For each of the following situations below, design a procedure to determine experimentally the unknown quantity specified in the problem. You may not damage or destroy any of the equipmentyou use, and your method must be feasible and practical.
In each case,
- List the equipment you would need, and include a labeled diagram.
- Write a brief but concise procedure, describing any measurements you
would make, assigning each measurement a symbol (e.g. time = t ) .
- Show explicitly using equations how the measured quantities would be
used to determine the unknown quantity.
- Indicate one possible source of experimental error and discuss how it
would affect your value for the unknown quantity you are ultimately
Key: B = appropriate for AP Physics B
C = appropriate for AP Physics C
BC = appropriate for both AP Physics B and C
Given: An air track and cart or low-friction rolling cart and track, a motion detector and CBL or computer, and a set of various d vs t,v vs t, and a vs t graphs.
Find: The proper placement of the track, cart, and motion detector to produce a motion that matches each of the given graphs.
Given: Motion detector, CBL. graphing calculator (or computer and data collection and analysis software), a basketball.
Find: A value for the acceleration due to gravity.
Given: 10 meters of string, two meter sticks, two protractors, the magnitude and direction of five displacement vectors, one of which is the resultant of the other four.
Find: The vector which is the resultant of the other four.
Given: A mounted dart gun, a protractor, string, and a meter stick,
Find: The initial speed of the dart as it leaves the dart gun.
Given: An inclined air track and cart (or a ramp and a low-friction rolling cart), index cards, scissors, tape, ruler, photogate, CBL and calculator or computer and software which can measure the time for a card of known length to pass through the photogate.
Find: The instantaneous speed of the front of the cart as it enters the photogate.
Given: Motion detector, CBL, graphing calculator (or computer and data collection and analysis software), several basket coffee filters.
Find: The relationship between the mass of the coffee filters (which is an indication of the air resistive force) and their terminal velocity as they fall.
Given: A spring scale, a set of known masses, a stopwatch, an elevator.
Find: The initial acceleration of the elevator, and its subsequent constant velocity.
Given: A ring stand, clamp, a light pulley, string, a set of known masses and weight hangers, and other commonly available equipment
Find: The acceleration due to gravity.
Extention: Find the normal force applied to the stand by the table while the masses are accelerating.
Given: A block of wood with randomly placed 1" holes drilled into it, and other commonly available objects.
Find: The center of mass of the block of wood.
Given: A block of wood, a board, and a protractor.
Find: The coefficient of friction between the block and the board.
Given: A brick, string, and spring scale.
Find: The coefficient of static friction and the coefficient of kinetic friction between the brick and the lab table.
Given: A fixed inclined board with a light pulley attached to the top, two blocks connected by a string, a protractor, any other commonly available equipment (including a Smart Pulley, or some data acquisition device which can measure the acceleration of the system.)
Find: The coefficient of friction between acting on the block on the ramp.
Extention: Place another block on top of the block which is on the surface, and find the coefficient of static friction between the surfaces of the two blocks.
Given: A ramp on a table with a marble at rest at the bottom end, another marble which can be rolled down the ramp, two meter sticks, white paper, carbon paper.
Find: Verify the law of conservation of momentum in one and two dimensions.
Given: Collision carts on an air track (or dynamics carts on a dynamics track), two photogates.
Find: Verify the law of conservation of momentum for elastic and inelastic collisions.
Given: A set of unequal masses which can be hung on a meterstick, a pivoting fulcrum which can be attached to a meter stick. Place the fulcrum and three unequal masses appropriately on the meterstick.
Find: An equation which describes static equilibrium for the system.
Given: A bicycle wheel without the tire on it, string, a set of known masses, other commonly available equipment.
Find: The rotational inertia of the wheel.
Given: 1.5 meters of string tied to the end of a meter stick and a push pin attached to the other end of the string, a protractor, a set of known masses and a weight hanger.
Place the end (without the string) of the meter stick against a wall so that it is perpendicular to the wall, pin the string to the wall directly above the meter stick so that the string makes an angle with the meter stick, and the end of the meter stick which is against the wall is held up perpendicular to the wall only by friction.
Find: The coefficient of friction between the wall and the end of the meter stick.
Given: A string passed through a tube held vertically, with a known weight hanging at the bottom of the string and a rubber stopper tied at the top of the string. As the string and stopper are swung with a constant speed in a horizontal circle.
Find: The tangential speed of the stopper, and the centripetal force acting on the stopper. Compare this centripetal force appropriately to the hanging weight at the other end of the string.
Extention: Design and experiment to verify the law of conservation of angular momentum.
Given: A rotating turntable, a penny, other commonly available equipment.
Find: The coefficient of static friction between the penny and the turntable.
Given: A long wooden board to be used as a ramp, a hoop (or disk) of known mass and radius, and other commonly available equipment.
Find: The rotational inertia of the hoop (or disk), and the coefficient of static friction between the (rolling) hoop and the board.
Given: One end of a meter stick is placed on the edge of a table with less than one cm resting on the table, while the student holds the other end of the meter stick so that the meter stick is horizontal and supported at both ends.
Find: The location at which a penny should be placed so that when the student-held end of the meter stick is dropped, the penny just loses contact with the meter stick as it falls.
