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Statics of Rigid Bodies

  • B3-12 PULLEY - MECHANICAL ADVANTAGE

    B3-12
    Illustrate pulley systems
    The system is initially balanced to account for the weight of the pulleys and rope by adding small weights on the free end of the rope, as seen in the photograph at the left. For every two kilograms hanging from the pulley, the system requires one kilogram hanging from the free end of the rope to obtain equilibrium. Show that deviation from the 2:1 ratio destroys the static equilibrium.
    FS1

  • B3-14: EQUILIBRIUM PARADOX - SCALES AND PULLEY

    B3-14
    Counterintuitive demonstration involving pulley system
    A frame containing the pulley and the lower scale hangs from the upper scale as photographed. The initial weight of the lower scale, pulley, and frame together is about 5 Newtons, as read on the upper scale; initially the lower scale reads zero. The difference in resultant force due to the pulley can be observed from the difference in the change of the two scales.
    FS2

     

  • B3-15: FOOL'S TACKLE

    B3-15
    Illustrate analysis of forces in a pulley system

    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.
    FS2

  • B3-21: CHISEL AS WEDGE

    B3-21
    Demonstrate the mechanical advantage of a wedge

    A wedge is used to split a piece of wood.

    For your safety, goggles are provided
    B3

  • B4-01 HOOKE'S LAW

    B4-01
    Demonstrate the linear relationship between force and stretching for a simple spring.
    Two weights are provided to show linearity over a factor of two in applied force.
    FS2

  • B4-02: HOOKE'S LAW - COMPRESSING A SPRING

    B4-02
    Demonstrate Hooke's law for a spring under compression.

    This tabletop demonstrations illustrates Hooke's Law in compression, for comparison to the typical hanging-spring examples. Add weights to observe that the compression of the spring is approximately proportional to the amount of weight added.
    FS2

  • B4-03: SPRINGS IN SERIES AND PARALLEL

    B4-03
    Show static combinations of springs
    Two springs with approximately the same spring constant can be placed in series and parallel to determine the effective spring constants. You should be able to illustrate the relationships:

    k(parallel) = k(1) + k(2)

    1/k(series) = 1/k(1) + 1/k(2)

    B4, FS1, OS0

  • B4-04: SPRING AND STRING THING

    B4-04
    Illustrate series and parallel springs in a counterintuitive way.

    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.
    FS2

    b4-04a b4-04b

  • B4-11: ELASTIC LIMIT OF RUBBER BAND

    B4-11
    Demonstrate Hooke's law and elastic limit.
    Load small weights to demonstrate Hooke's law. Hanging a few kilograms from the rubber band exceeds its elastic limit.
    FS2, ME1

    b4-11a

  • B4-12: ELASTIC LIMIT OF SOLDER SPRING

    B4-12
    Demonstrate the elastic limit for an inherently inelastic object.
    Place spring on overhead projector, and stretch and compress it. It will quickly become obvious when the elastic limit is exceeded.
    B4

  • B4-13: ELASTIC LIMIT OF A BALLOON

    B4-13
    Burst a balloon.
    Connect balloon to air compressor and blow up the balloon. The picture at the right shows how to connect the balloon to the compressor using a rubber cork and an o-ring.
    B4, I0

    b4-13a

  • B4-14: ELASTIC LIMIT OF WIRE

    B4-14
    Demonstrate the variation in tensile strength with wire diameter.
    Two wires are used: 24 AWG, 0.474 mm diameter, and 20 AWG, 0.786 mm diameter. The ratio of tension required to break two wires is proportional to the square of their diameters, for this case F2 / F1 = 2.75. The two wires can be broken, the required tensions read off the attached spring scale, and the ratio calculated.
    B4

  • B4-21: DEFLECTION OF BEAM - OPTICAL LEVER

    B4-21
    Demonstrate the small deflection of an aluminum beam due to weighting between supports.
    A mirror serves as an optical lever for the laser beam, with its fixed support legs on a lab jack and its other legs on the aluminum beam. The aluminum beam deflects as weights are added, causing the laser beam to move along the scale at the rear of the photograph.
    OS1, F1, ME1, LS1

    b4-21a b4-21b

  • B4-31: FAILURE OF WOOD IN COMPRESSION

    B4-31
    Demonstrate the dependence of the compressional strength of wooden dowels on their diameter and length.
    Place dowel vertically between the plates of the hydraulic press, and compress dowel until it collapses. A 5/8" dowel requires about 1.0 tons, a 7/8" dowel about 2.2 tons.
    B4, FS1

    b4-31a

  • B4-32: CAN CRUSHER - WALL STABILITY

    B4-32
    Show how a small change in the geometry of the can wall can dramatically affect its ability to support a load.

    An assistant balances carefully on one foot on an aluminum soft drink can. When the sides of the can are dimpled simultaneously by poking them sharply with pencil tips, the can immediately collapses, as can be seen in an mpeg video by clicking your mouse on the link below.

    Danger: Keep your fingers out of the way.
    SU15, OF1

  • B4-33: EGG CRUSHER

    B4-33
    Show that an egg can support unexpectedly high forces due to its curved shape.
    An egg is positioned vertically between the "egg crusher" base and top cylinder. The two surfaces are coated with heavy rubber discs to distribute the load. Up to 150 lbs of lead bricks (6 bricks) can be placed on the platform without breaking the egg, though no more than 4 bricks is usually recommended. The lower left photograph shows an egg in the crusher with 50 pounds of lead on it; the photograph at the right is a close-up of the egg in the center photo.

    Important note: Egg must be supplied by instructor.
    B4, FS1

    b4-33a b4-33b

  • C3-03 INERTIA - MASSES HANGING IN SERIES

    C3-03
    Dramatically demonstrate inertia
    Two identical masses are hung in series from a fixed point alternating with three identical strings. When you pull downward on the third (bottom) string, which of the strings will break: the top, the middle, or the bottom string? It depends on how you pull. If you pull very quickly, the bottom string will break, due to the inertia of the bottom mass. If you pull slowly, the top string will break, because the weights increase the tension in the top string.
    FS2

  • C3-06: INERTIA: JENGA

    C3-06
    Demonstrate inertia of rest.
    This commercial toy consists of a stack of blocks with each layer placed 90 degrees to the prior one. The object of the game is to remove blocks from the lower part of the tower without knocking the whole structure over. Trying to do this gently is usually doomed to failure: a quick flick of the finger is the most effective method.
    C3

    c3-06a

  • C4-61: ACCELERATION ON A SCALE

    C4-61
    Illustrate forces in an accelerating system.
    A rigid frame hangs from a spring scale as photographed. In the frame, a mass hangs from a spring. The mass is pulled down and attached to a hook at the bottom of the frame by a short thread loop. (Ask your students how this affects the weight shown by the spring scale.) In this position the spring scale reads about 8 Newtons. Q: When the string is burned, releasing the mass, will the reading on the spring scale immediately after the string breaks (a) increase, (b) decrease, or (c) stay the same? A: It will increase, as seen on the accompanying mpeg video. The last photograph shows details of the lower connection of the weight to the hook.

  • C6-01 INCLINED PLANE - FRICTION BOX AND WEIGHTS

    C6-01
    Shows that the coefficient of friction does not depend upon the mass of the object although the frictional force does.

    A box sits on an adjustable inclined plane. Masses can be placed in the box to change its weight, and thus the normal force exerted by the inclined plane.

    Set the empty box on the incline and increase the angle until sliding ensues. Add weights to the box and repeat the experiment. The weighted box begins to slide at the same angle.

    (Optionally, a string and pulley can be used to add add an additional force to the system.)

    C6, ME1