Fluids Archives • Nerd Notes

FRQ Atlas NEW
Courses

Enroll In Learn Physics Course

100+ hours of self paced lessons, worked examples, & targeted practice.

Course Platform

A platform to simplify and accelerate your learning.
Quiz Lab
UBQ
Learning Hub

All Resources

Everything you need to master Physics — for free.

AI Problem Solver

Meet Phy. The world's most advanced AI helper.

FRQ Atlas

NEW

Collection of every AP FRQ with rapid, rubric aligned grading.

UBQ Quiz Lab

NEW

Find, try, and create 100s targeted quizzes. For Pro level students.

UBQ

2000+ Physics problems & explanations to supercharge learning.

AP Speed Reviews

8 AP Physics units condensed into 8 short review guides.

AP Exam Prep Guides

Proven tips, tricks, and hacks to help you score that coveted 5.

Learn from Scratch

Learn Physics, from scratch, at your own pace.
Services

Elite 1-to-1 Coaching

Guaranteed performance boost in scores and understanding.

AP Exam Prep

5 weeks for a 5. Expedited progress. Stellar Results.

Learn AP Physics

100+ hours of guided instruction to simplify physics & boost grades

More Programs

Other 1-to-1 and group programs to accelerate Physics mastery.
Pricing
Be A Tutor

What we found:

A piece of aluminum with a mass of \( 1.0 \) \( \text{kg} \) and density of \( 2700 \) \( \text{kg/m}^3 \) is suspended from a light cord and then completely immersed in a container of water having density \( 1000 \) \( \text{kg/m}^3 \). Determine the tension in the cord when the aluminum is immersed in the container of water.

A raft of density \( 0.7 \rho_{w} \) floats partially submerged in a body of water of density \( \rho_{w} \). The raft has dimensions of length \( L \), width \( W \), and height \( H \), as shown in the figure. The height of the raft beneath the surface of the water is \( h \). Which of the following expressions is equal to \( h \)?

A block of iron, which has a density that is greater than the density of water, is at rest on the bottom of a pool. Which of the following claims about the magnitude of the normal force on the block and the weight of the block is true?

Cubes \( 1 \) and \( 2 \) are made of the same material. Cube \( 1 \) has edges of length \( L \) and is fully submerged in a fluid of density \( 0.5 \rho \). Cube \( 2 \) has edges of length \( 2L \) and is fully submerged in a fluid of density \( \rho \). The buoyant force on Cube \( 1 \) is \( F_{\text{B},1} \) and the buoyant force on Cube \( 2 \) is \( F_{\text{B},2} \). What is the ratio \( F_{\text{B},1} : F_{\text{B},2} \)?

A student designs an experiment to determine the density of an unknown fluid. The student pours the fluid into a graduated cylinder and attaches an object to a force probe. The object has a density greater than the density of the fluid. The student partially submerges the object into the fluid and records both the volume of fluid displaced in the graduated cylinder and the force probe reading. The student then submerges the object further and remeasures both values, repeating the trials until the object is fully submerged, and creates a graph of the reading on the force probe as a function of volume of fluid displaced. Which of the following statements correctly describes how a feature of the graph is related to the density of the fluid?

A large container holds a volume \( V_w \) of water that has a density \( \rho_w \). A cube with volume \( V_c \) and density \( \rho_c \) floats partially submerged in the water. Which of the following expressions is equal to the buoyant force on the cube?

A large, empty plastic jug with mass \( m_j \) and volume \( V_j \) floats in a pool of water, as shown in the figure. If the density of water is \( \rho_w \), which of the following expressions is equal to the volume of water \( V_w \) that must be added to the jug so that the top of the jug will be at the level of the water?

A large, open water tank has a small hole punctured in its side, a distance \( h \) below the water surface. Torricelli’s theorem, \( v = \sqrt{ 2 g h } \), describes the speed of the water exiting the hole. This theorem is a specific application of which fundamental principle?

Which of the following pairs of properties correctly describes an ideal fluid as defined in the AP Physics 1 curriculum?

A solid, uniform object is placed in a fluid. Which statement best describes the condition that will cause the object to sink?

Why is fluid pressure considered a scalar quantity, even though it is defined using force \( P = \frac{F_{\perp}}{A} \), which is a vector?

The absolute pressure at a certain point in a lake is \( P_{abs} \). If the local atmospheric pressure is \( P_{atm} \), which expression represents the gauge pressure \( P_{gauge} \) at that point?

A cube is fully submerged at a depth of \( 1 \) \( \text{m} \) in a large tank of water. It is then moved to a depth of \( 3 \) \( \text{m} \). How does the buoyant force on the cube at \( 3 \) \( \text{m} \) compare to the buoyant force at \( 1 \) \( \text{m} \)?

An ideal fluid flows through a horizontal tube of varying cross-section. According to Bernoulli’s equation, what is the relationship between the fluid’s speed and pressure?

A student measures the weight of an irregularly shaped metal object in air and finds it to be \( 15 \) \( \text{N} \). When the object is fully submerged in water, its apparent weight is \( 10 \) \( \text{N} \). What is the magnitude of the buoyant force acting on the object?

The gauge pressure at a certain depth in a fluid is \( P_{gauge} \). If you dive to a depth that is twice as deep in the same fluid, what will the new gauge pressure be?

Which of the following is a scalar quantity?

An ideal fluid flows through a horizontal pipe that smoothly narrows to \( \tfrac{1}{2} \) of its original diameter. How does the speed of the fluid in the narrow section \( v_2 \) compare to the speed in the wider section \( v_1 \)?

Torricelli’s theorem, \( v = \sqrt{ 2 g \Delta h } \), is a specific derivation of which fundamental physics principle?

