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Motion in Two Dimensions

  • B1-06: Double Cone - Large

    B1-06
    Demonstrate a center-of-mass paradox
    When a double cone is placed on the narrow end of a V-shaped rail, the cone will roll towards the wider end of the rail when released. The cone appears to be rolling uphill (from the narrow end to the wider end), but in reality the center of mass is moving down. Upon special request, we can also provide a cylindrical rod of the same length as the double cone to roll along the rails to show their actual slope. Challenge students to predict whether the cylindrical rod travel in the same direction as the double cone.

    Note: B1-07 is a smaller, more portable version of this demonstration.
    B1

  • B1-07: DOUBLE CONE - SMALL

    B1-07
    Demonstrate a center of mass paradox
    When a double cone is placed on the narrow end of a V-shaped rail, the cone will roll towards the wider end of the rail when released. The cone appears to be rolling uphill (from the narrow end to the wider end), but in reality the center of mass is moving down. Upon special request, we can also provide a cylindrical rod of the same length as the double cone to roll along the rails to show their actual slope. Challenge students to predict whether the cylindrical rod travel in the same direction as the double cone.

    Note: B1-06 is a larger version of this demonstration, suited to large classrooms.
    B1

    t

  • C1-01: CENTER OF MASS MOTION - BARBELL

    C1-01
    Demonstrate motion of the center of mass of an asymmetric object.
    A barbell with unequal ends is thrown through the air. The center of mass (red spot near large end) moves in a smooth parabolic arc despite the gyrations of the two asymmetric ends.

    An animation of the movement of an object of this kind can be viewed at http://www.acs.psu.edu/drussell/Demos/COM/com-a.html

    C1

  • C1-02: CENTER OF MASS MOTION - PLUMBER'S HELPER

    C1-02
    Illustrate the motion of the center of mass of an irregularly-shaped object.
    The center of mass of the plumber's helper is located by a bright red tape. When the object is thrown through the air with some rotation, the center of mass moves in a smooth parabolic arc.
    C1

  • C1-03: CENTER OF MASS MOTION - CLOWN

    C1-03
    Illustrate rotation about the center of mass of an irregular object.
    The clown is suspended by strings wound on a peg located at the center of mass, which is outside the body of the clown. As the clown descends, it rotates about the center of mass.
    FS2

  • C1-04: CENTER OF MASS - BEAR ON TIGHT ROPE

    C1-04
    Show stability in system where the center of mass is outside of the object.
    As the bear rolls along the tightrope, it remains stable because its center of mass is below the rope. Removing the weights and poles renders the system unstable.

  • C1-11: AIR TRACK - CENTER OF MASS PENDULUM

    C1-11
    Show uniform motion of the center of mass of a vibrating pendulum/glider system.
    A symmetric (balanced) pendulum is suspended from an air track glider. The mass of the pendulum bob is approximately the same as that of the glider, so the center of mass (marked by a fluorescent disc) is approximately at the midpoint of the rod between the bob and the center of the glider. When the pendulum oscillates, the center of mass moves uniformly in the horizontal direction or remains motionless (horizontally).

  • C1-21: AIR TABLE - TOPPLING STICK

    C1-21
    Illustrate how a rigid rod topples on a frictionless surface.
    A wooden dowel with its center of mass marked is held vertically with the bottom end supported by a very light air table puck. When it is released and allowed to topple, which point of the stick will be directly above the original support point: the top end, the bottom end, or the center of mass? Note that the stick has a small counterweight on its top end to compensate for the mass of the puck. Click your mouse on the photograph for an mpeg video.
    FS0

  • C2-09: FREE FALL WITH STROBE

    C2-09
    Show the position of a dropped ball at a series of equal time intervals
    Drop the ball with the strobe on at the desired flash rate (about 10-13 flashes per second, or 600-800 per minute, seem to work well). The increasing distance the ball falls between successive strobe flashes is readily apparent.
    C2, FS1, LS1

  • C2-11 RACING BALLS

    C2-11
    Illustrate linear kinematics

    Two balls are launched by a spring-operated launcher from one end of the track. They depart with the same velocities and the same kinetic energy imparted by the spring. As shown in the picture, one track runs in a straight line; the other dips down, runs straight for a time, then rises back up to the original level.
    Engagement Suggestion:
    Have students make predictions (and justify them):
    • Which ball will reach the end first, or if they will reach the end at the same time?
    • Which one (if either) will be moving faster at the end?
    Background:

    The ball on the straight track retains essentially the same velocity and the same kinetic energy throughout the length of its run, the kinetic energy from the spring. The ball on the dipped track, however, has a more complex path. When it goes downhill, it gains kinetic energy from gravitational potential, accelerating it. It travels along the lower section of track with this increased kinetic energy, and thus greater velocity. The ball then goes uphill again, losing that additional kinetic energy – it has returned to the same height, so the principle of conservation of energy dictates that it must return to the same gravitational potential as before, giving up kinetic energy equal to what it gained. It now has only the same kinetic energy it started with, as imparted by the spring. So its velocity is now the same as its starting velocity, and the same as the velocity of the other ball.

