A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m 3 liquid and 10 L of a 6,000 kg/m 3 liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s 2 .)

Everyone. So in this problem, we're gonna calculate the total pressure when we have 2 liquids, but there's something a little bit different about this problem. Hopefully, you guys try it on your own. Let's check it out. So we have a tall cylindrical beaker that's 10 centimeters in radius. So in other words, the radius of this little cylinder over here, I'm gonna say this is r is equal to 0.1. We're gonna mix 2 different liquids inside, right? So So we're gonna pour 5 liters of an 8,000, density, liquid and then 10 liters of a 6,000. Now remember, when you have 2 different densities, the higher one's going to settle towards the bottom. So in other words, this density over here is going to be 8,000. This volume here is going to be 5 liters and this one is gonna be 6,000 and this one's gonna be 10 liters. Right? Notice how it's kind of scaled. So what I'm just gonna do is I'm gonna call this 1 1 and this one 2 just to make it a little simple. Alright, so we're gonna calculate the total pressure at the bottom of the beaker. So in other words, the the place where we're trying to figure out the pressure is right here. I'm gonna call this Pbottom. Alright. Now in order to figure out Pbottom, I have to use my pressure equation. So we're gonna start off with a Ptop is equal to I'm sorry, Pbottom is equal to Ptopplusrowgh. Now there's 2 places where you could pick to be your ptop. Right? So basically the the very top of both of the liquids, or you could pick the red green boundary. Either one of those would work, except what happens is that we don't know what the pressure is at the red green liquid boundary. And so if we wanna calculate the other pressure, remember, we need to compare this to a pressure pressure that we know. So we're actually not going to use the boundary and instead what we're going to do is we're basically just going to start all the way from top and go through both liquids. Okay, so this is really where you're going to measure your P top from. And the reason this is advantageous, the reason you want to do this is because you know something about this P top, which is that it touches air and so therefore, this P top is really just equal to the standard air pressure around it. Alright. So this P top here is just the air pressure, so we know that. And so what happens here is if we're going from the top all the way down, there's actually 2 liquids that we're going through. We're gonna go all the way down the red liquid and then we're gonna have to cross the boundary and then go all the way down the green liquid. So we have h one and then we have h two. Because I'm going through 2 different liquids and their different densities, we actually can't just use one rho g h term. We have to use both of them. Alright? Remember that you can go from the top of the liquid all the way down to the bottom. You just have to have a rho g h term for every single liquid that you encounter. That's a different density. Alright? So just make this super simple. We're gonna have to do, super clear. We're We're gonna have to go through the first liquid, which is row 1gh1, plus and then row 2gh2. Alright? So we have that p bottom here. If you take a look at your variables, we know this p top here is gonna be. We know what the densities of both of the liquids are. The only thing that we don't have in this problem is we don't have the heights. Normally, in these problems, you do have the heights, but in this one, we actually don't. The only thing we know about these problems or about these liquids is their volumes. So somehow we have to go from height and we have to get sorry, somehow we have to go from volume and then get this basically to height. Now you might be thinking that you could use, the density equation. You might be thinking that you could use row equals mass over volume because we have volume. But this is only gonna help you solve for the mass, not the height. So that's not really gonna be the equation that you should use. Alright, so we're not gonna use rho, mass over volume. Instead, we're gonna use the volume equation. Remember that the volume of a cylinder, is really just the cross sectional area of the cylinders. In other words, the area of the circle thing like this. This is gonna be the area times the height, right? So that's the volume of a cylinder and the area of a circle is really just gonna be area circle equals Pi R squared. So I'm going to use Pi big R squared. So in other words, it's just Pi big R squared times the height over here. So this is how we're gonna get to the height here. Notice how we have an h term. So basically, here's what's going on here. So h one is going to equal the volume divided by Pi R squared. Just going right from this equation over here, right? If V cylinder equals Pi R squared times h, you can rearrange and solve for the heights. So basically what you can do is you can model both of these liquids as if they're just cylinders that are sort of stacked on top of each other. So h one is gonna be a v over pi r squared. You're gonna get, 4 you're gonna get 10 liters divided by Pi. This is gonna be 0.1 squared. Now it's important to sort of keep track of the units here. I remember, so you always want to keep track of units. This is going to be meters. This is going to be meters squared and this is going to be liters. Alright. Now what happens here is that I can't just go ahead and cancel these things because I have a liter over a meter cubed, and the liters is an SI. Right? So what I'm gonna have to do is I'm gonna have to, sort of rewrite this using a conversion factor that I know. One of the conversion factors that is really, really useful to know is that, 1 meter cubed is equal to I've got 10,000 liters. So So I wanna cancel out the liters and then basically, what you're ending up with is you're ending up with meters on top of meters that you can cancel. Alright? So when you work this out, you're gonna get here is you're gonna get a height of 0.32, and this is gonna be in meters. Alright. So that's the height of basically h one. Now you're gonna do the exact same thing. I'm gonna do a little bit faster with h 2. This cylinder here, we can model this as a cylinder. So in other words, it's gonna be v 2 divided by pi r squared. So, in other words, this is just gonna be 5 divided by pi times 0.1 squared. And rather than go through all the math again, basically, you can just do one over 1,000. You plug in all the units, you'll see that they cancel. One thing you can see here is that the numerator the denominators of both of these fractions are gonna be the same. So the only thing that's different about this is that this one is half of the other one that we calculated. So instead of getting 0.32, you're gonna get 0.16 meters, and that's gonna be your 2nd height. Okay, so just kinda like using a little shortcut there, but that's your h's. You got h one and h two. So now I'm just gonna put it all together into my pressure equation. So p p bottom is gonna equal, p top, which is air, which is gonna be a 101,000 plus, and then we've got, this is gonna be 6,000 times 9.8 times, and then we're gonna use, 0.32 plus and now we've got the other density, the other liquid at the bottom, which is gonna be your 8,000 times 9.8 times your 0.16. Now when you pull this all together in your calculator, you plug this whole mess in, what you're gonna get for the pressure at the bottom of this cup is you're gonna get a pressure of 1.33 times 10 to the 5th, Pascals. Alright? So we can actually see that even in just a small little container like this, right, with 10 liters and 5 liters, it's not a whole lot of liquid. The pressure actually changes significantly here, and that's because the densities of these materials, 6,008,000, are actually relatively dense. Right? They're like 6 and 8 times denser than fresh water. So it doesn't take a whole lot of liquid actually to change the pressure very drastically and only a certain amount of heights. Alright? So that's it for this one folks. Let me know if you have any questions.

