10a. Spring and Mass --- a spring and mass system are arranged vertically and set in oscillation. The conversion of spring potential to kinetic to gravitational potential can be pointed out.
10b. Air Track Oscillations --- a horizontal air track is arranged with two weak springs from either end attached to a massive car, of at least m = 1.5Kgm. The system closely approximates the idea of a single spring and frictionless surface. Period dependence on mass easily checked (T2Kg = .707 T1Kg, for example).
10c. Rolling Ball --- a ball is rolled down an incline into a loop of about 30 cm in diameter. From basic principles it is possible to predict from what height the ball must be released in order to complete the loop. The effect of starting from other heights may be shown, including the cases where the ball reaches the top with insufficient velocity to stay on the track. Kinetic energy due to rolling of the ball complicates quantitative predictions.
10d. Bowling Ball --- a bowling ball is suspended from the ceiling on a long, stout rope. The lecturer stands at one side of the hall with the ball held against his nose while standing quite rigid, the lecturer releases the ball and waits for its return, commenting that, by conservation of energy, he knows he is perfectly safe. It is advisable that there be no anticipation of the return of the ball, such as leaning towards it or the like.
10e. Simple Pendulum --- to show conversion from gravitational potential energy to kinetic energy, etc.
10f. Obstructed Pendulum --- a pendulum of length about 1.5 m swings freely for half its arc, but encounters a block at the bottom of its swing such that the effective length of the pendulum is reduced to about 50 cm. In spite of the difference in periods, the ball, released from any height will rise to the same height at the other end of its swing.
10g. F vs. X for a spring --- the extension of a spring for a given mass attached to its free end can be shown. Best to use loose coiled spring to avoid need for initial weight before spring begins to stretch.
10h. Hooke's Law --- the action of a spring as a measure of force may be determined, and demonstrated in the form of a spring balance, one of which may be dissected to show the innards.
10i. Air Track: Work and Energy --- a car on a level air track
is accelerated by a small mass on the end of a string attached to the car. The
attaching mechanism is arranged such that after the weight has fallen 50 cm, the
string goes slack and is released from the car. The velocity of the car is
then measured by the time clock system as the car goes one meter. From a couple
of trials, it is found that, within limits of experimental error, 1/2 mv2 + 1/2 Mv2 = mgh, where v is the velocity of the car and
M the mass of the car. h is the height through which the weight falls, and m is the
mass of the small weight. Usually the kinetic energy of the small mass can be
neglected.
11a. Equal masses - elastic --- two cars of equal mass,
preferably greater than 0.4 Kg are placed on the air track, one at the center,
the other against the car launcher. When the car is released from the launcher
and strikes the second, the first will be seen to stop, and the second to
continue with the same velocity as the first previously had. The experiment may
be made quantitative, using computer timers.
11b. Equal masses - inelastic --- as in 11-a,
except cars have velcro attached to their buffers, and hence stick together
on collision.
11c. Unequal masses --- as in 11-a and 11-b, using cars of
different masses. Of course, it is possible to collide small with large or
vice-versa. In all cases the experiment may be quantitative as above.
11d. Magnetic collision --- two cars of equal mass
have, in place of the spring bumpers, magnets with like poles facing. If one
car is placed stationary in the center of the air track and the other launched
at it VERY SLOWLY, the two will collide without touching, the collision taking
about 5 seconds. The second cart will acquire all of the momentum as a result
of the collision.
11e. Explosion --- two air track cars of equal mass are tied
together in such a way that their springs are compressed. When placed exactly
in the center of the air track and the string tying them together is burned
through the two cars will move away from one another such as to strike the ends
of the track at the same time. If allowed to continue, they will probably
collide at the center of the track. This is not certain, however, as the
bumpers at the ends of the track are usually slightly different. Note that
string tying carts together must exert its force through CM of each cart; a
bumpy explosion will occur otherwise.
11f. Explosion of Unequal Carts --- as in 11-e, using two
different masses. The starting point such that the masses will strike the ends
simultaneously, will not be at the center. It is, however, easily calculable.
Remember that the center of mass of the initial system is not located at the
compressed spring.
11g. Air Table 2-d collisions --- pucks are placed on the level
air table and made to collide using the launcher. From the geometry, the
trajectories of the pucks after collision can be calculated. Pucks of four
different masses are available, as are magnetic pucks for collisions wherein the
bodies do not touch.
11h. Gun --- a spring gun is arranged on top of a large air
track car. Upon pulling the release string, a ball is fired horizontally and
the car is seen to recoil.
12a. CM trajectory --- lamina of various shapes, outlined and
marked at their centers of mass with fluorescent paint, are thrown across the
lecture hall in the beam of light from the blacklight. The centers of mass are
seen to follow a parabolic trajectory, even though the lamina may be rotating
slightly.
12b. CM motion on air track --- a car of mass M has attached to it
a pendulum, also of mass M. The center of mass is marked by a fluorescent disc.
