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Density

Objectives

(from the 2016 Massachusetts Science and Technology/Engineering Standards)

8.MS-PS1-2. Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred… Properties of substances include density, melting point, boiling point, solubility, flammability, and odor.

HS-PS1-3. Cite evidence to relate physical properties of substances at the bulk scale to spatial arrangements, movement, and strength of electrostatic forces among ions, small molecules, or regions of large molecules in the substances….Examples of bulk properties of substances to compare include melting point and boiling point, density

HS-PS1-11(MA). Design strategies to identify and separate the components of a mixture based on relevant chemical and physical properties…. Relevant chemical and physical properties can include melting point, boiling point, conductivity, and density.

Teacher demonstrations: Explain how students will do their lab

  1. Use electronic balance to measure mass of several objects

  2. Use ruler to measure the volume of several objects (length, or radius)

  3. Immerse the object. Measure the change in volume using liquid displacement

  4. Note the difference in volume measured due to the 2 different measuring methods (experimental error)

  5. Calculate density = mass / volume d = m / v

 

Density depends on

the spacing between atoms

the number of nucleons/atom

or both factors

Here we see spacing between atoms changing density:

Let’s look at the same thing in 3d

Density also can change if the # of nucleons/atom changes.

What if we have 2 blocks of solid matter, with same number of atoms.

On the left is iron, on the right is phosphorus. Which would be denser? Why?

Why may we safely ignore the number of electrons when thinking about an object’s density?

http://quatr.us/chemistry/atoms/iron.htm

Density of liquids

 

Density of gases

Not all gases have the same density. Here we see a demonstration of sulphur hexaflouride gas.

Density sulphur hexaflouride gas GIF

Solids and liquids: Metals vary in density

Not all metals are the same density. Here an iron cannonball is demonstrated to be less dense than liquid mercury metal.

Cannonball in Mercury Density GIF

Student work

Day 1: Teacher demo & presentation. Followed by the density lab – To be done individually, or with 1 partner.

Day 2: Complete the density lab. Turn in sheet.

Day 3: “Finding densities” worksheet (double sided, turned in by end of class.) Homework: Read at home “Density test study guide”

Physics in film

up-balloon-1.jpg

Up movie balloons

Ok, I was already wrong. The first time I saw this trailer I thought the balloons were stored in his house. After re-watching in slow motion, it seems the balloons were maybe in the back yard held down by some large tarps. This is better than what I originally thought. Oh well, let me answer the question even though it is wrong. What if he had the balloons in his house and then released them? Would that make the house float more? Here is a diagram:

Up movie balloon house

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o, would one of these float more than the other? What makes things float? I have talked about this in more detail in the Mythbusters and the lead balloon, so I will just say that there is a buoyancy force when objects displace air or a fluid. This buoyancy force can be calculated with Archimedes’ principle which states: The buoyancy force is equal to the weight of the fluid displaced. The easiest way to make sense of this is to think of some water floating in water. Of course water floats in water. For floating water, it’s weight has to be equal to it’s buoyant force. Now replace the floating water with a brick or something. The water outside the brick will have the exact same interactions that they did with the floating water. So the brick will have a buoyancy force equal to the weight of the water displaced. For a normal brick, this will not be enough to make it float, but there will still be a buoyant force on it. Mathematically, the buoyant force can be written as:

i-bdc91755f0fe4e2400f78a097de38324-f-bouyancy-equation.jpg

Ok, back to the UP house. What is being displaced? What is the mass of the object. It really is not as clear in this case. What is clear is the thing that is providing the buoyancy is the air. So, the buoyancy force is equal to the weight of the air displaced. What is displacing air? In this case, it is mostly the house, all the stuff in the house, the balloons and the helium in the balloons. In the two cases above, the volume of the air displaced does not change. This is because the balloons are in the air in the house. (Remember, I already said that I see that this NOT how it was shown in the movie). So, if you (somehow) had enough balloons to make your house fly and you put them IN your house, your house would float before you let them outside.

How many balloons would you need to make the house float?