Indice

Skip topic navigation

0. Math Review31m

Math Review
31m

1. Intro to Physics Units1h 27m

Introduction to Units
24m

Unit Conversions
18m

Solving Density Problems
13m

Dimensional Analysis
10m

Counting Significant Figures
5m

Operations with Significant Figures
14m

2. 1D Motion / Kinematics4h 4m

Vectors, Scalars, & Displacement
13m

Average Velocity
32m

Intro to Acceleration
7m

Position-Time Graphs & Velocity
26m

Conceptual Problems with Position-Time Graphs
22m

Velocity-Time Graphs & Acceleration
5m

Calculating Displacement from Velocity-Time Graphs
15m

Conceptual Problems with Velocity-Time Graphs
10m

Calculating Change in Velocity from Acceleration-Time Graphs
10m

Graphing Position, Velocity, and Acceleration Graphs
11m

Kinematics Equations
45m

Vertical Motion and Free Fall
19m

Catch/Overtake Problems
23m

3. Vectors2h 43m

Review of Vectors vs. Scalars
1m

Introduction to Vectors
7m

Adding Vectors Graphically
22m

Vector Composition & Decomposition
11m

Adding Vectors by Components
13m

Trig Review
24m

Unit Vectors
15m

Introduction to Dot Product (Scalar Product)
12m

Calculating Dot Product Using Components
12m

Intro to Cross Product (Vector Product)
23m

Calculating Cross Product Using Components
17m

4. 2D Kinematics1h 46m

Intro to Motion in 2D: Position & Displacement
20m

Velocity in 2D
31m

Acceleration in 2D
12m

Kinematics in 2D
18m

Intro to Relative Velocity
23m

5. Projectile Motion3h 6m

Intro to Projectile Motion: Horizontal Launch
35m

Negative (Downward) Launch
24m

Symmetrical Launch
25m

Projectiles Launched From Moving Vehicles
15m

Special Equations in Symmetrical Launches
16m

Positive (Upward) Launch
50m

Using Equation Substitution
17m

6. Intro to Forces (Dynamics)3h 22m

Newton's First & Second Laws
16m

Types Of Forces & Free Body Diagrams
20m

Forces & Kinematics
12m

Vertical Forces & Acceleration
23m

Vertical Equilibrium & The Normal Force
18m

Forces in 2D
36m

Equilibrium in 2D
24m

Newton's Third Law & Action-Reaction Pairs
11m

Forces in Connected Systems of Objects
38m

7. Friction, Inclines, Systems2h 44m

Inclined Planes
20m

Kinetic Friction
17m

Static Friction
21m

Inclined Planes with Friction
37m

Systems of Objects with Friction
10m

Systems of Objects on Inclined Planes with Friction
19m

Stacked Blocks
16m

Intro to Springs (Hooke's Law)
20m

8. Centripetal Forces & Gravitation6h 41m

Uniform Circular Motion
7m

Period and Frequency in Uniform Circular Motion
20m

Centripetal Forces
15m

Vertical Centripetal Forces
10m

Flat Curves
9m

Banked Curves
10m

Newton's Law of Gravity
30m

Gravitational Forces in 2D
25m

Acceleration Due to Gravity
13m

Satellite Motion: Intro
5m

Satellite Motion: Speed & Period
35m

Geosynchronous Orbits
15m

Overview of Kepler's Laws
5m

Kepler's First Law
11m

Kepler's Third Law
16m

Kepler's Third Law for Elliptical Orbits
15m

Gravitational Potential Energy
21m

Gravitational Potential Energy for Systems of Masses
17m

Escape Velocity
21m

Energy of Circular Orbits
23m

Energy of Elliptical Orbits
36m

Black Holes
16m

Gravitational Force Inside the Earth
13m

9. Work & Energy1h 58m

Intro to Energy & Kinetic Energy
5m

Intro to Calculating Work
27m

Net Work & Work-Energy Theorem
25m

Work On Inclined Planes
16m

Work By Springs
16m

Work As Area Under F-x Graphs
7m

Power
19m

10. Conservation of Energy2h 54m

Intro to Energy Types
3m

Gravitational Potential Energy
