknown material is held completely submerged in the water. The block does not touch any part of the flask, and the person holding the block will not tell you whether the block is being pulled up (keeping it from falling further) or pushed down (keeping it from bobbing back up). Assume that no water spills out of the flask. (Figure 1). What is the new reading on the scale?
greater than 100 N
A 1.00 kg ball is thrown directly upward with an initial speed of 16.0 m/s. A graph of the ball's gravitational potential energy vs. height, Ug(h), for an arbitrary initial velocity is given in Part A. The zero point of gravitational potential energy is located at the height at which the ball leaves the thrower's hand. For this problem, take g=10.0m/s2 as the acceleration due to gravity.
h=12.8 E=128J based on the kinematic equations: -vfi^2=vi^2+2ad ( among the 4 available see notes) Etotal=KE+PE=0+mgh= (1kg)(10m/s^2)(12.8)=128J
As you found out in the previous part, Bernoulli's equation tells us that a fluid element that flows through a flow tube with decreasing cross section moves toward a region of lower pressure. Physically, the pressure drop experienced by the fluid element between points 1 and 2 acts on the fluid element as a net force that causes the fluid to __________.
increase in speed
The experiment is repeated with the six different blocks listed below. In each case, the blocks are held completely submerged in the water. Mass (g) Volume (cm3) A 100 50 B 100 200 C 200 50 D 50 100 E 200 100 F 400 50 Rank these blocks on the basis of the scale reading when the blocks are completely submerged.
B, (D/E), (A/F/C) All based on volume, because of the equation Fb=Density*V*g and volume is the only thing provided so all based on volume.
How will you make an electric dipole?
By sticking two oppositely-charged pieces of transparent tape together.
Sustained exercise can increase the blood flow rate of the heart by a factor of five with only a modest increase in blood pressure. This is a large change in flow. Although several factors come into play, which of the following physiological changes would most plausibly account for such a large increase in flow with a small change in pressure?
Dilation of the smaller blood vessels to larger diameters.
A pair of vertical, open-ended glass tubes inserted into a horizontal pipe are often used together to measure flow velocity in the pipe, a configuration called a Venturi meter. Consider such an arrangement with a horizontal pipe carrying fluid of density ρ. The fluid rises to heights h1 and h2 in the two open-ended tubes (see figure). The cross-sectional area of the pipe is A1 at the position of tube 1, and A2 at the position of tube 2. (Figure 1) --Find p1, the gauge pressure at the bottom of tube 1. (Gauge pressure is the pressure in excess of outside atmospheric pressure.)
p1 = ρgh1 ***The fluid is pushed up tube 1 by the pressure of the fluid at the base of the tube, and not by its kinetic energy, since there is no streamline around the sharp edge of the tube. Thus energy is not conserved (there is turbulence at the edge of the tube) at the entrance of the tube. Since Bernoulli's law is essentially a statement of energy conservation, it must be applied separately to the fluid in the tube and the fluid flowing in the main pipe. However, the pressure in the fluid is the same just inside and just outside the tube.
A 5.0 mL syringe has an inner diameter of 5.0 mm , a needle inner diameter of 0.24 mm , and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100. Assume the liquid is an ideal fluid. --What is the minimum force the nurse needs to apply to the syringe?
F=.26N
Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each block the same distance d. Ignore friction and assume that an equal force F⃗ is exerted on each block.
It is equal to the kinetic energy of the lighter block. --The work-energy theorem states that the change in kinetic energy of an object equals the net work done on that object. The only force doing work on the blocks is the force from the person, which is the same in both cases. Since the initial kinetic energy of each block is zero, both blocks have the same final kinetic energy.
If an ideal fluid element flows from a lower to a higher elevation, what happens to its energy?
Its potential energy increases, its kinetic energy decreases, and its total mechanical energy remains the same
An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe?
More than one of these outcomes is possible. ---If the fluid in the second container is less dense than the object, then the object will sink all the way to the bottom. If the fluid in the second container is denser than the object (though less dense than the fluid in the original container), the object will still float, but its depth will be greater than it was in the original container.