I realized while writing this that I am once again too slow. Others have already calculated this. First is the The Science and Entertainment Exchange. The other excellent coverage of this is from Wired.com. I think with both of these I will just describe how you could do this and leave it as a homework problem. You would need to estimate:

  • The size of the house.
  • The mass of the house (I would assume the whole house is like 10% wood and use the volume of the house and the density of wood – my first guess)
  • The volume of the air displaced. Again use the density of wood above.
  • The size of each balloon. A typical house hold balloon probably has a diameter of about 30-40 cm. You would also need to know the mass of the rubber in each balloon. This shouldn’t be too hard as you could get this from a deflated balloon (first guess 5 grams).
  • The above could give you an estimated calculation for the buoyant force from each ballon plus its weight, or the net force from each balloon. You could just estimate this also.
  • You would also need to estimate the amount of string needed, it would have a non-negligible weight.

Since I got “scooped” on my original investigation, I will give two bonus topics

Why doesn’t the balloon house keep rising?

The reason the balloon reaches a certain height is that the buoyant force is not constant with altitude. As the balloon rises, the density of the air decreases. This has the effect of a lower buoyant force. At some point, the buoyant force and the weight are equal and the balloon no longer changes in altitude.

http://scienceblogs.com/dotphysics/2009/06/03/physics-and-the-movie-up-floating-a-house/

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https://en.wikipedia.org/wiki/Larry_Walters

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Mythbusters : Lets talk buoyancy – Pirates of the Carribean

Adam and Jamie explore the possibility of raising a ship with ping-pong balls, originally conceived in the 1949 Donald Duck story The Sunken Yacht by Carl Barks.

MythBusters S02E13 Pingpong Rescue, 2004

Doing the math of MythBusters – Warning: Science content

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More on the movie Up! (or Upper) – Rhett Allain on June 9, 2009

If the house were lifted by standard party balloons, what would it look like? The thing with party balloons is that they are not packed tightly, there is space between them. This makes it look like it takes up much more space. Let me just use Slate’s calculation of 9.4 million party balloons. How big would this look? This could be tricky if I didn’t know how to cheat. How tightly packed do party balloons fit? Who knows? Pixar knows.

From that Slate post, Pixar said they used 20,600 balloons in the lift off sequence. From that and the picture I used above and the same pixel size trick, the volume of balloons is about the same as a sphere of radius 14 meters. This would make a volume of 12,000 m3. The effective volume (can’t remember the technical term for this) of each balloon would be:

And then this would lead to an apparent volume of the giant cluster of 9.4 million balloons:

i-ba11d2f602fe28075ae3eb39cd12e916-volume-of-cluster.jpg

If this were a spherical cluster, the radius would be 110 meters. Here is what that would look like:

How long would it take this guy to blow up this many balloons? You can see that there is no point stopping now. I have gone this far, why would I stop? That would be silly.

The first thing to answer this question is, how long does it take to fill one balloon. I am no expert, I will estimate low. 10 seconds seems to be WAY too quick. But look, the guy is filling 9.4 million balloons, you might learn a few tricks to speed up the process. If that were the case, it would take 94 million seconds or 3 years. Well, you can see there is a problem because that time doesn’t include union bathroom breaks. Also, a standard helium balloon will only stay inflated for a few days.

What if it was just 20,600 balloons like Pixar used in the animation? At 10 seconds a balloon, that would be 2.3 days (and I think that is a pretty fast time for a balloon fill). Remember that MythBusters episode where they filled balloons to lift a small boy? Took a while, didn’t it?

How many tanks of helium would he need? According this site, a large helium cylinder can fill 520 of the 11″ party balloons and costs about $190. If he had to fill 9.4 million balloons, this would take (9.4 million balloons)(1 tank)/(520 balloons)= 18,000 tanks at a cost of 3.4 million dollars. You could buy an awesome plane for that much. Oh, maybe he got the helium at cost.

http://scienceblogs.com/dotphysics/2009/06/09/more-on-the-movie-up-or-upper/

also

http://scienceblogs.com/dotphysics/2009/06/09/more-on-the-movie-up-or-upper/

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Weightless in Wonkaville

Everett Collection via popsci.com
In “Willy Wonka and the Chocolate Factory,” when Charlie and Grandpa Joe sip a bit of Wonka’s “fizzy lifting drink” on the sly, they are immediately lifted off their feet and into the air, floating among the bubbles. This, presumably, is the result of all that carbonation inside their stomachs, increasing Grandpa and Charlie’s buoyancy to the point where it can overcome the force of their own weight, lifting them into the air.

