Homework 1

buoyancy_updated-19m.pdf

PHYS 242 Buoyancy

PHYS 242 Buoyancy Lab

1. Introduction

In this laboratory, we will study the phenomenon of buoyancy and measure the buoyant force on an object by a liquid. When an object displaced in contact with any fluid (liquid or gas), there are forces exerted by the fluid on the object’s surfaces. (These forces are related to the pressure at the surface.) We describe the summation of these forces as the buoyant force. The buoyant force is an upward con- tact force whose magnitude is related to the volume of the object and the density of the surrounding fluid.

There are many aspects of the buoyant force that are confusing for students. First, the formally defined buoyant force is often confused with the more qualitative and intuitive notion of buoyancy. Consider two cubes of the same size but di↵erent mass. We often refer to the less dense cube as being ‘more buoyant,’ but it turns out that the two cubes will displace the same volume of liquid. Thus, the buoyant forces on the two cubes are actually equal.

Archimedes’ principle states that the magnitude of the buoyant force on an object is equal to the weight of the fluid displaced by the object. This principle is often misinterpreted as stating that the buoyant force is related to the weight of an object, but the weight of displaced fluid depends only on the volume of the object, the density of the fluid, and the strength of the gravitational field.

Lab Objectives: after completing this lab, students should be able to:

1. Describe and use a procedure for measuring the volume of liquid displaced by an object.

2. Describe and use a procedure for determining the magnitude of the buoyant force on an object that would sink.

3. Describe and use a procedure for determining the magnitude of the buoyant force on an object that would float.

4. Predict which quantities do and do not a↵ect the magnitude of the buoyant force.

Equipment

For this lab, you will be using the following simulation: https://iwant2study.org/lookangejss/02_newtonianmechanics_4massweightdensity/ejss_model_

buoyancycase/buoyancycase_Simulation.xhtml

We will also be using various videos, the links for which are on iLearn.

Here are two related simulations, which we will not use for this lab, but you might find interesting:

• https://amrita.olabs.edu.in/?sub=1&brch=1&sim=72&cnt=4 • https://go-lab.gw.utwente.nl/production/splash/build/splash.html?preview=

PHYS 242 Buoyancy

2. Measuring Displaced Volume

In this lab we will be using a buoyancy simulation from iwant2study.org, as well as videos of the Phet Simulation on Buoyancy. In many of the experiments in this lab you will be asked to make predictions and to check those predictions with the simulation. In each case, write down both your initial prediction and your observations. Resolve any inconsistency before proceeding to the next part.

(a) Displacement and mass

i. Open the simulation at: https://iwant2study.org/lookangejss/02_newtonianmechanics_4massweightdensity/

ejss_model_buoyancycase/buoyancycase_Simulation.xhtml

ii. Set ⇢1 (the density of the liquid) = 1.0 We’ll call this liquid “water.”

iii. Set ⇢2 (the density of the block) = 1.5

iv. Set the height of the block so that it is that the maximum height above the liquid.

v. Click on the depth tab and set the depth of the liquid so that it is just below the bottom of the block when it is at maximum height. We want the block to be able to be fully submerged in the liquid when we lower the height later. See the picture below for reference.

vi. Which of these scales currently tells you the weight of the block (top or bottom)? What is the weight of the block? Assume the units are Newtons.

(b) Methods of determining volume

i. We will call our ⇢2 = 1.5 block “Block A.” Now lower the block to its minimum height. It should be nearly submerged. What happens to the water level? Use the faint gray horizontal line as a reference point.

