Statistics of Rigid Bodies

PIRA classification 1J

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1J10. Finding Center of Gravity

PIRA #	Demonstration Name	Abstract
1J10.10	Center of Gravity	Toss into the air many different shapes all of which have their center of mass marked with a bullseye.
1J10.11	Wooden Map	Suspend a map of the state from holes drilled at large cities to find the "center of the state".
1J10.12	Hanging Irregular-shaped Board	Suspend an irregular board from several points and use a plumb bob to find the center of gravity.
1J10.15	Hanging Potato	Hang a potato from several positions and stick a pin in at the bottom in each case. All pins point to the center of gravity.
1J10.20	Meter Stick on Fingers	Slide your fingers together under a meter stick and they meet at the center of gravity. Add a baseball hat to one end and repeat.
1J10.25	Center of Gravity of a Broom	Find the center of gravity of a broom, hang a 1 kg mass somewhere on the broom, find the new center of gravity, calculate the weight of the broom by equating torques.
1J10.30	Loaded Beam - Moving Scales	Slide the scales together under a loaded beam noting the scale readings of the moving and stationary scales.
1J10.41	Your Center of Gravity	Two methods for measuring the center of gravity of a person are shown. [http://hypertextbook.com/facts/2006/centerofmass.shtml Your Center of Gravity]

Anchor(ExceedingCofG)

1J11. Exceeding Center of Gravity

PIRA #	Demonstration Name	Abstract
1J11.10	Leaning Tower of Pisa	A model of the tower constructed in sections. Adding the top will cause it to tip over.
1J11.11	Falling Cylinders	A tube, weighted at the bottom, falls when a cap is added. An upright cylinder, containing two balls, falls when a weighted cap is removed. [http://ajp.aapt.org/ AJP 34(9), 822]
1J11.15	Tipping Block on Incline	A block is placed on an incline and the incline is raised until the block tips.
1J11.20a	Leaning Tower of Lire	Stack blocks stair-step fashion until the top block sticks out beyond any part of the bottom block.
1J11.20b	Leaning Tower of Lire	Use 6"x6"x2' wood blocks and have a student sit under the stack as it is built.
1J11.21	Cantilevered Books	The number of books necessary to overhang 2,3,4, etc lengths.
1J11.30	Instability in Flotation	A device to raise the center of mass in a boat until it becomes higher than the center of bouncy, and the boat flips.
1J11.40	Center of Mass and Balance in People	Pictures of three center of mass objects and several person based center of mass tasks e.g., stand on your toes facing the wall, etc. [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000021000001000042000001&idtype=cvips&doi=10.1119/1.2341188&prog=normal Center of mass revisited]
1J11.50	Double Cone	As a double cone moves up a set of inclined rails, its center of gravity lowers.

Anchor(SUNE)

1J20. Stable, Unstable, and Neutral Equilibrium

PIRA #	Demonstration Name	Abstract
1J20.10	Bowling Ball Stability	A bowling ball is placed in, on, and along side a large plexiglass hemisphere to show the types of equilibrium.
1J20.11	Stability of Shapes	A cone balancing on its point is unstable, a block is stable, a sphere is neutral.
1J20.12	Wood Block Stability	A block and support have marks that show whether the center of gravity has moved up or down when the block is displaced.
1J20.15	Block on the Cylinder	A rectangular block of wood is placed on a cylinder first with the width less than the radius (stable) and then with the width greater (unstable).
1J20.16	Catenary Surface	A large block is always in stable equilibrium anywhere along this catenary surface. See Sutton M-40.
1J20.20	Fork, Spoon, and Match	Place a spoon and match in the tines of a fork and balance the assembly on the edge of a glass.
1J20.20	Two Forks and a Toothpick	Two forks and a toothpick can be balanced on the edge of a glass while the water is poured out.
1J20.25	Nine Nails on One	A technique to balance ten landscape spikes on the head of a single upright spike.
1J20.30	Sky Hook	A complete solution to the hanging belt problem. [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000014000008000499000001&idtype=cvips&doi=10.1119/1.2339469&prog=normal TPT 14(8), 499]
1J20.32	Spoon on Nose	Hang a spoon on your nose. Most effective with giant food service spoons.
1J20.35	Horse and Rider	Stable equilibrium of the horse and rider. Note that the COG is below the contact point.
1J20.40	Balancing Man	Stable equilibrium of the balancing man. Note that the COG is below the contact point.
1J20.45	Clown on Rope	A toy clown rides a unicycle on a wire.
1J20.46	tightrope walking model	A model of a tightrope walker shows the center of mass moves up with tipping.
1J20.50	Balancing a Stool	Construct a stool so that wires crossed diagonally will intersect at the center of gravity. The stool can be oriented in any direction.
1J20.51	Chair on Pedestal	Attach heavy weights in the ends of a chair's legs so it will balance on a vertical rod placed under the seat.
1J20.55	Broom Stand	Spread the bristles and a straw broom will stand upright.
1J20.60	Wine Bottle	Stick the neck of a wine bottle through a hole in a slanted board and the whole thing stands up.
1J20.65	Glass on Coin	A glass container 2/3 filled with water will balance on its edge on a coin.

