This unlikely-looking contraption is in neutral equilibrium when equal weights are placed onto the two outer arms, as shown, so it will remain at rest in any position. If a net weight is placed on either side, that side will go down.

Ask your students what they think will happen when the system is released in the configuration photographed at the left above. Draw attention to the similarity between the Roberval balance and the simple pan balance.

In the pulley system photographed, the weight hanging from the free pulley is W, and the pulleys are approximately massless. The rope will be pulled at its free end, and passes over the free pulley, under the pulley attached to the weight, and back over the fixed pulley to support the free pulley. With what force F must you pull on the free end of the rope to just barely lift weight W off the ground: W, W/2, W/3, or "other?"

Let your students guess before having one of them try to lift weight W by pulling on the end of the rope. Note that this is a "gag" demonstration! The reasons why the system stays set up as photographed are (1) the rope is pinned to the "free" pulley, and (2) the rope loop is stretched tightly between the upper and lower pulleys, so that the friction prevents the weight of the "free" pulley from falling. A video of the "action" is available below.

This result can be determined in about twenty seconds as follows: Pulling on the free end with a force F causes a tension F throughout the rope. The result is a force 2F downward and F upward on the "free" pulley, causing it to move downward.

Two springs connected in series support a weight. Strings slightly longer than the springs are connected in parallel with each spring, as photographed. The connecting wire loop between the two springs is then removed, forming two separate parallel routes, each consisting of a spring and a string in series. Comparing the final configuration with the initial configuration, will the weight be higher, lower, or at the same vertical position?

The pictures above show the system in its initial and final configurations, as well as in detail of how the springs and strings are coupled at the center.

This demonstration is an analog to paradoxical behavior in complex series/parallel arrangements for other mechanical, hydraulic, and electrical systems. Perhaps the most notable is Braess' paradox for traffic flow. In certain types of congested traffic flow situations, opening an additional new route between two points may actually increase the average time taken to travel between the two points.

An hourglass with its sand has a weight W when at rest on a scale as photographed. Before time t=0 the sand is held in the top of the hourglass by an invisible massless membrane. At time t=0 the membrane is removed by a massless demon, allowing the sand to fall into the bottom of the hourglass. At time t=T the sand is all in the bottom section. If the original and the final weight of the hourglass with sand is W, what is the force (or weight) read by the scale during the time interval from t=0 to t=T.

The answer involves two parts: (1) the start and stop of the sand flow, and (2) the steady-state flow. At the start, because there is some sand in the air, not being weighed, the scale momentarily falls. During the steady-state sand fall the extra force of sand hitting the bottom very nearly cancels the loss of weight of the sand in the air, so the scale reads very nearly W (see below). When the sand column is ending, the force of the sand hitting the bottom exceeds the loss of weight of the shrinking sand column, so the scale momentarily rises. This can be seen in an mpeg video by clicking on the link below above.

During the steady state fall, the downward frictional force of the sand on the inner surface of the funnel is accompanied by an upward reaction force exerted by the funnel on the sand. This force provides a very small additional "weight" seen by the balance, causing the steady-state reading to be slightly higher than the actual weight before or after the sand falls. This can be observed using an electronic balance that has been zeroed with the container and sand at rest, seen in the photograph at the left below. The picture, taken during the time when the sand was falling, shows the small reaction force created by the sand sliding through the funnel. Clicking on the link, below, starts an mpeg video of the action, showing the entire sequence: a momentary negative pulse at the start, the slightly increase in weight during the period when the sand is falling, and the positive pulse at the end.

This was once a popular toy, and has been used in "demonstrations" of psychokinetic abilities. This demonstration can be used to discuss how unexpected behaviour or difficult-to-observe variables can be used to confuse or mislead observers.

Of course, this is actually a demonstration of driven resonance - with a bit of practice, via small movements of your hands you can drive any one of the pendula you choose. Encourage your students to analyze pseudoscientific explanations for real phenomena.