Thanks to good old Archimedes’ principle, we can calculate the amount of air that would need to be displaced to perform the lifting, and thus the necessary increase in volume due to the drink’s carbonation of the bodies of Charlie and Grandpa Joe.

As you can see, to counteract the force of his mass (here we estimate his mass to be 70 kilograms), Grandpa would have to swell up to a massive 54 cubic meters-if he was a sphere, he would be five meters across (that’s over 15 feet).

For a more familiar reference, that’s at least twice as big as poor Violet’s sudden rotundity after sampling Wonka’s experimental three-course gum. Which, if you’re interested, would need to have a density of 6 x 109 kg/m3 to contain enough juice to fill Violet to the size depicted — that’s four or five thousand times the density of an average metal. Watch your fillings!

http://www.nbcnews.com/id/23943370/ns/technology_and_science-science/t/physics-realm-hollywoodland/#.VzORWNIrJMw
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Buoyancy is the force that makes something float. It depends on the volume of the floating object and the density of the liquid in which it is floating. For something to remain above the water level, the bouncy force must be greater than the force of gravity pulling down on the object.

In the case of Rose, Jack and the door, the buoyancy force of the ice cold salt water pushing up on them must be greater than the force of their combined weight. The force pushing up depends on the volume of the object submerged and the density of the water in which it is floating. So lets see how that stacks up. Looking at the raft in stills from the movie and looking up Kate Winslet’s height, we can estimate that the raft is about 6’x3’x5″ and the density of ice cold salt water is 1000kg/m^3. Our heros would survive only if the top of the raft were at least at the water level. So let’s assume the volume submerged is that of the full door, 0.254 m^3 (keeping it all in metric). Multiply this by the density of salt water and the pull of gravity and you find that the buoyant force is 2490N.

If the weight of Jack+Rose+door is greater than 2490N, they are all in hot water (or, I guess freezing cold water). Seeing as there was much controversy of Kate Winslet’s weight, it was easy to find out that at the time of the movie she weighed 125lbs, or 549N. It was a little harder to track down Leo’s weight, but he topped out at a whopping 161lbs or 715N.

Finding the weight of the door is a bit trickier. Weight is volume times density times the pull of gravity, but its not clear what the door is made of. There were three types of wood commonly used on the Titanic, teak, oak and pine with densities of 980kg/m^3, 770 kg/m^3 and 420 kg/m^3 respectively. If the door were teak, the weight would be 2,440N, oak would be 1,147N and pine tops out at 617N.

Teak would barely float on its own so Rose and Jack would be headed into an eternity of sappy music together. If the door were pine, the total force of Jack+Rose+Door would be 2,313N and all would have been well in the world of middle school girls across the globe. But darn you Mr. Cameron, pine was simply not good enough for your movie! The door was most likely oak which has a weight of 1,920N so adding the adorable couple would give a weight of 3,185N, just a little too heavy.

Subtract Jack and you get a force of 2,470N, just light enough to float and allow Rose to go on and live a long and happy life as Jack’s frozen body spent continued to bob in the ocean. Before he died in his melodramatic, tear-jerking manner, he made her make him a promise.

“You must do me this honor. Promise me you’ll survive. That you won’t give up, no matter what happens, no matter how hopeless. Promise me now, Rose, and never let go of that promise.”

She wouldn’t have had to make that promise if James Cameron had just used pine!

http://physicsbuzz.physicscentral.com/2012/09/sorry-girls-titanic-doors-were-made-of.html

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Pirates of the Carribean

http://physics.stackexchange.com/questions/106723/can-a-submerged-capsized-vessel-be-turned-into-a-sort-of-diving-bell-and-propell

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External resources

Multimedia lesson on density of aluminum and copper cubes
http://www.middleschoolchemistry.com/multimedia/chapter3/lesson1

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