10m

Intro to Conservation of Energy
32m

Energy with Non-Conservative Forces
20m

Springs & Elastic Potential Energy
19m

Solving Projectile Motion Using Energy
13m

Motion Along Curved Paths
4m

Rollercoaster Problems
13m

Pendulum Problems
13m

Energy in Connected Objects (Systems)
24m

Force & Potential Energy
18m

11. Momentum & Impulse3h 45m

Intro to Momentum
11m

Intro to Impulse
19m

Impulse with Variable Forces
12m

Intro to Conservation of Momentum
17m

Push-Away Problems
19m

Types of Collisions
4m

Completely Inelastic Collisions
28m

Adding Mass to a Moving System
8m

Collisions & Motion (Momentum & Energy)
26m

Ballistic Pendulum
14m

Collisions with Springs
13m

Elastic Collisions
24m

How to Identify the Type of Collision
9m

Intro to Center of Mass
15m

12. Rotational Kinematics3h 3m

Rotational Position & Displacement
28m

More Connect Wheels (Bicycles)
29m

Rotational Velocity & Acceleration
22m

Equations of Rotational Motion
20m

Converting Between Linear & Rotational
26m

Types of Acceleration in Rotation
26m

Rolling Motion (Free Wheels)
16m

Intro to Connected Wheels
12m

13. Rotational Inertia & Energy6h 51m

More Conservation of Energy Problems
54m

Conservation of Energy in Rolling Motion
45m

Parallel Axis Theorem
13m

Intro to Moment of Inertia
28m

Moment of Inertia of Systems
23m

Moment of Inertia & Mass Distribution
10m

Intro to Rotational Kinetic Energy
16m

Energy of Rolling Motion
18m

Types of Motion & Energy
24m

Conservation of Energy with Rotation
35m

Torque with Kinematic Equations
56m

Rotational Dynamics with Two Motions
56m

Rotational Dynamics of Rolling Motion
27m

14. Torque & Rotational Dynamics2h 5m

Torque & Acceleration (Rotational Dynamics)
15m

How to Solve: Energy vs Torque
10m

Torque Due to Weight
23m

Intro to Torque
26m

Net Torque & Sign of Torque
13m

Torque on Discs & Pulleys
35m

15. Rotational Equilibrium4h 8m

Equilibrium with Multiple Objects
30m

Equilibrium with Multiple Supports
30m

Center of Mass & Simple Balance
29m

Equilibrium in 2D - Ladder Problems
40m

Beam / Shelf Against a Wall
53m

More 2D Equilibrium Problems
28m

Review: Center of Mass
14m

Torque & Equilibrium
22m

16. Angular Momentum3h 6m

Opening/Closing Arms on Rotating Stool
18m

Conservation of Angular Momentum
46m

Angular Momentum & Newton's Second Law
10m

Intro to Angular Collisions
15m

Jumping Into/Out of Moving Disc
23m

Spinning on String of Variable Length
20m

Angular Collisions with Linear Motion
8m

Intro to Angular Momentum
15m

Angular Momentum of a Point Mass
21m

Angular Momentum of Objects in Linear Motion
7m

17. Periodic Motion2h 11m

Spring Force (Hooke's Law)
14m

Intro to Simple Harmonic Motion (Horizontal Springs)
32m

Energy in Simple Harmonic Motion
22m

Simple Harmonic Motion of Vertical Springs
20m

Simple Harmonic Motion of Pendulums
25m

Energy in Pendulums
15m

18. Waves & Sound3h 40m

Intro to Waves
11m

Velocity of Transverse Waves
21m

Velocity of Longitudinal Waves
11m

Wave Functions
31m

Phase Constant
14m

Average Power of Waves on Strings
10m

Wave Intensity
19m

Sound Intensity
13m

Wave Interference
8m

Superposition of Wave Functions
3m

Standing Waves
30m

Standing Wave Functions
14m

Standing Sound Waves
12m

Beats
8m

The Doppler Effect
7m

19. Fluid Mechanics4h 31m

Density
33m

Intro to Pressure
1h 10m

Pascal's Law & Hydraulic Lift
28m

Pressure Gauge: Barometer
13m

