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Statics of Rigid Bodies

  • B1-01 CENTER OF MASS - DISC SECTION

    B1-01
    Demonstrate finding center of mass for an irregularly-shapped object
    When the crescent shaped object is suspended from one of the holes along its perimeter, the center of mass will be directly below the suspension point, as defined by the plumb bob. When the object is suspended from the hole at its center of mass, it remains stable in any angular position.

    Questions: How do you find the position of the center of mass of this object? (A: From the intersection of lines) Why does the object remain stable when it is suspended at its center of mass?


    See also demonstration B1-09: CENTER OF MASS - TRIANGLE. These two demonstrations use the same stand and are often taught together.
    B2

  • B1-02: CENTER OF MASS - LEANING TOWER

    B1-02
    Demonstrate the effect of center of mass location
    A model tower is comprised of two sections; an askew bottom component and a top component. The bottom component is in a stable equilibrium when sitting on a horizontal surface since the horizontal position of its center of mass is within the perimeter of the base. As the top section is placed onto the base tower, the horizontal position of the center of mass will shift outside the base perimeter, thereby causing the system to be unstable and topple.

    Questions: Would anything change if the tower was hollow? Would the center of mass change? What should you do in order to keep the tower (consisting of both components) stable?

    B1

  • B1-03: CENTER OF MASS - LEANING TOWER ON INCLINED PLANE

    B1-03
    Demonstrate equilibrium when its center of mass is above its base
    This is a variation of B1-02. On a horizontal surface, the addition of the top component onto the base component of the tower shifts the center of mass outside the base perimeter, causing the configuration to change from stable (without top) to unstable (with top). When the tower is placed on an inclined plane, the horizontal position of the center of mass will be shifted more towards the center of the base thereby making it stable even with the top since the center of mass will still be over the base.

    Invite your students to discuss: What would happen if the inclined plane was removed? Is there any other way to make the complete tower (with both the top and base components) stable?

    B1, FS1

  • B1-04: Center of Mass - Brass Barbell

    B1-04
    Demonstrate stable equilibrium when supported at center-of-mass

    A brass barbell with two different disc-shaped masses, one on each end, is supported by a stand at its center of mass.

    Compare this to lifting up an asymmetrical barbell in the gym with one hand, and finding that it is the easiest to hold it at its center of mass.

    Engagement Suggestion:
    Ask students to make predictions:
    • What would happen if the brass barbell is shifted so that the heavier mass is closer to the middle?
    • Would the barbell rotate and if so, in what direction?
    • Would it remain on the stand?
    B1

  • B1-05: CENTER OF MASS - PLUMBER'S HELPER

    B1-05
    Locate the center of mass of an irregular object
    A plunger balances when its center of mass is directly above the support point. Ask your students: Why isn’t the center of mass located at the middle of the stick of the plunger? Is there any other position to balance the object?
    B1

  • B1-08: STATES OF EQUILIBRIUM - CONE

    B1-08
    Illustrate stable, unstable, and neutral equilibrium

    The cone resting on its base is in a stable equilibrium. When it is balancing on its tip, the cone is in an unstable equilibrium. Lying on its side makes it in a neutral equilibrium.

    Questions: Why does balancing the cone on its tip cause it to be in an unstable equilibrium? What is the difference between a stable and neutral equilibrium?

    B1

     B1 08 1

  • B1-09: CENTER OF MASS - TRIANGLE

    B1-09
    Demonstrate the process of locating the center of mass

    TA triangular shaped object can be suspended from any corner by a nail at the top of the support. The center of mass will be directly below each corner, as defined by the plumb bob. Lines of the vertical position of the bob’s string is drawn on the object. The intersection of all the lines is the position of the center of mass.

    See also demonstration B1-01: CENTER OF MASS - DISC SECTION. These two demonstrations use the same stand and are often taught together.

    Ask students: What would happen if the triangle was suspended at its center of mass?
    B2

  • B1-11: BALANCE MAN

    B1-11
    Illustrate stable equilibrium
    When set on a pedestal, the Balance Man will rock back and forth without falling off no matter the position it is in. The center of mass and the center of gravity is along the line of symmetry of the figure, which is a short distance below the legs. Since the Balance Man’s center of gravity always remains below its pivot point, when it is pulled to one side, gravity will always exert a restoring force which will pull it back to an upwards position. Question: Will the Balance Man be in stable equilibrium if it is set on one leg? (Yes, it will always be in a stable equilibrium since the center of gravity is below the pivot point). Why does the toy rock back and forth instead of falling off the pedestal?
    B1

  • B1-12: CENTER OF MASS - HINGED STICK PARADOX

    B1-12
    Illustrate the center of mass in a surprising way
    To demonstrate center of mass, find how the hammer is supposed to be positioned in order to have it hanging from the loop on the bottom of the board so that the board sticks out horizontally. Question: How can you hang the hammer from the loop on the bottom of the hinged board so that the board will stick straight out horizontally? (A: Insert the handle into the loop so that the head of the hammer is pointing back toward the hinge.)
    B1, tools

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  • B1-13: CENTER OF MASS - FORK AND SPOON ON TOOTHPICK

    B1-13
    Illustrate the center of mass in a surprising way
    Insert a spoon between the tines of a fork and a toothpick through an interstice of the fork. The system will be balanced when the toothpick is set at the edge of the glass. Question: If the toothpick were to be burned from the inside, would the system fail? (Show this). If not, why does the spoon and fork remain balanced?
    B1

