Pendulums and deriving the work energy equation

Obviously deriving the work energy equation is not a demonstration (other than a demonstration of one’s memory and math ability). This demonstration was used by Ben Sill to illustrate the terms in the work energy equation that can then form the basis for the derivation.

Equipment

You will need either a string pendulum with a weight on the end or a spring with some mass on the end. I use the spring mass system that I also use for dimensional analysis.

Photo Apr 21, 11 16 48 AM

Demonstration

Start the pendulum or spring moving with some initial deflection. Talk to the students about what they observe. Perhaps ask them to predict what will eventually happen (maybe a clicker question). Maybe get them to reflect on why the amplitude of the oscillation decreases over time. Once there is a substantial, noticeable reduction in the amplitude stop the demonstration.

Analysis 

Write down a generic work energy equation

Total energy at time (2) = Total energy at time (1) + work done on the system – losses (i.e. work done by the system)

I keep the losses separate even though they are work done by the system and hence work done with a minus sign. This just keeps things a little more physically accessible as students seem to be able to think in terms of losses rather than in terms of the pendulum or spring doing work on the surroundings. The work done is the energy spent initially raising the pendulum or pulling down the spring. The total energy at time (1) is zero if you take this time to be before you touch it. The losses are due to drag on the object and internal damping. There is no need to get into details of how to model these terms, it is the bulk equation that you want to demonstrate.

From this point it is possible to derive the work energy equation with the caveat that the energy terms are energy fluxes and the work and loss terms are rates of work and loss.

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 the “Definition of a fluid – sliding OHP transparencies” demonstration

Here are the videos from the “Definition of a fluid – sliding OHP transparencies” demonstration. the full videos are linked from the GIF titles

Shearing a solid (book) showing finite deformation

book-shear

Shearing a fluid showing continuous deformation

fluid-shear

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.

Definition of a fluid – sliding OHP transparencies

From now on this is how I am going to start each semester teaching fluid mechanics. The definition of a fluid that is use is

A fluid is a material that deforms continuously under the action of a shear stress.

This demonstration illustrates the continuous deformation.

Equipment

  1. Overhead projector
  2. Two transparency sheets
  3. A viscous liquid such as dish soap (easy to clean up) or honey (not so easy to clean up)
  4. A text book (they have to be good for something)

fluid-def

Demonstration

  1. Remind the class that a when you apply a shear force to a solid it deflects a finite amount
  2. Demonstrate this by applying a shear to the text book. The book is a useful prop because you can get it to noticeably deflect.
  3. Place one of the transparencies on the OHP and pour some of the soap onto the middle of the sheet
  4. Place the second sheet on top of the first.
  5. Slowly pull the two sheets apart horizontally while stating that a fluid differs from a solid in that a fluid deforms continuously under the action of a shear stress.

I then write the definition on the board and launch into fluid properties. Obviously there is no analysis to be done 5 minutes into the first class of a fluids course, but it can help students clearly visualize the difference right from the start.

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 the “Atmospheric pressure, hydrostatics, and upside down water glasses” demonstration

Here are videos of the “Atmospheric pressure, hydrostatics, and upside down water glasses” demonstration. The full videos are linked form the GIF titles

Demonstration with the cup full

full

Demonstration with the cup only partially full

part-full

Again thanks to Henry Burridge for this demonstration.

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.

Atmospheric pressure, hydrostatics, and upside down water glasses

Courtesy of Henry Burridge

Background

The demo was inspired by a suggestion in the Cambridge engineering supervisions for first years and a question that Colm Caulfield asked me during a summer school. The question was “Given that the atmospheric air pressure is roughly equivalent to a 10m head of water, why can’t we build 10m deep swimming pools and turn them upside down?”.

This question works well with engineers when being introduced to hydrostatics, who (typically) are quick to appreciate that it is relatively simple to create a structure that can support a pressure drop across it of 1 atmosphere. Hence, one can imagine building a 10m deep swimming upside down, the ‘ceiling’ of which is exposed to atmospheric air pressure above and near zero pressure within the water just below.

So if we could fill the upside-down swimming pool with water to a depth of 10m then the water at the ceiling could be at near zero pressure whilst the water 10m below would be roughly at atmospheric pressure.

Equipment:

  1. A pint glass.
  2. A piece of thin waxy card, just a bit bigger than the size of the rim of the pint glass (a postcard, photographic paper, or the cover of a CD case should work).
  3. A piece of fine metal gauze or mesh, just a bit bigger than the size of the rim of the pint glass. I have used wire mesh with mesh gaps of about 0.5mm to 1mm and a metal plate perforated with holes of about 3mm diameter.
  4. Some Blu-Tack which can be used to seal the gauze or mesh to the rim of the glass.
  5. A bucket – just to catch any spills.

Equipment required for the first part of the demonstration (no gauze)

Photo Aug 21, 8 03 06 AM

Aim

To encourage consideration of hydrostatic pressures and the role of atmospheric pressure (useful for engineers and the concept of gauge pressures).

Demonstration

After posing the above question to them and having a discussion around it, I usually tell the students to think about it whilst we test the ideas on a smaller scale. I then tell the students that I’m going to fill the pint glass with water and, whilst holding the card in place on the top of the glass, turn the glass upside down. I ask them to think about what will happen, and why, when I remove my support from the card. The answer is that nothing happens (except perhaps the card bowing slightly) – I suggest that the reason nothing happens is that the upside-down glass can support a lower than atmospheric pressure in the water at the top and hence the water at the bottom of the glass can be at atmospheric pressure and hence there is no net pressure forcing the water out of the glass. Thus, the weight of the card can be supported by the surface tension in the interface that forms between the glass and the card.

I then ask them to think about what will happen if we only partially fill the glass with water – the results are the same (since any pressure drop within the air contained inside the glass, required to attain atmospheric pressure within the water at the base of glass, is slight and any expansion of the air typically is small and hence the interface between the card and glass remains small). Finally, to convince them that there really is no pressure force ‘pushing’ the water out of the glass, I repeat the demonstration with the card replaced with the wire mesh or perforated plate (note that until the glass is inverted it is wise to cover the mesh or plate with the card!).

Having convinced them (hopefully) that there really is no force driving the water from the glass, I then return to the question of the upside-down 10m swimming pool and again emphasize that such a situation is in equilibrium but the equilibrium is unstable. It is worth reminding them of more familiar examples of unstable equilibrium, e.g. a pencil balancing vertically on your finger, a ball on the apex of a convex surface. The discussion then typically follows onto to the fact that the density difference across the interface makes the interface unstable and thus any tiny perturbation (or vibration) will take the system away from the unstable equilibrium. However, surface tension is able to stabilize the interface if length of the interface is small – hence since the holes in the mesh or the plate are small enough, surface tension is able to stabilize the interface to small perturbations.

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.