Physics -Fluid and Elasticity questions –

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Physics -Fluid and Elasticity questions
Professor: Manuel Diaz-Avila
Conceptual Question 1 (5 points): In the hydraulic arrangement shown below, the larger piston has an area which is 50 times that of the smaller piston. The strongman hopes to exert enough force on the large piston to raise a 10 kg mass that rests on the small piston. If the man can only exert a force of 2000N, do you think he will be successful? Please explain your reasoning.
Conceptual Question 2 (5 points): A water tower is a common sight in many communities. One of the most famous water towers is the one in Riyadh city, Saudi Arabia shown in the picture below. Notice the particular shape of the tower. Please explain why is it desirable for a water tower to have this highly unstable shape rather than being shaped as a tall cylinder of the same height and inner diameter (see figure on the right). Hint: Think about where the level of water be in each case if both have lost equal volume of water.
Conceptual Question 3 (5 points): The figure below shows four situations in which a red liquid and a gray liquid are in a U-tube. In one situation the liquids cannot be in static equilibrium (at rest).
a) Which situation is that? Please explain your reasoning. (2)
b) For the other three situations, assume static equilibrium. Which of the three situations correspond to the red liquid having a larger density than the grey liquid? Please explain your reasoning. (3)
5.30 m
Problem 1 (5 points): Alloy Density: The mass of a particular alloy is 75.0% gold and 25.0% silver. Given that the densities of pure gold and pure silver are 19300 and 10500 kg/cm3 respectively, please calculate the density of the alloy described above. Notice that you don’t need the mass of the alloy to solve the problem.
Problem 2 (5 points): Eardrum Damage: If the force on the tympanic membrane (eardrum) increases by about 1.5N above the force from atmospheric pressure, the membrane can be damaged.
a) When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.2 mm in diameter. The average density of sea water is 1030 kg/m3. (3)
b) When you go climbing high elevations, above what elevation could damage to your eardrum start to occur? The average density of air is 1.29 kg/m3. (2)
Problem 3 (5 points): Giraffe’s Blood Pressure: In a giraffe its head 2.65 m above its heart, and 2.65 m above its feet while standing and the hydrostatic pressure ?gd in the blood at its heart is 250 mmHg. Assume the giraffe stands upright and the blood density is 1060 kg/m3. ( 760 mmHg = 1.013×105 Pa).
a) Calculate the pressure difference between the giraffe’s brain and its heart. This pressure differential is enough to perfuse the brain with blood to prevent the giraffe from fainting. (1)
b) Calculate the pressure difference between the giraffe’s feet and its heart. This pressure differential must be countered by tight-fitting skin acting like pressure stocking to prevent edema formation on the giraffe’s legs. (1)
c) If the giraffe were to lower its head to drink from a pond without splaying its legs and moving slowly, what would be the increase in the blood pressure in the giraffe’s brain? This action would be lethal for the giraffe i.e. its head would explode. (1)
d) Please do a quick research and briefly explain the biophysical mechanism under which the giraffes’ circulatory system prevents the blood rushing too quickly back to the heart from the brain when the animal is erect (in this scenario the giraffe will faint) , or down to the brain when animal’s head is lowered (in this scenario giraffe’s head will explode). Your explanation most include the effect of the fascia, the system of small blood vessels called the rete mirabile, and the benefit of giraffe’s diet consisting of acacia leaves which act as vasodilators. (2)
You may want to visit this site to learn about this:
Why Giraffes Don’t Have Brain Damage
Problem 4 (5 points): Atmospheric Pressure on Mars: An astronaut is standing at the surface of Mars. In her hands she holds a cap bottle completely filled with water, so no air is inside it. The bottle is 0.20 m long. To measure the atmospheric pressure on Mars, she makes a small hole at the bottom of the bottle. The water starts to flow slowly and then the flow stops completely, leaving a column of water of 0.19 m high.
a) Please explain why the water starts to flow and then it stops leaving a column of water in the bottle. (1)
b) Please calculate the atmospheric pressure on Mars as measured by the astronaut, knowing that the density of water is 1000 kg/m3, g=GM/R2, with G =6.67×10-11 Nm2/kg2, M =6.42×1023 kg and R =3.40×106 m for Mars. (3)
c) What would happen to the water in the bottle if the astronaut removes the cap of the bottle? Please explain your reasoning. (1)
Problem 5 (5 points): Physics at the Zoo: A 70 kg student in the figure below balances a 1200 kg elephant on a hydraulic lift.
a) What is the diameter of the piston the student is standing on? (2)
b) When a second student joins the first, the piston sinks 35 cm. What is the second student’s mass? (3)
Problem 6 (5 points): Forces on Pool’s Walls: A swimming pool is 5.0 m long, 4.0 m wide, and 3.0 m deep.
a) Calculate the net force exerted by the water and the atmosphere at the bottom surface of the pool.
b) If we neglect the force due to the atmosphere, show that the force exerted on the side walls of the pool as function of depth y is given by: This part of the problem requires integration. You may want to review my notes, particularly the dam problem.
where w is the width of the wall in question.
c) Calculate the net force exerted on each side wall. (2)
Problem 7 (5 points): Modeling Atmospheric Pressure on Earth: It is possible to use the ideal gas law to show that the density of the Earth’s atmosphere decreases exponentially with height z. For this, we assume the density is proportional to the pressure, namely ooPP??=, where ?o and Po are the values of density and pressure at sea level (?o=1.28 kg/m3 and Po=1.013×105 Pa).
a) Starting from ,gdzdP?-= and using your calculus knowledge, show that the atmospheric pressure is given by: ozzozePP-= where, ooogPz?= (4)
b) Calculate the atmospheric pressure in Calgary (1084 m above sea level) and at the top of Mount Everest (8848 m above sea level). (1)

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