Pasco Scientific ME-6956, Instruction Manual And Experiment Manual

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012-07558A PAScar Accessory Track Set (2.2 Meter)
®
Experiment 6: Springs in Series and Parallel
EQUIPMENT NEEDED:
– PAScar with Mass (ME-6950) – Base and support rod (ME-9355)*
– Dynamics Track with End Stop – Mass balance (SE-8723)*
– (2) Springs (646-04445)* – Stopwatch (SE-8702B)*
Purpose
The purpose is to measure the period of oscillation of springs in series and parallel and
compare it to the period of oscillation of one spring.
Theory
For a mass attached to a spring, the theoretical period of oscillation is given by
where T is the time for one complete back-and-forth motion, m is the mass that is oscil-
lating, and
k
is the spring constant. If the period of oscillation is measured, the spring
constant can be determined:
When two springs are combined in series or in parallel, the spring constants add in
different ways. One possible way to add two spring constants is
k
effective
= k + k = 2 k .
Another way is
which means that
Measuring k For a Single Spring
1. Use the balance to find the mass of the car. Record this value at the top of Table 6.1.
2. Set the car on the track and attach a spring to one end of the car by inserting the end of
the spring in the hole provided in the car. Then attach the other end of the spring to the
end of the track (See Figure 6.1).
NOTE:
Remove the leveling feet for this experiment.
3. Incline the track by raising the end of the track that has the spring attached. As the end of
the track is raised, the spring will stretch. Keep the inclination angle of the track small
enough so that the spring is not stretched more than half the length of the track.
*Not included in Track Set
Procedure
k
effective
= 12 k
T = 2
π
m
k
Κ
effective
=
1
k
+ 1
k
= 2
k
k
= 4
π
2
m
T
2