Anchor(ResolutionofForces)

1J30. Resolution of Forces

PIRA #	Demonstration Name	Abstract
1J30.10	Suspended Block	Forces parallel and perpendicular to the plane will support the car when the plane is removed.
1J30.15	Normal Force	A block on an incline has an arrow mounted from the center of mass perpendicular to the surface with "N" on the arrowhead and another arrow hanging from the center of mass with a "g" on the arrowhead.
1J30.18	Hanging the Plank	A heavy plank is suspended from three spring scales in several configurations: series, parallel, and a combination.
1J30.20	Tension in a String	The weight of a mass hung from a single spring scale is compared to the weight shown on a spring scale between two masses over pulleys.
1J30.22	Tension in a Spring	Two students pull against each other through one and then two spring scales.
1J30.23	Tension in Springs	Masses are hung at the ends of a series of spring scales.
1J30.25	Rope and Three Students	Two large strong students pull on the ends of a rope and a small student pushes down in the middle of the rope until it touches the floor.
1J30.25	Clothesline	Hang a 5 N weight from a line and pull on one end of the line with a spring scale.
1J30.26	Rope and Three Weights	Suspend a rope over two pulleys with masses on the ends and hang another mass from the center. Measure the deflection. An alternative set up would be a rope mounted to a frame with a spring scale measuring the tension.
1J30.30	Break Wire with Hinge	Suspend a 5 kg mass from a length of wire. Break a length of similar wire by placing the same mass on the back of a large hinge. And opening it by pushing down.
1J30.35	Pull the Pendulum	A long heavy pendulum is displaced with a horizontal force, measured by a spring scale.
1J30.40	Horizontal Boom	A boom is supported by a wire. The tension in the wire is measured with a spring scale for two different boom structures and angles.
1J30.50	Blackboard Force Table	A blackboard with grid lines on which to draw forces in chalk.
1J30.51	Vertical Force Table	A vertical force table that permits a continuous range of angles.
1J30.52	Force Table on Overhead	A plexiglass force table for the overhead projector. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000041000009001115000001&idtype=cvips&doi=10.1119/1.1987490&prog=normal AJP 41(9), 1115]
1J30.53	Force Table with Torque Apparatus	The standard force table, three dimensional force table, and torque apparatus.
1J30.54	Force Table	Three scales and a ring to show forces add by parallel construction. Not the usual. See 1J30.52.
1J30.55	Bosun Chair Force Table	Sit on a chair suspended from two supports equipped with protractors and commercial load cells. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000051000006000571000001&idtype=cvips&doi=10.1119/1.13207&prog=normal AJP 51(6), 571]
1J30.57	Blackboard Force Table - Rubber Band	Determine the spring constant of rubber bands, then predict the mass of an object hung in a nonlinear configuration. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000013000004000246000001&idtype=cvips&doi=10.1119/1.2339136&prog=normal TPT 13(4), 246]
1J30.57	Blackboard Force Table - Springs	Use screen door springs in place of spring balances.
1J30.60	Sail Against the Wind	Use a large fan to blow at an air track car or a boat with a sail. Sailboats can sail into the wind, though not directly. Most boats have a forbidden sector of 90 degrees, 45 degrees on either side of the wind direction. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000040000008001172000001&idtype=cvips&doi=10.1119/1.1986783&prog=normal AJP 40(8), 1172]
1J30.61	Sail a Trike Against the Wind	A wind driven tricycle moves against the wind. A windmill on the boat drives a wheel. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000049000003000282000001&idtype=cvips&doi=10.1119/1.12627&prog=normal AJP 49(3), 282]
1J30.64	Sail Against the Wind	A wind driven boat accelerates against the wind. A windmill on the boat drives a propeller underneath. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000046000010001004000001&idtype=cvips&doi=10.1119/1.11415&prog=normal AJP 46(10), 1004]
1J30.65	Floating Ladder Problem	A stick is hung by a thread at one end with the other attached to a large float on water. The 'ladder' can be put at any angle but since the float is floating it will move in such a way to reach equilibrium.
1J30.70	Sand in a Tube	Place a tissue on the bottom of an open glass tube, fill with a few inches of sand and push down on the top of the sand with a rod. A couple of inches of sand held in a tube by tissue paper will support about 50 lbs.
1J30.75	Stand on an Egg	Three eggs in a triangle pattern in foam depressions between two plates will support a person. A raw egg can be squeezed between two hard foram rubber pads with a force of over 150lbs.
1J30.80	Rolling Wedge	Three cylindrical rollers are mounted together to form a wedge. At the bottom of the inclined plane is a hinge that connects it to a plank that goes all the way back up to the top and sits on top of the roller car. A weight is placed on top of the plank. As the wedge rolls down the plane it lifts the weight. See Sutton M-19.
1J30.90	Inverse Catenary	A string of helium balloons tied at each end forms an inverse catenary. See [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000059000005000472000001&idtype=cvips&doi=10.1119/1.16825&prog=normal AJP 59(5), 472]

