Video of “Buoyancy: Throwing rocks from boats (and weighing coins)”

Here is the video of the “Buoyancy: Throwing rocks from boats (and weighing coins)” demonstration. The two GIFs show the dropping of the coins into the cup and then the dumping of them into the water. The full video is linked here.

Dropping the coins into the cup showing that 9 quarters displaces 50 ml of water.

drop

Dumping the coins out showing that, when submerged, they displace a lot less than 50 ml.

dump


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Buoyancy: Throwing rocks from boats (and weighing coins)

This is a simple demonstration of a classic buoyancy question about throwing a rock out of a boat (the full scale problem in discussed by Physics Girl here). The question is ‘if you are sitting in a boat holding a rock and throw the rock into the water will the water level go up or down’. The answer is that, when the rock is in the (floating) boat it displaces its weight but when it is thrown in the water (and sinks) it displaces its volume. Therefore, the water level drops when it is thrown out of the boat.

This is a simple scaled down version that clearly demonstrates the puzzle result but can also be used to weigh the heavy object (in this case coins).

Equipment

  1. Small plastic cup
  2. measuring cup
  3. syringe (for small adjustments in the volume of water in the measuring cup
  4. a hand full of identical coins (I used 9 US quarters).

Photo May 10, 1 53 34 PM

Demonstration

  1. fill the measuring cup so that the water level is one line below the top volume measurement when the empty cup is floating in the water
  2. drop the coins in one by one until the water level rises up to the top line (record the number of coins needed)
  3. pour the coins into the water and put the plastic cup back on the water.
  4. note that the water level is below what it was when the coins were floating in the cup.

Analysis

The puzzle answer is fairly straightforward. However,the demonstration can also be used to estimate the weight of the individual coins (hence the need to use all the same coins). The change in volume recorded as the coins are added is equal to the volume displaced by the coins (see figure below). Therefore, the volume change multiplied by the density of water will equal the mass of the coins added. I measured a 50 ml change in volume when I added 9 quarters. The density of water is approximately 1 g/ml so the 9 coins have a mass of 50 g. The weight of the individual quarters is, therefore 50/9=5.56 g (which is very close to the actual standard mass of a quarter of 5.67 g). It is also possible to work out the volume of the coins by measuring the volume they displace when they sink (see figure). My measuring cup did not have enough resolution to get a good volume. The total volume of the 9 coins would be 7.5 ml based on US Mint dimensions.

boat

Figure showing (from left to right) the cup displacing the coins weight, the empty cup, and the coins displacing their mass with the water level lower than when the coins are floating in the cup.

The other great thing about the demonstration is that it is easy to ask a lot of questions around the demonstration. Obviously you can pose the original question about the water level going up or down. There are also simple calculations that can be asked such as “what is the mass (or weight) of the coins?”, “what is the approximate density of the coins?”. The US mint website has information about size and metal content that can be used to calculate the actual density for comparison.

Ii is also really easy to have this as an activity in class. I used a version of it on the last day of class one semester using pennies.I used small and large plastic cups and gave the students the dimensions of the small cup and the equation for the cup volume (here). In this case you count how many pennies it takes to sink the cup so that the mass of pennies matches the density of water multiplied by the cup volume.  You will also need a roll of paper towel for the clean up. I did not explain the demonstration I just gave them the equipment and told the to calculate the weight of a penny. It was well received by the students though I had to give some groups a hint or two as to how it worked.


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Videos of “Buoyancy – Balancing ping-pong balls”

Here are the videos of the “Buoyancy – Balancing ping-pong balls” demonstration. The full video is here. The GIF titles link to shorter videos. Obviously the YouTube videos from @veritasium here, here, and here have slightly higher production standards.

Setup 1

balance1 00_00_00-00_00_16~1

 

Setup 2

balance2 00_00_00-00_00_27~1

The payoff

balance3 00_00_01-00_00_06~1

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Buoyancy – Balancing ping-pong balls

Background

I saw this demonstration on Veritasium’s YouTube channel (see Beaker Ball Balance Problem video). It is really simple to run as long as you have a good balance. The result is not obvious and so the reason for the result requires a little analysis. Therefore, I think it would be good to write it up and provide a more detailed explanation of the demonstration complete with free body diagrams.