    However, during the time it was on the lowered section track, it had greater kinetic energy and greater velocity, so it traveled that distance faster than the ball on the straight track. And thus the ball on the dipped track reaches the end first, but with the same final velocity and the same final kinetic energy.
    OS0

  • C2-21 PROJECTILES DROPPED AND SHOT

    C2-21
    Demonstrate the independence of horizontal and vertical components of motion

    A latchable spring launching mechanism is mounted at the top of a stand. Two metal cubes are attached to the mechanism. When the latch is released, one cube will be projected horizontally while the other is dropped straight down. They strike the floor at the same time.
    Engagement Suggestion
    • Before showing the experiment, challenge students to predict what will happen. Will the horizontal motion of one pellet make it strike the floor before or after the other?
    • Afterwards, discuss why or why not.
    Background

    The gravitational force on each of the cubes is the same, so they experience the same downward acceleration. So since they started from the same height with zero vertical velocity, they reach the floor at the same time, even though one has traveled some distance horizontally in the meantime.

    This is an example of the independence or separability of the components of motion. We can define the axes along which we measure, and treat vectors as the sum of their components along those axes.
    FS2

  • C2-22 MONKEY AND HUNTER

    C2-22
    Demonstrate the independence of horizontal and vertical components of motion
    A physical example of a classic textbook illustration, this demonstration shows the independence of the components of motion and the equal acceleration of bodies due to gravity.

    The launcher is aimed at the monkey and shot. As the projectile leaves the muzzle of the gun it breaks a circuit producing the magnetic field which holds the monkey in place. The monkey then begins to fall at the same time the projectile is fired directly at the monkey. Due to independence of horizontal and vertical components of motion, the projectile will strike the monkey.

    Note that the angle can be varied to show different horizontal and vertical components.
    FS1

  • C2-23: TRAJECTORY OF A BALL - MODEL

    C2-23
    Illustrate the position of a projectile at equal time intervals
    This apparatus is a model which shows the position of a projectile at equal time intervals after it is projected. The angle can be changed by tilting the meter stick from which the balls are suspended.

  • C2-24: WATER DROP PARABOLA

    C2-24
    Demonstrate the parabolic path of a projectile.
    A water stream is projected in front of a cartesian coordinate grid that can be shadow projected using a bright point source (not photographed). If desired, coordinates of the water stream can be read. The reservoir is a bottle which provides constant water pressure even as the water level drops in the container.
    C2, LS1

  • C2-25: FUNNEL CART

    C2-25
    Demonstrate the independence of horizontal and vertical components of motion
    A ball is placed in the funnel and the funnel cocked by compressing a spring. The cart is then pushed across the track. At a certain point a bump below the track trips a lever, releasing the spring and ejecting the ball vertically. Because the ball and the cart both move with the same horizontal speed, the ball stays directly above the funnel at all times, and falls back into the funnel. Before doing the experiment, ask your students where the ball will fall: in front, behind, or in the funnel.
    C2, OS0

  • C2-26 FUNNEL CART WITH MASS OVER PULLEY

    C2-26
    Demonstrate the independence of horizontal and vertical components of motion
    A ball is placed in the funnel and the funnel cocked by compressing a spring. A mass on a string passing over a pulley is attached to the funnel cart, and the cart released so that it accelerates across the track. At a certain point a bump below the track trips a lever, releasing the spring and ejecting the ball vertically. Due to the acceleration of the cart, the ball falls behind the funnel.
    C2, OS0

  • C2-27 FUNNEL CART ON INCLINE

    C2-27
    Demonstrate the independence of horizontal and vertical components of motion
    A ball is placed in the funnel and the funnel cocked by compressing a spring. The track is raised at one end so that when it is released the cart accelerates down the track. At a certain point a bump below the track trips a lever, releasing the spring and ejecting the ball perpendicular to the track
    C2, OS0

  • C2-28: TRAJECTORY OF BALL DROPPED BY WALKER

    C2-28
    Demonstrate the independence of horizontal and vertical components of motion
    The subject walks along a line with their arm straight out holding a ball. Have the students make suggestions as to, as the subject passes a bucket, where must they release the ball so that it will fall into the bucket?
    OS3

  • C2-41: VECTOR ADDITION OF VELOCITIES

    C2-41
    Illustrate addition of two orthogonal velocity components
    A billiard ball is placed at the corner of the apparatus. When the two mallets are pulled back and released they strike the ball simultaneously, giving it two orthogonal velocity components. The relative amount of each component is determined by how high each mallet is raised. Use the floor tiles to define your coordinates and show that equal forces in two orthogonal directions produce motion at 45 degrees with respect to the axes.
    C2

  • C3-21: INERTIAL MASS CART

    C3-21
    Demonstrate the inertial property of mass

    Load the arms with equal masses at the same or different distances from the center, and observe what happens when the cart is accelerated by hand along the track. Alternatively, load the arms with masses in the ratio of 10:1 which look the same, and ask students to account for the behavior of the apparatus. By lifting one end of the track, show that when a force (gravity) is allowed to act uniformly on all parts of the apparatus the crossarm will not rotate regardless of how it is loaded.

    A simple demonstration sequence is to place more mass on one side (at front in pictures above) and accelerate the cart with your hand to illustrate inertial mass, then let the cart accelerate down the inclined track to illustrate gravitational mass.
    C3

    c3-21a