Pressure Gauge: Manometer
14m

Pressure Gauge: U-shaped Tube
21m

Buoyancy & Buoyant Force
1h 4m

Ideal vs Real Fluids
3m

Fluid Flow & Continuity Equation
21m

20. Heat and Temperature3h 11m

Temperature
16m

Linear Thermal Expansion
14m

Volume Thermal Expansion
14m

Moles and Avogadro's Number
14m

Specific Heat & Temperature Changes
12m

Latent Heat & Phase Changes
20m

Intro to Calorimetry
21m

Calorimetry with Temperature and Phase Changes
15m

Advanced Calorimetry: Equilibrium Temperature with Phase Changes
9m

Phase Diagrams, Triple Points and Critical Points
6m

Heat Transfer
44m

21. Kinetic Theory of Ideal Gases1h 50m

The Ideal Gas Law
32m

Kinetic-Molecular Theory of Gases
1m

Average Kinetic Energy of Gases
10m

Internal Energy of Gases
14m

Root-Mean-Square Velocity of Gases
15m

Mean Free Path of Gases
20m

Speed Distribution of Ideal Gases
15m

22. The First Law of Thermodynamics1h 26m

Heat Equations for Special Processes & Molar Specific Heats
15m

First Law of Thermodynamics
22m

Work Done Through Multiple Processes
16m

Cyclic Thermodynamic Processes
20m

PV Diagrams & Work
12m

23. The Second Law of Thermodynamics3h 11m

Heat Engines and the Second Law of Thermodynamics
31m

Heat Engines & PV Diagrams
18m

The Otto Cycle
28m

The Carnot Cycle
21m

Refrigerators
22m

Entropy and the Second Law of Thermodynamics
31m

Entropy Equations for Special Processes
24m

Statistical Interpretation of Entropy
11m

24. Electric Force & Field; Gauss' Law3h 42m

Electric Charge
15m

Charging Objects
6m

Charging By Induction
3m

Conservation of Charge
5m

Coulomb's Law (Electric Force)
47m

Electric Field
40m

Electric Fields in Capacitors
16m

Electric Field Lines
16m

Dipole Moment
8m

Electric Fields in Conductors
7m

Electric Flux
21m

Gauss' Law
32m

25. Electric Potential1h 54m

Electric Potential Energy
7m

Electric Potential
29m

Work From Electric Force
32m

Relationships Between Force, Field, Energy, Potential
25m

The ElectronVolt
5m

Equipotential Surfaces
13m

26. Capacitors & Dielectrics1h 54m

Capacitors & Capacitance
8m

Parallel Plate Capacitors
19m

Energy Stored by Capacitor
15m

Combining Capacitors in Series & Parallel
15m

Solving Capacitor Circuits
29m

Intro To Dielectrics
18m

How Dielectrics Work
2m

Dielectric Breakdown
4m

27. Resistors & DC Circuits3h 8m

Intro to Current
6m

Resistors and Ohm's Law
14m

Power in Circuits
11m

Microscopic View of Current
8m

Combining Resistors in Series & Parallel
37m

Kirchhoff's Junction Rule
4m

Solving Resistor Circuits
31m

Kirchhoff's Loop Rule
1h 14m

28. Magnetic Fields and Forces2h 22m

Magnets and Magnetic Fields
21m

Summary of Magnetism Problems
9m

Force on Moving Charges & Right Hand Rule
25m

Circular Motion of Charges in Magnetic Fields
11m

Mass Spectrometer
33m

Magnetic Force on Current-Carrying Wire
22m

Force and Torque on Current Loops
17m

29. Sources of Magnetic Field1h 54m

Magnetic Field Produced by Moving Charges
10m

Magnetic Field Produced by Straight Currents
27m

Magnetic Force Between Parallel Currents
12m

Magnetic Force Between Two Moving Charges
9m

Magnetic Field Produced by Loops and Solenoids
42m

Toroidal Solenoids aka Toroids
11m

30. Induction and Inductance3h 38m

Intro to Induction
5m

Magnetic Flux
12m

Faraday's Law
28m

Lenz's Law
22m

Motional EMF
18m

Transformers
8m

Mutual Inductance
24m

Self Inductance
18m

Inductors
7m

LR Circuits
22m

LC Circuits