Equipment

  1. Balance
  2. Three identical cups
  3. Water
  4. Two ping pong balls, one filled with sand of something to weigh it down (actually any two balls with the same diameter as long as at only one of them floats)
  5. Tape
  6. String
  7. A stand

Photo Aug 12, 11 06 18 AM Photo Aug 12, 11 06 23 AMPhoto Aug 18, 4 17 13 PM

Procedure

  1. Place identical volumes of water in two cups but leave enough space for at the top of the cups so that it will not overflow when you place the balls in the cups.’
  2. lock the balance so that it is level for steps 3-7.
  3. Take the empty ping-pong ball and tape some string to it and then tape the string to the base of the empty cup. Use as little string as possible. When you pour the water in, the ball has to be fully submerged.
  4. Pour the water from one of the cups into the one with the taped ball.
  5. Place the two cups with water (one with a ball attached) on either side of the balance.
  6. Suspend the heavy ball from the stand into the second cup such that it is fully submerged.
  7. Poll your students to see which way they think the balance will tip when it is released.
  8. Unlock the balance and observe which way the balance tips (it should go up on the side with the ball taped to the bottom of the cup)

Analysis

We start by looking at the setup (see figure below). The two cups have identical volumes of water in them and both have a submerged ball with identical volumes which, therefore, displace identical volumes of water. Therefore, the depth of water in each cup is the same. For the purposes of this explanation light ball is denoted as ball (1) and the heavy suspended ball is ball (2).

balance1

We now examine the forces acting each ball (see figure below). Ball (1) has weight down (W1), buoyancy force up (FB), and the tension force in the string acting down (T1). The forces sum to zero as the system is in equilibrium. Ball (2) has the same set of forces acting on it. However, for ball (2) the tension force (T2) is acting up as the ball is denser than water such that the buoyancy force is less than the weight. Hence the ball must be suspended from above. The only important thing here is that the balls displace the same volume of water such that the water levels in each cup are identical.

balance2

We now turn our attention to the forces acting on the cups (see figure below).

balance3

For cup (1) there is the hydrostatic pressure force acting down, PA, that depends only on the cup geometry and the depth of water in the cup. There is also the weight of the cup (Wcup), the tension on the string acting up (T1) and the force due to the scale Fscale(1). Therefore,

Fscale(1) = PA+Wcup-T                                                                                                (1)

The forces acting on cup (2) are the hydrostatic pressure force acting down, PA, the weight of the cup (Wcup), and the force due to the scale Fscale(1). Therefore,

Fscale(2) = PA+Wcup                                                                                                        (2)

As the cups are identical and the water depth in is the same in each then both PA and Wcup are the same in equations (1) and (2). Therefore, subtracting (1) from (2) gives

Fscale(2) – Fscale(1)= T1

or

Fscale(2) > Fscale(1)

and the balance goes down on the side with the suspended ball.

In fact, you could run this test with any two sized balls as long as:

  1. One ball floats and is tethered to the base of a cup
  2. One ball does not float and is suspended from above
  3. The water level in the two identical cups is the same.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Other fluids education resources III: YouTube channels

Prior posts on other resources (1, 2) linked  to particular websites, books, blogs, and videos. Here I just want to highlight a couple of YouTube channels that have some great fluid mechanics content. In general they tend to focus on fairly accessible stuff like surface tension and buoyancy though there is also other content as well. In no particular order they are:

Physics Girl (on twitter @thephysicsgirl) posts videos covering a very broad range of physics much of which is fluid mechanics. Her videos cover topics such as surface tension, vortex dynamics, and the Coanda effect. There are also some cool videos on calculating Pi with a dart board and momentum from dropping stacked balls.

Veritasium (on twitter at @veritasium) is another general physics YouTube channel with a couple of very nice fluids videos. One of the best is this set on buoyancy forces (second & third). There is also one on jet packs. A lot of it is not fluids but there are a ton of other interesting videos including this one on our willingness to take risks.

Benjamin Drew teaches at the University of Western England. He has posted a large number of his fluid mechanics lectures online. The lectures are well organized and, given the number of posted videos, there is quite broad coverage. He has also posted a bunch of lectures from other courses he teaches on a broad range of subjects.

Vsauce (on twitter @tweetsauce) doesn’t do much on fluid mechanics other than this video on water. However, there are a lot of interesting general science videos. Well worth following.

With the exception of Ben Drew’s videos there is not a whole lot of math or theory in this set but there they are all well produced, well presented, and well worth following.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.