If a perpendicular force \( F \) is applied to a surface area \( A \), resulting in a pressure \( P \), what is the new pressure if the force is doubled and the area is quadrupled?

A weighted balloon is filled with air and just barely floats (is neutrally buoyant) at the surface of a lake. If you push the balloon slightly downward, what will happen to its motion?

Which of the following would occur if a fluid had viscosity, a property that ideal fluids lack?

According to the microscopic description of fluids, what is the fundamental cause of the pressure exerted by a fluid on the walls of its container?

If an object is floating in equilibrium at the surface of a liquid, which of the following statements must be true regarding the forces acting on it?

An object is lowered into a container of water. As the object is submerged deeper into the water (without touching the bottom), what happens to the buoyant force exerted on it?

In the context of fluid dynamics, what does the term ‘mass flow rate’ represent in the continuity equation?

A cube of side length \( L \) is completely submerged in a fluid of density \( \rho \). The top of the cube is at a depth \( d \). What is the magnitude of the net force exerted by the fluid on the two vertical side faces of the cube?

According to the Continuity Equation for an incompressible fluid, what happens to the speed of the fluid as it moves from a wide pipe into a narrower section?

An ideal fluid flows through a horizontal pipe that narrows from a radius of \( R \) to a radius of \( \frac{R}{2} \). If the initial speed of the fluid is \( v \), what is the new speed, and how does the internal pressure change?

A certain object has a density of \( \rho_{\text{obj}} \). If you cut the object exactly in half, what is the density of one of the remaining pieces?

Why does the pressure of the Earth’s atmosphere decrease as you move to a higher altitude, and how does this relate to the definition of an ideal fluid?

Which of the following best describes the implication of an ideal fluid being ‘incompressible’?

A horizontal pipe carries water that flows from Point A to Point B. If the speed of the water at Point B is greater than at Point A, how does the pressure at Point B compare to Point A?

An object with a density of \( 4000 \) \( \text{kg/m}^3 \) is weighed in air and then weighed while fully submerged in a fluid with a density of \( 1000 \) \( \text{kg/m}^3 \). What is the ratio of the ‘apparent weight’ in the fluid to the actual weight in air?

If the absolute pressure at a depth of \( 10 \) \( \text{m} \) in a lake is \( 2 \) \( \text{atm} \), what would the absolute pressure be at a depth of \( 20 \) \( \text{m} \) in the same lake? (Assume \( 1 \) \( \text{atm} \) is the surface pressure).

Which of the following best describes ‘gauge pressure’ at a certain depth in a static fluid?

A student monitors the gauge pressure at the bottom of a cylinder filled with water. If the student pours out half of the water and replaces it with an equal volume of oil (which is less dense than water and does not mix), how does the gauge pressure at the bottom change?

A student measures the pressure at the bottom of a vertical column of liquid to be \( P_{total} \). If the atmospheric pressure \( P_{atm} \) doubles, what happens to the gauge pressure at the bottom of that same column?

A block of uniform material is cut into two pieces, where one piece is cut to have a volume that is \( 3 \) times the volume of the other. How does the density of the smaller piece compare to the density of the larger piece?

A block of wood floats in a beaker of water placed inside an elevator. If the elevator begins to accelerate upward at a rate of \( a = \frac{1}{2} g \), how does the volume of the block submerged in the water change?

Which of the following statements correctly characterizes the nature of pressure \( P \) as a physical quantity within a fluid?

A student is asked to calculate the pressure at the bottom of three different shaped vessels: a cylinder, a cone (wide base), and a funnel (narrow base). All three are filled with the same liquid to the exact same height \( H \). Which vessel has the highest pressure at the bottom?

A student creates a graph of Absolute Pressure \( P \) on the vertical axis versus Depth \( h \) on the horizontal axis for a static, incompressible liquid. What does the slope of this graph represent?

Two identical spheres are held under water. Sphere A is made of aluminum (density \( 2700 \) \( \text{kg/m}^3 \)) and Sphere B is made of lead (density \( 11300 \) \( \text{kg/m}^3 \)). When both are released and remain fully submerged, how do the buoyant forces \( F_{BA} \) and \( F_{BB} \) compare?

Two identical containers are filled to the same height. Container A is filled with water \( \rho_w \), and Container B is filled with oil \( \rho_o \), where \( \rho_w > \rho_o \). How does the gauge pressure at the bottom of Container A compare to the gauge pressure at the bottom of Container B?

A large open-top tank is filled with water to a height \( H \). A small hole is poked in the side at a height \( h \) from the bottom. If the tank is now sealed with a pressurized air pocket at the top such that the pressure at the surface is \( 2P_{atm} \) instead of \( P_{atm} \), how does the efflux speed \( v \) change?

A U-tube contains a liquid of density \( \rho \). One arm of the U-tube is sealed, trapping a volume of air, while the other arm remains open to the atmosphere. Initially, the liquid levels are equal. If more of the same liquid is added to the open arm, how will the new equilibrium levels compare?

A hydraulic lift consists of two circular pistons. The input piston has a radius \( r \) and the output piston has a radius \( 3 r \). If a force \( F \) is applied to the input piston, what is the magnitude of the force exerted by the output piston?

Consider a U-shaped tube open to the atmosphere on both ends, filled with an ideal fluid. If a piston of mass \( M \) and area \( A \) is placed on the right arm, what is the difference in height \( \Delta h \) between the fluid levels in the two arms?

An object is weighted in air and found to have a weight \( W_{\text{air}} \). When fully submerged in an open container of water, its apparent weight is \( W_{\text{app}} \). If the container is now moved to a location with higher atmospheric pressure, how will the apparent weight \( W_{\text{app}} \) change?