35m

LRC Circuits
14m

31. Alternating Current2h 37m

Alternating Voltages and Currents
18m

RMS Current and Voltage
9m

Phasors
20m

Resistors in AC Circuits
9m

Phasors for Resistors
7m

Capacitors in AC Circuits
16m

Phasors for Capacitors
8m

Inductors in AC Circuits
13m

Phasors for Inductors
7m

Impedance in AC Circuits
18m

Series LRC Circuits
11m

Resonance in Series LRC Circuits
10m

Power in AC Circuits
5m

32. Electromagnetic Waves2h 14m

Intro to Electromagnetic (EM) Waves
23m

The Electromagnetic Spectrum
7m

Intensity of EM Waves
22m

Wavefunctions of EM Waves
19m

Radiation Pressure
24m

Polarization & Polarization Filters
30m

The Doppler Effect of Light
6m

33. Geometric Optics5h 47m

Ray Nature Of Light
10m

Reflection of Light
9m

Index of Refraction
16m

Refraction of Light & Snell's Law
22m

Total Internal Reflection
5m

Plane Mirrors
19m

Concave Mirrors
1h 25m

Convex Mirrors
32m

Thin Lenses
33m

Ray Diagrams For Mirrors
35m

Mirror Equation
19m

Refraction At Spherical Surfaces
9m

Ray Diagrams For Lenses
22m

Thin Lens And Lens Maker Equations
24m

34. Wave Optics1h 15m

Diffraction
8m

Diffraction with Huygen's Principle
14m

Young's Double Slit Experiment
24m

Single Slit Diffraction
27m

35. Optical Instruments1h 7m

Lenses in Combination
27m

Cameras
27m

Telescopes
13m

36. Special Relativity2h 10m

Inertial Reference Frames
14m

Special Vs. Galilean Relativity
17m

Consequences of Relativity
52m

Lorentz Transformations
45m

19. Fluid Mechanics

Intro to Pressure

Physics with Algebra

19. Fluid Mechanics

Intro to Pressure

Problema precedenteProssimo problema

Difficoltà con Physics with Algebra?

Unisciti a migliaia di studenti che si affidano a noi per superare al meglio i loro esami!

Scelta multipla

A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m³ liquid and 10 L of a 6,000 kg/m³ liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s².)

3.20×10⁴

3.52×10⁴

1.33×10⁵

1.36×10⁵

0 Commenti

Problema precedenteProssimo problema

17:4m

Guarda il prossimo

Padroneggia Pressure and Atmospheric Pressure con una breve spiegazione video di Patrick Ford

Video correlati

Pratica correlata

Scelta multipla

A large warehouse is 100 m wide, 100 m deep, 10 m high:

a) What is the total weight of the air inside the warehouse?

b) How much pressure does the weight of the air apply on the floor?

views

Scelta multipla

The deepest known point on Earth is called the Mariana Trench, at ~11,000 m (~36,000 ft). If the surface area of the average human ear is 20 cm2, how much average force would be exerted on your ear at that depth?

views

Scelta multipla

A wooden cube, 1 m on all sides and having density 800 kg/m³ , is held under water in a large container by a string, as shown below. The top of the cube is exactly 2 m below the water line. Calculate the difference between the force applied by water to the top and to the bottom faces of the cube (Hint: calculate the two forces, then subtract. Use g=10 m/s².)

views

Mostra altri esercizi

Non vendere le mie informazioni personali

Difficoltà con Physics with Algebra?

A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m3 liquid and 10 L of a 6,000 kg/m3 liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s2.)

Guarda il prossimo

A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m³ liquid and 10 L of a 6,000 kg/m³ liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s².)