The leaves of a tree lose water to the atmosphere via the process of transpiration. A particular tree loses water at the rate of 3×10−8m3/s; this water is replenished by the upward flow of sap through vessels in the trunk. This tree's trunk contains about 2000 vessels, each 100 μm in diameter. --What is the speed of the sap flowing in the vessels?
v = 1.91×10−3 ms
The nurse empties the syringe in 4.0 s . What is the flow speed of the medicine through the needle?
v = 28 m/s
Water flowing through a 1.7-cm-diameter pipe can fill a 300 L bathtub in 3.2 min . --What is the speed of the water in the pipe?
v = 6.9 m/s
Find v1, the speed of the fluid in the left end of the main pipe. Express your answer in terms of h1, h2, g, and either A1 and A2 or γ, which is equal to A1A2.
v1=A2*sqrt((2g(h1-h2)/A1^2-A2^2) **Note that this result depends on the difference between the heights of the fluid in the tubes, a quantity that is more easily measured than the heights themselves.
River Pascal with a volume flow rate of 5.9×105 L/s joins with River Archimedes, which carries 1.01×106 L/s , to form the Bernoulli River. The Bernoulli River is 180 m wide and 30 m deep. ---What is the speed of the water in the Bernoulli River?
vB = 0.30 m/s
A neutral metal sphere is attracted to a positively-charged amber rod. Why does this occur?
Negative charges in the metal sphere move to be closer to the positively-charged rod; the attractive force is larger than the repulsive force between the positive charges on the far side of the sphere and the rod.
Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true?
Object B has a greater density than object T. ----Since both objects float, the buoyant force in each case is equal to the object's weight. Block B displaces more fluid, so it must be heavier than block T. Given that the two objects have the same volume, block B must also be denser. In fact, since the weight equals the buoyant force, and B is fully submerged, ρBVg=ρliquidVg, where all the symbols have their usual meaning. From this equation, one can see that the density of B must equal the density of the fluid.
To practice Tactics Box 13.2 Finding whether an object floats or sinks. If you hold an object underwater and then release it, it can float to the surface, sink, or remain "hanging" in the water, depending on whether the fluid density ρf is larger than, smaller than, or equal to the object's average density ρavg. These conditions are summarized in this Tactics Box. --
Object sinks: **An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid: ρavg>ρf.** Object floats: **An object rises to the surface if it weighs less than the fluid it displaces, that is, if its average density is less than the density of the fluid: ρavg<ρf.** Object has neutral buoyancy: **An object hangs motionless if it weighs exactly the same as the fluid it displaces—that is, if its average density equals the density of the fluid: ρavg=ρf.**
Which of the software applications below are used to aid the understanding of this material?
PhET simulation
A soda straw (a hollow insulating cylinder) is uniformly positively charged, so that the (positive) charge is the same everywhere on the straw. At the center of the straw, in what direction will the electric field point?
The electric field is zero at the center of the straw.
What pressure difference is required between the ends of a 2.0-m-long, 1.0-mm-diameter horizontal tube for 40∘C water to flow through it at an average speed of 4.0 m/s? Express your answer using two significant figures.
ΔP = 1.8×105 Pa
Smoking tobacco is bad for your circulatory health. In an attempt to maintain the blood's capacity to deliver oxygen, the body increases its red blood cell production, and this increases the viscosity of the blood. In addition, nicotine from tobacco causes arteries to constrict. For a nonsmoker, with blood viscosity of 2.5×10−3Pa⋅s, normal blood flow requires a pressure difference of 8.0 mm of Hg between the two ends of an artery. If this person were to smoke regularly, his blood viscosity would increase to 2.7×10−3Pa⋅s, and the arterial diameter would constrict to 90 % of its normal value. --What pressure difference would be needed to maintain the same blood flow?
ΔP = 13 mm of Hg
The average density of the body of a fish is 1080 kg/m3. To keep from sinking, the fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. --By what percent must the fish increase its volume to be neutrally buoyant in fresh water? Use 1.28 kg/m3 for the density of air at 20∘C.
ΔVV = 8.0 %
