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  • C8-05: CONSERVATION OF ENERGY IN VERTICAL PROJECTILE

    C8-05
    Show the relation between initial velocity and height of a vertical projectile.
    A projectile is launched vertically. The laser and photocell timer setup is used to determine the initial upward velocity of the projectile. The height is measured using the scale behind the projection device. The measured height h and the measured velocity v are related by the equation v**2 = 2 gh, where g is the acceleration of gravity. Result is good to better than ten percent.
    C8, LS1, ME1

  • C8-12: JUMPING MASSES WITH INTERNAL SPRINGS

    C8-12
    Demonstrate conversion of internal energy of a spring into kinetic energy and then gravitational potential energy.
    Set device so as to store energy in the spring by compressing or twisting the spring. Release rapidly or as required to allow conversion of energy stored in the spring into other forms.
    C8

  • C8-13: BUNGEE JUMPER MODEL

    C8-13
    Determine the minimum value of the spring constant of a bungee rope to ensure a safe jump.

    Student of mass M jumps from a cliff of height H tied to a bungee rope of unstretched length Lo. Assume a vertical jump with initial velocity of zero. Neglect air resistance and mass of the rope.

    When the spider jumps off the platform the spring extends to within a few inches (or centimeters in physics) of the floor before pulling the spider back up.

    DANGER - IMPORTANT NOTE: Bungee cords are made of shock cords (elastomers) or from rubber. They DO NOT behave as linear springs. It would be dangerous to assume linearity of a real bungee jumping cord and make calculations on this basis.
    FS1

    c8-13a

  • C8-23: WORK DONE BY PUSHING ON WALL

    C8-23
    Illustrates that the wall and the floor do no work.
    The instructor, while standing on a cart weighted with two lead bricks, pushes off against the wall. The energy comes from the pusher, not from the wall or the floor or the air. Be careful. This can be dangerous if you get unbalanced. Of course, this danger to the instructor heightens the interest of the students.

  • C8-32: POWER - CLIMBING LADDER

    C8-32
    A simple method for illustrating power and the unit of the horsepower.
    Climb the ladder at a constant rate, say one foot per second. From your weight you can then calculate your power, in foot-pounds per second or in horsepower.

  • C8-33: POWER - USING GRAVITY

    C8-33
    Demonstrate mechanical power.

    A one-half kilogram mass provides a force of about 5 Newtons hanging over the pulley. Under the specially selected 5 Newton force the wooden box moves at a nearly constant speed. The distance and time can be measured and the power calculated.

    Add small masses to the wooden box or to the pulley weight to adjust the motion as necessary.
    C8, ME1

  • C8-34: POWER - INSTRUCTOR DRAGGING CONCRETE BLOCK

    C8-34
    Demonstrate power
    Drag block with uniform speed and measure the force. Calculate the power from the force, the distance traveled, and the time elapsed.
    FS1, ME1

    c8-34a

  • D1-02: PELLET VELOCITY FROM ROTATING DISCS

    D1-02
    Determine the speed of a B-B using rotational kinematics.
    A B-B is shot from the air gun with a linear velocity v, such that it passes between the two rotating discs which have a separation d and are rotating with an angular velocity w. The angle a that the two discs rotate while the B-B is traveling between them is determined by inspecting the two discs. The velocity of the B-B is then determined by using the relation: v = w d / a. In this case the angular velocity w of the rotating discs is 1800 rpm, and the distance d between the discs is 1 meter. CAUTION: Lift apparatus by handles only. Pump just before firing to assure uniform velocity for several trials. See also Demonstrations C7-51: BALLISTIC PENDULUM - PELLET GUN and C7-53: AIR TRACK - SPEED OF AIR GUN PELLET for other ways to determine the B-B velocity.

  • D1-03: VELOCITY WHEEL

    D1-03
    Demonstrate uniform acceleration in a rolling body.
    The wheel is released from rest and rolls down the inclined parallel track with a small acceleration. When the end of the track is raised as shown the linear acceleration of the wheel is about 0.05 cm/sec/sec. Times can be measured for various distances to show that a = 2s / t^2 is a constant.
    D1

  • D1-21: ANGULAR VELOCITY - OBERBECK CROSS

    D1-21
    Measure the angular velocity of a rotating object.
    Various masses M can be hung on a string wound around an axle of either of two radii R to provide a torque T = MgR. Four brass masses m can be positioned along the arms at one of four distances l from the axis of rotation to provide a moment of inertia I = 4ml^2. The angular acceleration a = T/I = MgR/4ml^2 can then be calculated. The angular acceleration can be determined experimentally by measuring the time required for the system to rotate one complete revolution starting from rest: a = 2 d/t^2, where t is the time required for the device to rotate through the angle d in radians. The angular velocity can be determined by simply measuring the time per revolution.
    FS1, ME1

  • D1-30: TRAJECTORY FROM CIRCULAR ORBIT - OVERHEAD PROJECTOR

    D1-30
    Show that the instantaneous velocity of an object executing uniform circular motion is tangent to the circle.
    A marble is rolled around the inside of the circular band on an overhead projector. When the ball leaves the end of the circular segment it will travel in the direction tangent to the circle at the point where it leaves.

    A transparent sheet is available with an outline of the circle and various possible paths. This can be used to challenge the students to guess the outcome of the experiment before performing it.

