Test: Fluids at Rest - MCAT MCQ

• The buoyant force is the upward force by the fluid that opposes the downward force of gravity, and in the case of a floating object, the two forces are equal and opposite.
• The formula for buoyant force is F_B = _pV_g, where V is the volume of the object submerged. So the buoyant force does not depend on the volume of the object.
• The buoyant force does not depend on the viscosity of the liquid since viscosity refers to fluids in motion and is the resistance to shearing flows.
• In the formula for buoyant force, the density in question is that of the liquid, so to reiterate:
  

• When the cube is submerged, the object floats in equilibrium.
• There must be a buoyant force keeping the object afloat pushing upward.
• According to Newton’s Third Law, there should be an equal and opposite force downwards.
• That additional force will cause the scale to register a weight greater than 80 pounds.

• Look at the forces in the y-axis to figure out the buoyant force: F_y = ma_y becomes W_a + F_b - mg = ma_y 
• 22.5 + F_b - 25.0 = 0, so the buoyant force F_b is equal to 2.5 N. 
• To find the volume of the crown, approximate g as 10 and use 1000 for ρ of water. So ρg = 10000. and F_b = ρgV, so V = 2.5 / 10000 = 2.5 x 10^-4 m³  
• To find the mass of the crown. divide the weight by 10. so mass of crown is 2.5 kg. 
• To find the density, divide mass by volume: 2.5 kg/2.5 x 10^-4 m³ = 10.000 kg/m³. 
• Based on the density value. it is likely that the crown is made of brass and onjly covered in gold. 

• 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.
• To use the tire example, if the gauge is 414 Pa, then absolute pressure would be 101,314 Pa. Absolute pressure increase by a factor less than 2.

• The formula for hydrostatic pressure is P = P₀ + ρgh, where ρ is the density of the fluid.
• Plug in 109.3 kPa for absolute pressure, P, and use 101.3 kPa for the atmospheric pressure (P₀)
• Solve for h: h = ΔP/ρg and plug in the values.
• 109.3 kPa - 101.3 kPa / (9.8 m/s² * 1020 kg/m³) = 8000 Pa / 10000 kg/m²s² = 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.
  The answer is 1.7 meters.

• Recall the hydrostatic pressure equation, P = P_o + gh. Recognize that it is a manifestation of y = mx +b, which is the formula for a linear function.
• y is P, and x is h. P_o​ start subscript, o, end subscript would be b, and ρg together represents m. Eliminate any choices that are not showing a linear or straight line function.
• On the moon, there is less atmospheric pressure due to its much smaller mass and would be less than P_o, specifically defined as atmospheric pressure on Earth. The y-intercept would start below P_o.  
• This is the correct graph:
  

• Pascal’s Law states that pressure is transmitted undiminished to every portion of the fluid and to the walls of the container.
• This allows us to write the equation P₁ = P₂, and  then F₁/A₁ = F₂/A₂, as well as F₁d₁ = F₂d₂.
• As a result, we can explorate that a small force applied on a small area over a long distance will produce a large force applied on a large area over a short distance.
• We also can deduce that W1/V1 = W2/V2. Since work is the same on both sides, the volume displaced by one side will be equal to the volume displaced on the other side in a hydraulic lift.

• 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.
• Setup a ratio of F_{B(aceticacid)}/W_object = p_aceticacid/_pobject
• ​60/300 = 1.06/x, so 60·5 = 300 and 1.06·5 must equal x, which is 5.3.

According to Pascal's law, the pressure in a fluid increases with depth. This is because the weight of the fluid above exerts a force on the fluid below, resulting in an increase in pressure as we move deeper into the fluid.

Incompressibility is the property of a fluid that allows it to exert pressure equally in all directions. Since the fluid cannot be compressed, any force applied to it is transmitted equally in all directions, resulting in equal pressure distribution.