* Gravitational force causes a cart to accelerate down the track
* Spring force in opposite direction opposes downward movement
* Distance travelled is proportional to the height of the track.
You can click on the picture to download it in gif format.
Further information on Theory, Apparatus,
Procedure, and Helpful Hints
are available. Bearing track and cars are available
in 302. Other cars maybe available in 402 or 403.
The purpose of this demo is to show the students firsthand a classic physics exam
question, that of a mass falling a certain distance to stretch a spring.
A mass will fall a certain distance, including the distance it
compressed/stretched the spring. This total fall is proportional to the
change in potential energy of the mass. At this point, all motion has
stopped and the mass-spring system again has no internal kinetic energy,
this energy being again transferred into the potential energy of the
spring.
m*g*sin(theta)=k* [x(e)-x(0)]
2m*g*sin(theta)=k*[x(max)-x(0)]
x(0) is measured from the point where the spring just becomes
taught.
* A bearing track
* bearing cart
* spring
* string
* meter stick
* bent small piece of cardboard
* mass
The setup involves the spring attached to the end of the track
and to the cart by a short string. One end of the track is elevated.
The cart is released and pushes the small piece of cardboard ahead of it
until it reaches its lower stopping point.
The angle of the track's inclination can be measured, and as the
cart travels along the track a certain distance the corresponding total
change in height is proportional to the total potential energy of the
system. The small piece of cardboard is an indicator (just a little
orthogonality symbol shape) of how far the cart has travelled.
The cart slides down the track, picking up speed. The string pulls
tight and stretches the spring, as the front end of the cart pushes the
small cardboard piece down the track. This piece will remain where the
cart stopped moving forward. This will give the total distance the cart
has travelled and (measuring the distance to the piece while holding the
cart to the point where the string is tight but the spring is
unstretched) the distance the spring was stretched.
From this information it is possible to show the total kinetic and
potential energies equal, find the spring constant, or find the mass
(all depending on other information such as prior measurement of the
spring constant or knowledge of the mass).
(1) Choose the right spring. The spring must be light enough so
that the class can see it stretch out.
(2) Scraping the track. If the spring attaching the cart and the
end of the track lies along the track, it will scrape. This can be
reduced by having it scrape over a smooth piece of paper or laying down
some scotch tape on the track where it comes in contact. Another method
is to suspend the spring, either by balancing it on a rolling device or
attaching it pendulum-like by attaching strings to the coils from an
overhead attachment such as a crossbar on a ring stand.
(3) Any such method in (2) should be tested before class begins to
ensure that the particular arrangement doesn't result in large error in
any calculations the class might conceivably do. Improper suspension of
the spring or an excessively massive spring will affect the quantitative
results.
You can click on the picture to download it in gif format.