Videos of “More on surface tension – floating Ping-Pong balls”

Here are the videos of the “More of surface tension – floating Ping-Pong balls” demonstration. The full videos are linked from the GIF captions.

Cup partially full with ball drawn to the edge of the cup

Video Apr 22, 11 17 01 AM 00_00_30-00_00_36

Cup over full with ball drawn tot he middle of the cup. 

 

Video Apr 22, 11 18 39 AM 00_00_27-00_00_34


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.

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More on surface tension – floating Ping-Pong balls

This is not a new demonstration but rather an extension of a previous post “Surface tension – floating Ping-Pong balls” The equipment is just a ping-pong ball, a cup and some water.

Photo Apr 22, 11 16 28 AM

In the previous demonstration the ball was placed in the middle of the cup and was dragged to the side by a surface tension imbalance. Soap was then added as a surfactant to reduce the imbalance and allow the ball to float near the middle of the cup. In this extension (see, for example, various Martin Gardner books 1,2) the first part of the demonstration is the same as in “Surface tension – floating Ping-Pong balls“. However, in the second part, the ball is held in the middle by changing the curvature of the water surface rather than reducing the surface tension.  The water surface curvature is changed by overfilling the cup so that the water surface curves up above the lip of the cup. In this case the minimum area occurs when the ball is centered in the cup. Again, see John Bush’s lecture notes here for a more formal discussion of surface tension.


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.

Pump efficiency calculations

Just a quick note on an extension of the pump performance curves demonstration that was suggested by Ed Maurer of SCU. The initial demonstration had students calculate the head rise – flow rate relationship for a cheap aquarium pump. Ed extended this with the addition of an inline power meter (such as the Kill A Watt meter). Simply record the power consumed (P in watts) for each flow rate (Q) and pump head rise (Ep=height over which water is pumped plus tubing and exit head loss) . The efficiency can then be calculated as

η=γQEp/P.

You can then plot the pump efficiency against flow rate on the same plot as the head rise vs flow rate. When Ed Maurer did this he reported very low efficiency peaking around 20%. This is not terribly surprising as they are cheap pumps (typically only cost around $20).


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.

Video of “Drag, added mass, and Spring-Mass systems”

Here are the videos of the “Drag, added mass, and Spring-Mass systems” demonstration. The full videos are linked to the GIF captions.

0.15 kg oscillating in air

Video Mar 14, 2 03 01 PM 00_00_00-00_00_09

0.15 kg oscillating in water (lower frequency than in air)

Video Mar 14, 2 05 08 PM 00_00_01-00_00_11


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.

Drag, added mass, and Spring-Mass systems

The concept of added mass can be a useful but perhaps a little hard to visualize (either the added mass or the impact of added mass on a system). This is a simple demonstration adapted from Granger’s Experiments in Fluids to illustrate the impact. The basic idea is that a solid accelerating in a fluid will accelerate fluid in its wake effectively increasing its inertia. The method for demonstrating this is to use a spring-mass system that is released and oscillates in air and then water. The added mass in water is much larger than that in air, increases the system inertia, and reduces the frequency of oscillation.

Equipment

  1. Container of water
  2. Spring
  3. Mass
  4. Support structure
  5. Stop watch

Photo Apr 11, 11 50 01 AM

Demonstration

  1. Mount the mass on the spring in air, extend the spring, and release.
  2. Measure the time taken for the mass to oscillate 20 times (may be more or less depending on the losses in the system and frequency of oscillation).
  3. Mount the mass on the spring and place it in the water container (ideally only the mass on a long cord with the spring dry), extend the spring and release.
  4. Measure the time taken for the mass to oscillate 20 times (this may be harder and you may have to have fewer oscillations this time as the water damps out the motion fairly quickly).

Analysis

The frequency of oscillation (f) of the system is

f~(k/m)1/2

where k is the spring constant and m is the mass. There are a number of methods for getting to this result. Dimensional analysis is an easy method where the dimensions of the parameters are [f]=T-1, [k]=MT-2, and [m]=M. Alternatively one can write down the equation of motion

m(d2x/dt2)=-kx

and solve to get

x=x0cos((k/m)1/2t+Θ)

giving an oscillation frequency of

f=(k/m)1/2/2π.

Regardless of how you get there, the main result is that the frequency of oscillation is inversely proportional to the square root of the mass, i.e.

(2πf)2=k/m.

When the mass is immersed in the water the effective mass of the system increases due to the added mass. Therefore, the Frequency of oscillation of the system will also drop. Denoting the added mass by ma the frequency in water (fw) is given by

(2πfw)2=k/(m+ma).

For a known mass, the spring constant can be calculated from the frequency of oscillation in air. The added mass can then be calculated from this data and the frequency of the system in water.

I ran a test using the equipment shown above. In this case the mass was 0.15 kg and the frequency in air was f=1.6 hz giving a spring constant of

k=(2πf)2m=15 N/m.

The frequency of the system when immersed was fw=1.45 hz giving and added mass of

ma=(k/(2πfw)2)-m=0.031 kg

or 20% of the original mass.


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.