When the car system is set in oscillation, with a small angle of swing, the center of mass
will be seen to be stationary. If the system is made to translate as it
oscillates, the C of M will move with constant velocity. It is best to do this
experiment with the large blacklight on, and all the room's lights off. The
collision of this car with the end of the track is very interesting. If the
oscillations are made large, the marker at the C of M will oscillate vertically
as
the car is constrained to one dimension, whereas the pendulum is constrained to
2.
12c. Two-cart oscillator --- two cars are attached by a long
leaf spring to form an oscillating system. The C of M is marked by a light bulb
attached to and receiving its power from a weak spring. With the lights off in
the hall, the system is made to oscillate while the C of M is seen to be
stationary. If the system is now made to translate, the bulb is seen to move
with constant velocity, while the cars can still be seen to be oscillating.
12d. "Uphill Cone" --- a double cone is seen to, of its own
accord, run up a V shaped incline. The student is asked to explain.
13a. Equal masses --- two billiard balls are hung on bifilar
suspensions such that they collide evenly. One side of the balls has attached
to it pieces of velcro, the other sides are clean. The balls may thus be made
to collide either elastically or inelastically simply by reversing the
suspensions.
13b. 2:1 Mass ratio --- two metal balls of masses M & 2M
are suspended as simple pendula. The collisions between the two are quite
elastic and the repetition of the collision allows sufficient time for a
complete explanation.
13c. Ballistic Pendulum --- the ballistic pendulum may be
demonstrated. A spring gun fired ball being caught by a massive pendulum, is
quite safe and reliable.
13d. Five in a row --- five balls are suspended in a row by
bifilar cords such that each touches the next. Any number may be collided with
the remaining balls and the result of the collision predicted.
14a. Vertical spring and mass --- a mass is suspended from a
spring vertically and set in oscillation. The dependence of the frequency of
oscillation on the mass may be measured using a time clock for frequency
measurements. Can also be done on air track with springs. See 10-b.
14b. Circular motion and SHM --- a turntable turning at 33 rpm
has a pingpong ball placed on it and its shadow projected onto the screen. As
the turntable turns, the one-dimensional projection of the circular motion will
be seen to be simple harmonic. This can be extended by having a pendulum,
consisting of a small metal sphere, on a thread whose frequency is the same as
that of the turntable, suspended above the turntable. By starting the two in
phase it will be seen that the pendulum
executes simple harmonic motion. Relative phase can be adjusted by rotating
the turntable box about a vertical axis.
14c. Simple pendulum --- either of arbitrary or specific length
is set in oscillation and period per ten oscillations is measured. Using
standard formulas the value for the local gravitational constant, g, can be
calculated.
Using different masses with same pendulum length can show absence of mass effect
on measured period.
14d. Torsional oscillation --- a massive disc is suspended by a
small fiber, or metal wire from a stand and set oscillating in a torsional mode.
The small amplitude oscillations are simple harmonic motion. If necessary, the
mass of the disc and the torsional constant for the wire may be measured and the
frequency of the oscillation calculated.
14e. 2D SHO --- a mass is suspended from a square frame by four
springs of similar spring constants. When the mass is set in motion it will
execute a two-dimensional harmonic oscillation. Alternatively, a puck may be
held on the air table by 4 springs, one to each side. The motion of the puck
may be made to be circular or elliptic oscillations.
14f. Sand Lissajous --- a sand pendulum is set up using a
bifilar suspension. When the pendulum is set in motion with sand falling from
its aperture, the sand pattern formed below the sand pendulum will be a complex
two-dimensional harmonic oscillation.
14g. CRTO Lissajous --- two oscillators are connected to the
oscilloscope, one to the horizontal deflection plates, one to the vertical
deflection plate. Combinations of frequencies of these two oscillators form
Lissajous figures.
14h. Inclined air track, SHM --- the air track is set up
steeply inclined and the car placed at the center. A weak spring is run from
the car to the top end of the air track. Oscillations about the equilibrium
position are simple harmonic and amplitude independent.
14i. Level air-track SHM, see 10-b. Can damp free oscillations using magnets taped to cart. Variable drive frequency being developed.
14j. Physical pendula --- an aluminum bar is placed
in a knife edge bearing system arranged such that the bearing may be placed
anywhere along the length of the bar. With the bearing at one end, the pendulum
oscillates as a compound pendulum of length L, where L is the length of the
equivalent simple pendulum. As the bearing system is moved towards the center
of mass the period of oscillation increases until at the center of mass the
system becomes unstable. Also, a disc of metal is suspended from a stand
by a hole close to one edge of the disc. The oscillations executed when the
system is displaced are simple harmonic. Also, a ring of metal is placed on a
knife edge bearing and set in oscillation. The motion is simple harmonic. The
ring pendulum is a nice quantitative experiment. Uses parallel axis theorem to predict I andhence the period.
15a. Cavendish Balance --- is available for measurement of the
gravitational constant. It is usually not advisable to attempt to perform this
experiment in the lecture hall as the time it takes for the experiment can
exceed two hours. The suspension fiber is extremely weak and prone to damage.
The film loop available in the Audio-Visual Room performs the same experiment
using the same apparatus. The apparatus is available in a second form as a non-
working model, wherein suspension is replaced by a thread.