PHYS 242 Buoyancy

ii. Now consider a block with a density of 2.5. Let’s call this block “Block B.” Raise the height of the block so it is once again out of the water. Set ⇢2 = 2.5. What is the weight of this block? Has the volume of the block changed?

iii. PREDICT: If Block B is submerged in water, will the final water level be greater than, less than, or equal to the final water level when Block A was submerged?

iv. Check your prediction by lowering Block B into the water until it is submerged. Describe what happened. Was your prediction correct?

v. PREDICT: How would the volumes of water displaced compare if a single block were lowered to di↵erent depths?

vi. To test our prediction, watch the video “1 – Block at Di↵erent Depths” on iLearn, in which a block is submerged at di↵erent depths. For now, don’t worry about the buoyancy force, just pay attention to the changing water level. What do you notice? Was your prediction correct?

vii. The di↵erence in the initial and final water level reading is referred to as water displaced. What is the value of the volume of water displaced by the block in the video when it is fully submerged?

PHYS 242 Buoyancy

i. When the block is completely submerged, how does the volume of the block compare to the volume of liquid displaced? The volume of the block can be found in the upper left-hand side of the screen in the video.

ii. What determines the volume of liquid displaced by a submerged object? (Does it depend on the object’s mass, its volume, or its depth?)

iii. PREDICT: How would the volumes of liquids displaced compare if you submerged one alu- minum block in water and an identical aluminum block in a liquid with a di↵erent density than water (e.g oil)? Explain.

iv. Test this by watching “2 – Block in Di↵erent Liquids” on iLearn, in which an aluminum block is submerged in di↵erent liquids. Once again, ignore the buoyant force for now and just focus on the displacement of the liquid. Was the fluid displaced di↵erent as a result of the changing fluid? Was your prediction correct?

3. Determining the magnitude of the buoyant force

(a) Consider two identical blocks hanging from a scale, one submerged in water and one in air.

PHYS 242 Buoyancy

i. PREDICT how the scale readings would compare. Is the reading of the scale supporting the block in water greater than, less than, or equal to the reading of the scale supporting the block in air?

ii. Check your prediction using the simulation. Change ⇢2 back to 1.5 and ⇢1 to 1.0. Check the reading on the top scale when the block is in air and when it is submerged. Were your predictions correct?

iii. What does your result imply about the direction of the force exerted on the block by water?

The force exerted by the water is known as the buoyant force. There is a buoyant force exerted by the air as well, but this force is small enough that it is typically ignored. In some cases, like a hot air balloon, the buoyant force of the air cannot be neglected. For the remainder of this lab, ignore buoyant forces by the air unless advised otherwise.

(b) Draw a free-body diagram for each block in section 3(a). (Use the notation B for the buoyant force.)

Check your free-body diagram with your instructor before continuing.

(c) Use your free-body diagram and Newton’s second law for an object at rest to write an equation that relates the weight of the block to the other forces. (Hint: what is the net force acting on each block?)

i. Block submerged in water

PHYS 242 Buoyancy

ii. Block in air

iii. If the reading on the scale for the submerged block is T1 and the reading on the scale of the block in air is T2, write an equation for B in terms of T1 and T2.

iv. The equation in the previous question suggests a procedure for determining the magnitude of the buoyant force on a completely submerged object. By measuring the scale reading (the tension force) on the block when it is in water and when it is in air, you can simply determine the magnitude of the buoyant force. Briefly describe the procedure you will follow.

v. Try out your equation with our Block A (⇢2 = 1.5).

Check your results with your instructor before you proceed.

4. Variables that influence the buoyant force

(a) Mass

i. PREDICT how the buoyant forces would compare for two blocks of di↵erent mass but equal volume submerged in water.

ii. Check your prediction using the video “3 – Di↵erent Mass” on iLearn. The magnitude of the buoyant force is given by the size of the pink arrow. Was your prediction correct?

PHYS 242 Buoyancy

(b) Volume

i. PREDICT how the buoyant forces would compare for two objects of di↵erent volume but equal mass submerged in water.

ii. Check your prediction using the video “4 – Di↵erent Volumes” on iLearn. Was your prediction correct?

i. PREDICT how the buoyant force would compare for two identical blocks submerged at dif- ferent depths (e.g. near the surface and near but not touching the bottom).

ii. Check your prediction using the video “1 – Block at Di↵erent Depths” on iLearn. For this question, ignore the box that is only partially submerged.