  • B1-14: CENTER OF MASS - BOTTLE

    B1-14
    Illustrate the center of mass in a surprising way
    When the neck of a wine bottle is position inside a hole of a plastic support, the system will be in a stable equilibrium therefore the wine bottle will remain at rest in an unlikely position. Question: Why is this system in equilibrium? (A: The center of mass of the system is above the base area of the plastic support).
    B1

  • B1-15: TOPPLING CYLINDERS

    B1-15
    Illustrate stable and unstable equilibrium in a surprising way

    The tilted cylinder at the left topples when the top is added, the classical toppling tower demonstration. The vertical cylinder in the center topples when the top is removed, due to the presence of two heavy balls in the hollow cylinder. The tilted cylinder at the right topples when the top is removed and replaced, due to a weighted top which is rotated when it is replaced. Note that all three cylinders are constructed from the same tubing, and that none has a bottom.
    B1

  • B1-16: CORBELED ARCH

    B1-16
    Illustrate how the center of mass affects the stability of an arch
    Description: Identical blocks are piled up with successively greater fractions of their lengths (slightly less than 1/12, 1/10, 1/8, 1/6, 1/4, and 1/2, respectively, from bottom to top) extending over the edge of the preceding block, as shown in the photograph. Even though the top block is entirely over the edge of the base, the center of mass of the system remains above the base, so the configuration is stable. Questions: What happens when you remove the bottom tile from the pyramid?

    (Note: The toy automobile is not inherently part of the demonstration, but one can be made available upon request. :D )

    B1

    sta

  • B1-17: CENTER OF MASS - STICKS

    B1-17
    Illustrate the center of mass in a surprising way
    There are two sticks identical in appearance, but one is uniform in density and the other is weighted at one end. Since the center of masses for each stick will be different, they will have different balance points. The professor can mark the sticks either at their center of masses or where it appears to be, leaving the student to explain the peculiar behavior of the weighted stick when it is balanced. Questions: Which stick will balance at its center and why?

    These sticks also do double-duty as part of the demonstration D2-04: MOMENT OF INERTIA RODS.
    B1

  • B1-18: Center of Mass - Soda Can and Water

    B1-18
    To demonstrate how an object's behaviour can change when its center of mass does
    An empty soda can can sit upright on its bottom, or can be laid on its side, but cannot be at rest at any angle between these. However, this can be changed by adding a liquid to the system. Pour approximately 150ml of water into the can, and then try carefully balancing the can at an angle, as seen in the photo above. (This may require experimenting to find the exact right amount of water for any given can; we recommend doing this in front of the class so they can see the process.)

    Ask your students why this should happen? The mass has increased, but why does that change how it balances?

    The water moves when the can tilts, causing the center of mass to shift – with just the right amount of water, the new center of mass will be above the edge of the can, and so it will balance.

    Some cans will tend towards a particular orientation and will roll along the edge to that point, displaying a damped oscillation – invite students to hypothesize why this is.

  • B1-21: BALANCE BEAM - VARIATION ON THE TIGHTROPE WALKER

    B1-21
    Show how arms or a pole are used to obtain greater stability
    As someone walks across the balance beam without a pole, tell the student to take notice how the person’s arms are used to maintain balance in order to keep the center of mass of the system over the beam surface. Now use the pole to walk across the beam to show that walking is easier. Questions: Why does using the pole make walking easier? (A: It increases the moment of inertia.) What happens to the center of mass of the system when the pole is held lower than the person’s center of mass?
    OS0

  • B1-22: CENTER OF GRAVITY USING TEETER TOTTER

    B1-22
    Determine the center of gravity of the human body
    The fulcrum of the teeter totter is used to locate the vertical plane through the pivot line of the board. If desired, a piece of tape can be used to indicate this plane when the teeter totter is nearly balanced. Planes can be determined with the subject lying on the board, standing on the board facing forward, and standing on the board facing to the side. The intersection of these three planes is the center of mass of the body. It is not easy to obtain an exactly balanced position; usually the best that you can do is to oscillate back and forth about the equilibrium point by slight shifts in your position. Questions: Would the board remain in an equilibrium position if masses were placed on each end? If so, what are the requirements?

  • B1-24: CENTER OF MASS - CARTS ON BALANCE BOARD

    B1-24
    Show that the center of mass may remain at rest during motion within the system.
    The board is balanced on its fulcrum with the carts touching one another at the center of the board. Releasing the spring causes the carts to push against each other and separate, but the board remains balanced. Questions: What would happen if the two carts had different masses? Would the board become lopsided?

    The experiment can be made more complex by putting an extra weight into one cart, so that the masses of the carts are unequal.

  • B2-01: SUM OF FORCES IN A LINE

    B2-01
    Demonstrate that forces in one dimension add algebraically
    This demonstration consists of two strings connected at one end of a brass spring that is suspended at the other end from one side of a support frame. The strings run over pulleys attached to each side of the frame, and are then connected to weights. Different masses can be hung on the two sides, creating differing forces in each direction. Using the scale provided, the displacement of the spring can be measured, and the forces can be seen to add algebraically.
    B2, FS1

  • B2-02: SUM OF FORCES - SPRING SCALES

    B2-02
    Show that the sum of forces exerted on the mass by the scales is constant
    A weight is set on a platform scale, and the upper spring scale hooked to the weight. As an upward force is applied, the sum of the readings of the two spring scales remains constant, equal to the initial weight on the platform. In these photos, the sum of the forces on the 1kg mass remains slightly less than 10N as more of the lifting is transferred to the upper scale.
    B2, ME1