Fluids at Rest

Which of the following scenarios most accurately represents Pascal's law? A. The volume displaced by piston 1 is equal to the volume displaced by piston 2 in a hydraulic lift. B. When you push down on the stopper of a big water jug with 10 N, the same force of 10 N is transmitted undiminished to the larger bottom surface of the jug. C. A person pushes the brake with a small area with a small force over a short distance to produce an equivalent force to stop the car. D. When a pregnant mother is riding in a car that crashes, the fluid surrounding the fetus will help to dissipate any force from the crash.

A. The volume displaced by piston 1 is equal to the volume displaced by piston 2 in a hydraulic lift. Pascal's Law states that pressure is transmitted undiminished to every portion of the fluid and to the walls of the container.

A patient is scheduled to receive an intravenous injection of medication that must be at least 109.3 kilopascals at the injection point before going into surgery. If the patient is lying on a bed 0.9 meters high, what is the minimum height above the ground that the nurse must suspend the bag to achieve that pressure at the injection point? (ρ(fluid) = 1020 kg/m³) A. 0.80 m B. 1.7 m C. 2.3 m D. 2.0 m

B. 1.7 m P = Po + ρgh 109.3 = 101.3 + ρgh (109.3 - 101.3) / ρg = h h = (109.3 - 101.3) / 1020 * 10 h = 0.8 m This will give us the height above the patient's arm to place the bag, so we must add 0.9 meters to figure out the height above the ground. 0.8 + 0.9 = 1.7 m

A 30 kilogram object is dropped into acetic acid, which has a specific gravity of 1.06. Once it is immersed in acetic acid, the object has an apparent weight of 240 N. What is the object's specific gravity? A. 8.5 B. 5.3 C. 1.3 D. 0.17

B. 5.3 Convert 30 kg to Newtons, which would be 300 N. With an apparent weight of 240 N, the buoyant force gives it an upward push of 60 N. The buoyant force of 60 N accounts for the displaced volume of acetic acid, and we know the object weighs 300 N. Fb (acetic acid) / W(object) = ρ(acetic acid) / ρ(object) 60 / 300 = 1.06 / x x = 5.3

A gold crown recently acquired is suspected to be brass covered in gold. The crown weighs 25.0 N in air and has an apparent weight of 22.5 N in fresh water. Based on these results, which of the following conclusions is correct? (ρ(gold) = 19,300 kg/m³, ρ(brass) = 8300-8700 kg/m³) A. It is likely that the crown is made of half brass and half gold. B. It is likely that the crown is made of brass covered in gold. C. It is likely that the crown is made of gold only. D. It is likely that the crown is made of brass only.

B. It is likely that the crown is made of brass covered in gold. the buoyant force is 25 - 22.5 = 2.5 N Fb = ρvg --> use 1000 for density of water 2.5 / 1000 * 10 = v v = 0.00025 To find the mass of the crown, divide the weight by 10, so mass of crown is 2.5 kg. ρ = m/v ρ = 2.5 / 0.00025 ρ = 10,000 slightly higher than the density of brass, so it's probably covered in gold

On which of the following does the buoyant force on an object floating on the surface of a liquid most directly depend? A. mass of the liquid B. density of the liquid C. volume of the liquid D. viscosity of the liquid

B. density of the liquid

When the gauge pressure is doubled, what happens to the absolute pressure? A. It doubles B. It stays the same C. It increases by a factor less than 2 D. It is halved

C. It increases by a factor less than 2 Absolute pressure is equal to atmospheric pressure plus gauge pressure. Atmospheric pressure is 101,300 Pa, while a typical gauge pressure for a tire is 30 psi or 207 Pa. Since atmospheric pressure is relatively large compared to most gauge pressures, doubling the gauge pressure would not end up doubling the absolute pressure.

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result? A. The scale will remain at 80 pounds until the cube is floating on top of the water fully submerged. B. The scale will remain at 80 pounds unless the cube touches the bottom of the bowl. C. The scale will register a weight greater than 80 pounds due to Newton's Third Law. D. The cube's density must be provided to predict what will happen.

C. The scale will register a weight greater than 80 pounds due to Newton's Third Law.

buoyant force formula

Fb = ρvg

Pascal's Principle

When force is applied to a confined fluid, the change in pressure, is transmitted equally to all parts of the fluid

A strange property of the buoyant force

it stays the same regardless of how deep you go; it is independent of the surrounding pressure

Archimede's principle

the buoyant force on an object is equal to the weight of the fluid displaced by the object

buoyant force

the upward force exerted by a fluid on a submerged object