15b. Inertial Balance --- is used as an aid in showing the equivalence of inertial and gravitational masses. The frequency of oscillation of the inertia balance depends only on the inertial mass, not on the gravitational mass of the object.
15c. Inverse square law --- the motion of a particle in a
forcefield where the force depends on the inverse square of the distance may be
shown using the Van de Graaff generator and a charged pith ball. The pith ball
is suspended by a long fine thread from the ceiling, the Van de Graaff being
placed on the floor. With the Van de Graaf running flat out, the pith ball is
charged with an opposite charge rod, and then swung in a circular motion about
the Van de Graaff. With great care being taken to start the motion of the pith
ball, it is possible to get elliptic orbits with the Van de Graaf at one focus.
It is imperative that the mass of the pith ball be as small as possible and the
length of the suspending thread be as long as possible so as to minimize the
effects of the gravitational force on the pith ball. This experiment can only
be performed during the winter term when the humidity is very low.
16a. A Pascal Vase apparatus is used to show the variation of
pressure with height, not with cross-section of containers. Three vases are
available: a cylinder, a flared cylinder, and a constricted cylinder. Fluid is
placed in the Pascal Vase and the pressure, measured in arbitrary units,
displayed on the apparatus's scale. The three cylinders may be changed in
succession and it may be shown that for a specific height of fluid in the
cylinder the pressure is the same.
16b. Hg column barometer A tube, closed at one end, is filled
with mercury and inverted into a trough of mercury. Can also use vacuum pump to
"pull" Hg column up from a dish of Hg. The height of the mercury in the column
is a function of the atmospheric pressure.
16c. Bernoulli Principle A styrofoam ball is supported on the
air jet emitted from the pressure side of a vacuum cleaner or special fan-in-
tube device. The nozzle may be tilted from the
vertical. If the air flow is reasonably uniform, the ball will stay floating
on the airjet up to angles of approximately 45°.
16d. Pressure drop and flow A long glass tube has a constriction in the middle. At four places along the length of the tube side arms are used to connect two J-tube pressure indicators. Air from the high pressure airline is allowed to flow through the tube. The flow of air may be
indicated by a paddle wheel placed at the atmospheric end of the tube. The
pressure variations in the flowing fluid are shown by displacements of the fluid
in the J-tube. The experiment is best observed under ultraviolet light with
fluorescein in the water.
16e. Bernoulli Principle The vacuum created by a fluid flowing
through a nozzle as in the standard chemical vacuum aspirator may be
demonstrated using the glass version. Fluorescein dyed water may be sucked in
the apparatus to show clearly the fluid flow.
16f. Bernoulli Principle A airjet is arranged to blow between two sheets of paper hanging vertically. When the air is turned on, the two sheets of paper will move closer together.
16g. The syphon is demonstrated using two jars of fluorescein
dyed water at different heights. The syphon is usually best started by sucking
on the low side of the tube. That air pressure is necessary for the syphon to
function may be demonstrated by arranging a small syphon under a bell jar. When
the air pressure is removed by the vacuum pump, the syphon will stop.
16h. Cartesian Diver The glass vial with a small amount of air in it is arranged so that it just floats in a cylinder of water. Across the top of the cylinder is placed a rubber diaphragm or a syringe. Upon depressing the diaphragm, the vial is seen to sink as the pressure is transmitted from the diaphragm to the air in the vial compressing it. The weight of the vial therefore increases and goes above that of water.
16i. Pascal Vases Colored water is poured into an apparatus that consists of number of tubes of various shapes arranged in a common base. The fluid level in each tube is the same.
16j. Magdeburg Hemispheres Two hemispheres are arranged to
seal tightly against one another. When the air is removed from inside it will
be found almost impossible to separate the two halves.
16k. V(h) A vertical tube (or a gallon can) with holes drilled at the bottom, middle, and top is fed with water from the faucet. Of the three jets emanating from the holes, the jet at the bottom will be found to go the furthest, the middle the second furthest, the top the least distance.
16l. A hydraulic jack is available for demonstrating Pascal's
principle. The mechanical advantage of the system is in part due to the ratio
of the diameters of the cylinders and in part due to the ratio of the lever arm
of the pump handle. The system is capable of bending nails, crushing wood,
etc.A 2 x 4 piece of lumber is impressive to use.
16m. Archimedes' principle may be demonstrated using aluminum,
brass, steel, or lead blocks. The change in apparent weight of each block as it
is immersed in fluid and the volume of fluid displaced are used to calculate the
specific gravity of the material.
16n. A Pitot tube is used to show Bernoulli's principle. As a
gas flows over the Pitot tube the pressure difference at the end and edge of the
tube is measured using a u-tube manometer. Using water as the fluid in the u-
tube, the velocity of the air flow is simply given by V=(2ghρ'/ρ)1/2 where ρ is the density of the gas, ρ' is the density of the fluid in the u-tube, h is the displacement of the fluid in the u-tube. See file card for diagram.
11. AIR TRACK COLLISIONS/EXPLOSIONS