lab 9

Lab #9
Hooke’s Law and the
Physics 111 Simple Pendulum Name:
I. Hooke’s Law: F = k Δx
= k x − x ) = k(
x − )
spring
(
0
x unstretche d
A. The drawing shows a stationary mass hanging from a hypothetical
spring with linear behavior governed by Hooke’s Law.
ceiling
x 0
x
[4 pts] Draw the free body diagram for
the mass. Correctly label all forces on
your free body diagram.
Δx=17cm
[4 pts] If the mass of the block is 250g, find the spring constant of the spring in units of
Newtons/cm.
B. The brass spring at your table exhibits the full range of spring behavior, including non-linear
behavior. You’re going to use the computer interfaces to investigate this behavior.
The spring at your table is called a “zero-length” spring. These springs have a tension on them
even with no stretch. This is an example of non-linear behavior.
x 0
For this part of the lab, do the following:
Start with the spring on the table with no tension on it.
T
“Zero” the force probe with it touching nothing.
On the table, use chalk to mark the initial position x 0 of the end of the spring. Then, mark
every 4.0cm beyond that to at least 50cm.
Use the force probe to pull the spring out to various lengths Δx.
Hold these in place for a couple of seconds so the computers can record the spring force.
Stretch the springs out until you reach Δx~48cm.
Use your data to fill out the table on the next page. NOTE: The units of the spring constant
“k” will be Newtons/cm. You should only have 2 significant figures for “k.”
Hooke’s Law & the Simple Pendulum HW–1

Lab #9
Hooke’s Law and the
Physics 111 Simple Pendulum Name:
Stretch Δx(cm)
x 1 = 0.0
Force (N)
F 1 = 0.0 N
x 2 = 4.0 F 2 = k=(F 2 –F 1 )/(x 2 –x 1 )=
x 3 = 8.0 F 3 = k=(F 3 –F 2 )/(x 3 –x 2 )=
12
16
20
24
28
32
36
40
44
48
Data Table [15 pts]
Spring constant k=ΔF/Δx (N/cm)
(2 significant figures)
[6 pts] On the graph provided to the
right, plot your values for F and Δx.
F (Newtons)
These “zero length” springs have some
initial tension built into them so their
“resting state” is contracted. Once you
get these springs stretched out just a
little way, they act like traditional
springs with a spring constant.
[2 pts] What trend do you notice with
your graph?
0
0
Δx (cm)
[2 pts] Approximately how far do you have to stretch
the spring until it behaves like the traditional springs
discussed in class?
[2 pts] What value does the spring constant settle into?
Hooke’s Law & the Simple Pendulum--2

Lab #9
Hooke’s Law and the
Physics 111 Simple Pendulum Name:
II. The simple pendulum—simple harmonic motion example
Set the photogate timers on “pend” and the timing accuracy (on their undersides) to “1ms.”
Put a 100g mass on your string. Make the length of your string L=1.0 meter.
A. [8 pts] Use the initial amplitudes listed below and determine the period of oscillation for each.
Keep your length and mass constant.
Amplitude A
very small (~5cm)
small (~10cm)
medium (~15cm)
large (~20cm)
very large (~25cm)
Period T (sec)
Does the amplitude affect the period of oscillation of a pendulum? yes no (circle one)
B. [8 pts] Use the masses listed below and determine the period of oscillation for each.
Mass m
50g
100g
200g
500g
Period T (sec)
Does the mass on the pendulum affect the period of oscillation of a pendulum? yes no
C. [8 pts] Use the string lengths listed below and determine the period of oscillation for each.
For each of these,
pay attention to
large differences
only.
Length L
40 cm
60 cm
80 cm
100 cm
120 cm
Period T (sec)
Does the length affect the period of oscillation of a pendulum? yes
no
As you have seen, not all of the variables of mass m, string length L and amplitude A come into play
with the period of a pendulum. Oddly enough, the variables that you might suspect “surely would”
determine the period of the pendulum have no effect. Thus, any equation that describes a simple
pendulum should reflect that some variables matter while others don’t.
Hooke’s Law & the Simple Pendulum--3

Lab #9
Hooke’s Law and the
Physics 111 Simple Pendulum Name:
The period T and length L of a simple pendulum are related by the equation
2
2 4π L
T = .
g
Here, g is the gravitational acceleration at the location of the pendulum. This assumes the oscillations
have settled down into a consistent rhythm, and the amplitude of the oscillations is not too large. (The
phrase “amplitude…not too large” means not more than about 20 0 away from the vertical.)
[8 pts] Use your data with the various lengths on the previous page to calculate g for all 5 cases. Show
your work for all 5 cases below. Your answers should have 3 significant figures.
L=
L=
L=
L=
L=
T=
T=
T=
T=
T=
If any of your calculations indicate problems with the data, it is legitimate to throw out that point.
[3 pts] Take the average of your values above for g: g = .
[3 pts] How does your average value compare to the value of g=9.8 m/s 2 we so often use in class?
Hooke’s Law & the Simple Pendulum--4