    Compare D1-31 and D1-32, other demonstrations showing similar effects.
    D1

  • D1-31: TRAJECTORY FROM SPIRAL

    D1-31
    Show that forces are required to create circular motion.
    The apparatus pictured is positioned on a horizontal surface. A small ball bearing (in container at lower left of picture) is blown through the spiral hose, emerging at the right side and moving downward (in the picture), toward one of the five aluminum tube targets. Ask your students to predict: Which of the targets will it hit, and why?

    Consider using in conjunction with D1-30 or D1-32 to show the effect in a less complex scenario.
    OS10

  • D1-39: PENNY AND COAT HANGER

    D1-39
    Demonstrate centripetal force and centrifugal reaction in a dramatic way.
    Balance the penny (face up) on the flattened coat hanger tip, as shown in the photograph. Start slowly swinging the hanger back and forth like a pendulum, then rotate it in a complete circle. With practice, it is possible to rotate the system several times and stop the motion without dislodging the penny.
    D1

  • D1-40: CENTRIPETAL FORCE ON ROTATING RUBBER BAND

    D1-40
    Demonstrate centripetal force and centrifugal reaction.
    A rubber band is stretched around a disc which can be rapidly rotated. Use stroboscope to stop the motion, showing that the rubber band stretches when the disc is rotated. The stretch becomes greater as the angular velocity is increased.
    D1, N2, LS1

  • D1-42: ROTATING WATER BUCKET WITH SPONGE

    D1-42
    Illustrate centripetal force and centrifugal reaction with a trick.
    Pour water into the can, then rotate the can over your head in vertical circles. Rotate the can more and more slowly as you move toward the class, so that the can stops upside down over some student's head. Then remove the sponge and squeeze the water back into the can.

  • D1-55: ROTATING ELASTIC RINGS

    D1-55
    Demonstrate "centrifugal reaction" and to indicate why the earth is oblate.

    We have a pair of thin steel rings mounted on a rotating base. The top of the rings is free to slide along its axis, while the bottom is fixed to the rotating base.

    Turning the crank causes the elastic rings to rotate about the vertical axis. The rotation mechanism here uses the mechanical advantage of a large cranked wheel driving a smaller pulley to give the rotating rings a very high angular velocity.

    Engagement Suggestion
    Before rotating at high speed, invite students to predict what will happen to the rings when you get it spinning as fast as you can. Will they:
    • a) keep their circular shape
    • b) flatten at the top and bottom and bulge in the middle
    • or c) extend upwards and grow narrower in the middle?
    Afterwards, encourage students to relate this to other physical phenomena.
    Background
    As the rings rotate, their form distorts, growing wider around the center and flattening at the top and bottom. Interestingly, this is not due to a true outward force acting on the metal at this point, but is an artifact of its rotating reference frame and the forces acting to keep it moving in a circle. This is often termed a centrifugal reaction or centrifugal force, though it is technically a pseudo-force arising from the reference frame.

    This effect is seen in astronomy and geography, as rotating planets, stars, and other bodies take on similarly oblate spheroidal forms.
    D1

  • D1-61: Rolling versus Sliding

    D1-61
    Applies conservation of energy to a rolling object

    An aluminum cylinder rolls down an inclined plane. An identical aluminum cylinder has tiny bearings on one end, so that it slides without friction down the incline.

    Invite the students to make a prediction: If the two cylinders are started from the top at the same time, will the rolling cylinder or the sliding cylinder reach the bottom of the incline first?

    Background
    The two cylinders start at the same height with the same potential energy. As they slide or roll down the ramp, that potential energy is converted into kinetic energy. Linear kinetic energy is proportional to the mass of the cylinder and the square of its velocity. However, the rolling one also has rotational kinetic energy, which is proportional to the moment of inertia of the cylinder and the square of its angular velocity. So for the rolling cylinder, some of the potential energy is converted into rotational kinetic energy as it rolls, and only some of the potential energy is converted into linear potential energy, giving it a lower velocity as it goes down the ramp. So the sliding cylinder reaches the bottom first.
    D1, FS2

  • D1-63: MAXWELL PENDULUM - LARGE

    D1-63
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Used as a large-scale yo-yo, transformation of energy can easily be observed by a large class. Wind the string around the small spool radius, hold with the axis horizontal, and release. The initial gravitational potential energy is converted primarily into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, with conversion back to gravitational potential energy after the spool reaches its minimum position and moves back upward.

  • D1-64: MAXWELL PENDULUM - SMALL

    D1-64
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Wind the string up on the small axel, giving the device some initial gravitational potential energy. When released, this gravitational potential energy is converted into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, then converted back as it rises. Two different sizes of small axels are available.

  • D1-82: ROLLING FRICTION

    D1-82
    Show the direction of the frictional force when a rolling object is accelerated.
    One of the three cylindrically symmetric rollers is positioned on the base as shown in the photograph. The base has a rubber top surface and rolls almost without friction on small bearings on the horizontal surface below. The cloth web is held horizontally and yanked, causing the roller to move in the direction of the applied force. The frictional reaction force on the cart is indicated by the direction the cart will move when the roller is yanked off. For a solid disc (moment of inertia less than mr^2) the reaction force is in the direction opposite to the pull, and the base will move backward. For a spool rolling on its smaller radius r (moment of inertia greater than mr^2) the reaction force is in the direction of the applied force. For a thin ring (moment of inertia equal to mr^2) there is no reaction force on the base and it will remain motionless. Because the cylindrical shell has a finite thickness there is some reaction force and a slight amount of motion occurs. However, compared with the solid cylinder and the spool the reaction force is minimal.