Anchor(StaticTorque)

1J40. Static Torque

PIRA #	Demonstration Name	Abstract
1J40.10	grip bar	A thin rod mounted perpendicular to a broom handle holds a 1 Kg mass on a sliding collar.
1J40.10	grip bar	Use wrist strength to lift a 1 kg mass at the end of a rod attached to a broom handle.
1J40.10	grip bar	Use wrist strength to try to lift 1 kg at the end of a rod attached perpendicularly to a handle.
1J40.10	grip bar	A thin rod mounted perpendicular to a broom handle holds a 1 Kg mass on a sliding collar.
1J40.10	torque bar	Use wrist strength to lift a weight suspended at various distances from the handle.
1J40.15	torque wrench	Modify a Sears torque wrench so weights can be hung at different distances.
1J40.15	torque wrench	A torque wrench is used to break aluminum and steel bolts.
1J40.16	different length wrenches
1J40.20	meter stick balance	Hang weights from a beam that pivots in the center on a knife edge.
1J40.20	torque beam	Hang weights from a beam that pivots in the center on a knife edge.
1J40.20	torque beam	Weights are hung from a horizontal bar pivoted on a knife edge.
1J40.20	torque beam	Weights are hung from a meter stick suspended on a knife edge.
1J40.20	torque beam	Weights on a meter stick supported at the center.
1J40.20	balancing meter stick	Use a meter stick, suspended at the center, as a torque balance.
1J40.21	hinge board	Use a spring scale to lift a hinged board from various points along the board.
1J40.23	torque beam	Put a quarter (5 g) on the end of a meter stick and extend it over the edge of the lecture bench until it is just about to tip over.
1J40.24	walking the plank	Place a 50 lb block on one end of a long 2x6 and hang the other end off the lecture bench. Walk out as far as you can.
1J40.25	torque disc	Weights can be hung from many points on a vertical disc pivoted at the center.
1J40.25	torque disc	Various weights are hung from a board that can rotate freely in the vertical plane.
1J40.25	torque wheel	Use a wheel with coaxial pulleys of 5, 10, 15, and 20 cm to show static equilibrium of combinations of weights at various radii.
1J40.26	torque disc	An apparatus to show the proportionality between torsional deflection and applied torque.
1J40.26	torque disc	Twist a shaft by applying coplanar forces to a disc.
1J40.27	torque double wheel
1J40.30	opening a door
1J40.30	opening door
1J40.32	opening a trapdoor
1J40.32	opening trapdoor
1J40.40	loaded beam	Move a weight along a 2X4 on two platform scales.
1J40.40	loaded beam	Large masses can be placed on a board resting on two platform balances.
1J40.40	loaded beam	A model bridge is placed on two platform scales and a loaded toy truck driven across.
1J40.40	loaded beam	A heavy truck is moved across a board supported on two platform scales.
1J40.40	bridge and truck	A plank rests on two spring scales forming a bridge. Move a toy truck across.
1J40.41	loaded beam	Support the loaded beam with spring scales instead of platform balances.
1J40.45	Galileo lever	Same as Sutton device.
1J40.45	Galileo lever	A simple device to demonstrate the law of moments.
1J40.45	Galileo lever	A simple device to show the law of moments.
1J40.50	Roberval balance	Large Roberval balance.
1J40.50	Roberval balance	A reminder and picture of the Roberval balance. Reaction to TPT 21, 494 (1983).
1J40.50	Roberval balance	A large model of the Roberval or platform balance.
1J40.50	Roberval balance	Neutral equilibrium is maintained at any position on the platform.
1J40.51	Roberval balance	A version of the Roberval balance where a rigid assembly has upper and lower arms on one side.
1J40.55	balances	The equal-arm analytical balance and weigh bridge.
1J40.56	balances	The steelyard.
1J40.60	suspended ladder	Model of a ladder suspended from two pairs of cords inside an aluminum frame.
1J40.65	hanging gate	A gate initially hangs on hinges, then add cords and remove the hinges leaving the gate suspended in mid air.
1J40.65	hanging gate	Construction and use of a model of the swinging gate.
1J40.70	crane boom
1J40.75	arm model	Place a spring scale on a skeleton in the place of the biceps muscle and hang a weight from the hand.
1J40.75	arm model	Use an arm model simulating both biceps and triceps muscles to throw a ball.

[:Demonstrations:Demonstrations]