Given: A small marble of known mass slides down a curved ramp so that it exits the end of the ramp horizontally. Using commonly available equipment.
Find: The speed with which the marble leaves the ramp, and the energy dissipated while the marble is on the ramp.
Given: A block of wood is hung so that it can swing in a plane. A dart is fired at the stationary hanging block at close range and embeds itself in the block, causing the block and dart to rise to a maximum height. Using commonly available equipment.
Find: The speed of the dart just before it strikes the block.
Given: Two meter sticks, white paper, carbon paper, a steel ball attached to the end of a string which is hung vertically to act as a pendulum. Another steel ball is placed at the lowest point of the swing on a table so that the pendulum ball strikes the target ball, knocking it off the table.
Find: The loss in energy and momentum after the collision.
Given: A spring, clamp, ring stand, and any other commonly available equipment.
Find: The spring constant k of the spring.
Extention: You want to use this spring in a calibrated spring scale to measure the weight of an object which will exceed the limits of the spring
if hung directly on it. How would you use the spring scale and other commonly available equipment to measure the weight of the object?
Given: one meter of string, a protractor, three large one-hole rubber stoppers, and other commonly available equipment.
Find: The relationship between the period of a pendulum and its mass, length, and amplitude.
Extention: Measure a value for the acceleration due to gravity.
Given: one meter of string, a protractor, three large one-hole rubber stoppers, and other commonly available equipment.
Find: The tension in the string at the bottom of the swing when the pendulum is released from a known angle. Show the equations relating the known quantities and the measured quantities to the tension.
Given: Tuning forks of known frequency, a graduated cylinder of water, a PVC pipe which is slightly longer than the graduated cylinder.
Find: The speed of sound in air.
Given: one meter of string attached to amounted vibrating machine of known frequency, a pulley mounted to a ring stand, a weight hanger, a set of known masses, a meter stick.
Find: The fourth harmonic and the velocity of the wave in the fourth harmonic.
Given: A graduated cylinder half full of water, a small object of unknown uniform density, a string and a stand from which to hang it, a mass scale.
Find: The density of the object.
Given: A graduated cylinder half full of a liquid of unknown density, a small object of known mass and uniform density, a spring of known spring constant, a millimeter ruler.
Find: The density of the fluid.
Given: A graduated cylinder half full of water of known mass, a small object of known mass and uniform density, a string and a stand from which to hang it, a mass scale.
Find: Predict the reading on the mass scale when the graduated cylinder of water is placed on it and the object is (a) set on the bottom of the cylinder, and (b) suspended by the string while in the water.
Given: An air-blower, a strip of paper of known mass and area.
Find: The speed of the air passing over the strip of paper.
Given: A two liter soft drink bottle full of water, with a hole in the side,
and a meterstick.
Find: The speed at the exit point of the hole and the range.
Given: A solid rectangular block of transparent plastic or glass (or a transparent liquid in a transparent container), a laser, a box of sewing pins, a protractor, meter stick, a white opaque screen.
Find: The index of refraction of the transparent material, and the speed of light in the transparent material.
Given: A diffraction grating of known slit spacing, a laser, a protractor, meter stick, white opaque screen.
Find: The wavelength of the laser light.
Given: A convex and or a concave lens of unknown focal length which can be mounted on a meterstick, a candle, matches, a white opaque screen.
Find: The focal length of the lens, and produce an image of the candle which is real, inverted, and larger than the candle itself.
Extention: Draw the ray diagram to scale depicting the above set-up.
IX. Electricity and Magnetism
Given: Four identical light bulbs, a 12-V battery, 10 wires of negligible resistance, a voltmeter, and an ammeter.
Find: An arrangement of all of the above components in which each bulb has a nonzero current flowing through it, but in which the current from the battery is as small as possible, and then another arrangement in which the current is as large as possible.
Extention 1: Given a particular arrangement of bulbs or known resistors in a circuit which is a combination of both series and parallel, determine the bulb which is the brightest, or the resistor which dissipates the most power through it.
Extention 2: Repeat the procedure above by creating a muttiloop circuit with more than one battery.
Given: A selection of resistors and capacitors, several "D" batteries, wires, a three-way switch, current and voltage probes, or ammeters and voltmeters.
Find: An appropriate combination of a resistor and a capacitor placed in a circuit with the batteries so that the charging and discharging of the capacitor can be easily watched in realtime. Also, find the value of an unknown capacitor, and the maximum charge on the capacitor.
Given: 1 meter of bendable, insulated wire, a size "D" battery, a disk magnet, two paper clips, sandpaper, wire strippers, masking tape.
Design: A working electric motor.
Given: A cathode ray tube in which the cathode ray is visible, an adequate power supply for the cathode ray tube, a horseshoe magnet with unknown poles.
Find: Which of the poles of the horseshoe magnet is the north magnetic pole.
Given: A selection of resistors and inductors, several "D" batteries, wires, a three-way switch, current and voltage probes, or ammeters and voltmeters.
Find: An appropriate combination of a resistor and a inductor placed in a circuit with the batteries so that the changing current is easily watched in real time. Also, find the value of an unknown inductor.