(d) Density of object

i. PREDICT how the buoyant forces would compare for two objects of the same density but di↵erent size.

ii. Check your prediction using the video “5 – Same Density” on iLearn. Was your prediction correct?

(e) Density of fluid

i. Honey has a density greater than that of water. PREDICT whether the buoyant force on an object submerged in honey is greater than, less than, or equal to the buoyant force on the same object submerged in water.

PHYS 242 Buoyancy

ii. Check your prediction using “2 – Block in Di↵erent Liquids” on iLearn. Was your prediction correct?

(f) Summarize your results from this section by identifying the factors that influence the magnitude of the buoyant force exerted on a submerged object by a fluid. (Recall that you tested mass, volume, depth, density of object, and density of fluid.)

5. Measuring the buoyant force on an object that sinks

(a) In this section, we’ll be looking at the buoyant force on small (3 L), medium (6 L), and large (9 L) aluminum blocks. For each block:

i. Fill in the columns for block mass, weight, and buoyant force in the table. You can find the mass and buoyant force using the video “6 – 3 Sizes” on iLearn. (Mass is in the upper left-hand corner of the screen).

ii. Determine the volume (using the video) and weight of water displaced by the block when completely submerged. (Hint: the density of water is 1 g/cm

3 ). Fill in the remainder of the

table below.

Block Water Displaced

Volume (L) Mass (kg) Weight (N) Buoyant Force

(N) Volume (L) Weight (N)

3 L

6 L

9 L

(b) Generalize your results by answering the following questions about objects that sink:

i. Is the volume of water displaced by a submerged object greater then, less than, or equal to the object’s own volume?

PHYS 242 Buoyancy

ii. Is the weight of the water displaced greater than, less than, or equal to:

• the weight of the block?

• the buoyant force?

(c) Use your answer to question (b) above to write an expression for the buoyant force on a submerged object in terms of the volume of the water displaced (Vdisp) and the density of water (⇢water). (How is the weight of the water displaced related to the density and volume of the water displaced?)

Is your expression consistent with your results from Section 4 (Variables that influence the buoyant force)? (According to those results, which variables influence the buoyant force on a submerged object?)

Check your expression for the buoyant force with your instructor.

6. Measuring the buoyant force on an object that floats

(a) Consider a block that floats in water.

i. What is the direction of the force exerted by the water?

ii. Draw a free-body diagram for a block floating in water. How does the buoyant force compare in magnitude to the weight of the block? (What is the net force on the block?)

PHYS 242 Buoyancy

iii. Use your answers to describe a procedure for determining the magnitude of the buoyant force exerted on a floating block. (What single measurement can you make to determine the buoyant force on a floating object?)

(b) Generalize your results by answering the following questions about floating objects.

i. How does the volume of water displaced by a floating object compare the object’s own total volume?

ii. How does the weight of the water displaced compare to

• weight of the block?

• buoyant force?

(c) Use your answers to Questions (a)-(b) to write an expression for the buoyant force on a floating object in terms of the volume of the water displaced (Vdisp) and the density of the water (⇢water). (How is the weight of the water displaced related to the density and volume of the water displaced?)

7. Conclusion

(a) Generalize your results by answering the following questions.

i. What does the buoyant force on a submerged object depend on? Identify specific experi- ments that support your answer. Show how your general expression for the buoyant force is consistent with these results.

PHYS 242 Buoyancy

ii. What does the buoyant force on a floating object depend on? Identify specific experiments that support your answer. How how your general expression is consistent with these results.

(b) Archimedes’ principle states that the magnitude of the buoyant force on an object is equal to the weight of the liquid displaced by the object.

i. Is your result for the magnitude of the buoyant force on a submerged object consistent with Archimedes’ principle? Explain.

ii. Is your result for the magnitude of the buoyant force on a floating object consistent with Archimedes’ principle. Explain.

iii. Placing additional weight on a floating object causes it to rest lower in the water. Explain this observation in terms of the buoyant force and Archimedes’ principle.