Name: _____________________________________Date: ___/____/____ Course/Lab Section: _______
Name of Lab Instructor: _________________________
PreLab
The Jolly Balance
Instructions: Prepare for this lab activity by answering the questions below. Note that this is a PreLab. It
must be turned in at the start of the lab period. Time cannot be given during the lab activity for PreLab work.
After the start of lab activities PreLabs cannot be accepted.
Q1. This lab activity involves Part I and Part II. One uses a static technique, the other uses a dynamic
technique. Which one is which? Explain.
Q2. The only purpose of the Jolly Balance is to verify Hooke’s law and measure spring constants. Is this
statement correct? Explain.
Q3. What is the meaning of the negative sign in Hooke’s law?
Q4. What happens to the period of oscillation of a spring if its spring constant is doubled?
Q5. Write the equation of the straight line represented in the graph below. What is the intercept and what is
the slope of this line?
y
10
5
0
1
2
3
4
5
x
Q6. The angle corresponding to the slope actually is larger than it looks like from a first and quick look at the
plot. Why is that so?
The Jolly Balance
Purpose: The purpose of this lab activity is to verify Hooke’s law and the equation for the period of an
oscillating spring while measuring the spring constant of the spring. This lab activity is intended to assist you
to:
 Develop a better understanding of the relationship between force and extension in elastic materials.
 Perform experimental measurements that allow the determination of the spring constant of springs.
Introduction: The Jolly Balance was invented around 1874 by the German professor Phillipp Gustav von
Jolly. It can be used to determine the spring constant of springs and the specific gravity of materials. The first
purpose is the object of this lab activity. We start with the Hooke’s law expressed mathematically by the
equation
F = -k x ,
(1)
where F is the restoring force exerted by the stretched (or compressed) spring, x is the corresponding
change in displacement, and k is a proportionality constant called spring constant. The negative sign takes
into account that the restoring force is always opposite to the direction of the displacement. In Part I of this
experiment a series of masses will be suspended from a spring and the displacements measured in
equilibrium. Under these conditions the magnitude of the spring force will be equal to the weight of the
suspended masses, i.e.,
k x = ma g ,
(2)
where ma is the applied mass. This equation is used for determining the value of the spring constant k.
In Part II we verify the equation for the oscillatory motion of the suspended masses. The equation is
meff
,
(3)
T  2
K
where T is the period, meff is the effective mass, and K is the spring constant. We then use this equation to
compute the value of the spring constant K and compare the result with the value of k obtained in Part I.
Note that ma and meff are not the same. Before any mass is suspended from the spring in Part I, the spring is
 weight and the weight of the pan to which the masses are added.
already stretched a bit due to its own
Therefore the effective mass meff is the applied mass ma added to the mass of the pan and some lower portion
of the spring that we combine together and call mo. So,
meff = ma + mo .
(4)
Procedure:
Part I: Verifying Hooke’s law and determining the spring constant k
a. Suspend the spring from the upper support allowing it to hang freely. Attach the weight pan to the bottom
by hooking the double bar at the bottom spring hook. Bring the slide mechanism up and insert the double bar
through the slot into the hole. The double bar should be centered in the hole. If it is not, the leveling screws
in the base, the upper support and the spring hook at the upper support may be used to adjust it so that it is
centered. Once the double bar is centered in the hole, place a 50 g mass on the platform and lower the slide
mechanism until the mass hangs freely. The double bar should be centered, or nearly so, at this point too. If it
is not, the leveling screws will probably allow you to make the needed adjustment.
b. With no mass on the pan adjust the slide mechanism such that the dividing line between the white and the
black parts of the double bars is at the level of the hole in the slide mechanism. Note that, even when the set
screw is tightened, there is some up and down play at the end of the slide bar. See the Fig. 1 below.
(a)
Fig 1: (a) The Jolly Balance,
(b)
(b) Detail of the sliding mechanism for reading the scale.
The scale will be read at the meter stick as indicate on the sketch above. However, there may be as much as
three of four millimeters variation at the end of the bar for a given scale reading. In order to minimize errors,
you should always take up the slack by pushing the end of the bar either up or down before taking the
reading. Whether you decide for up or down, it must always be in the same direction. With the bar so
adjusted and centered at the white-black junction, read and record the scale reading on the DATA TABLE.
Use this same procedure for all readings.
c. Place a five gram mass on the pan, read and record the scale reading. Repeat adding five grams at a time
until this portion of the DATA TABLE is complete.
Analysis I
We wish to determine the relation between the force mag and the change in displacement x. For each force
determine x by subtracting the initial displacement (when F = 0) from each of the successive displacements.
Record the values in the x column of the DATA TABLE. Plot a graph of F versus x (F on the y-axis).
Label it Graph I.
Analysis II
Use Graph I to help you write the equation for the relationship between F and x and determine the value of
the constant k.
Part II: Verifying the equation for the period of oscillation
a. Remove the double bar from the hole in the slide mechanism and lower the slide as far as it will go. Raise
the upper support to within a centimeter or so from the top.
b. Raise the weight pan slightly and release it allowing it to oscillate. Using the stopwatch time 50 complete
oscillations. Divide this time by 50 and record it on the DATA TABLE as the period T.
c. Increase the mass in steps of five grams and repeat step b above to complete the DATA TABLE.
Analysis I
Plot a graph of ma versus T with ma on the y-axis. Label it Graph II. What form does the graph seem to have?
Can the mathematical relation between ma and T be determined from this graph? Think about what to do
next.
Analysis II
Determine and record the values of T 2. Plot a graph of ma versus T 2 positioning the graph on the paper to
allow for negative values of ma. Label it Graph III. Use the equation for the slope of a line to derive the
equation for the relationship between ma and T 2. In doing this let K represent the slope and mo represent the
magnitude of ma at the mass intercept. Use the mass intercept as one of the points in the slope equation.
Final analysis and remarks
a. In Part II above you should have obtained
K
ma  (mo ) ma  mo

T2  0
T2
(5)
from the slope equation. Use Eq. (4) to write
K
 (3) and write it as
We now square Eq.
k
4
2
From Eqs. (6) and (7) we
conclude that

m eff
T2
meff
T2
.
(6)
.
(7)
k  4 2K .
(8)
Plug in this equation the value of K obtained in Part II and compute the value of k. This k is, of course, the
 be the same as that obtained in Part I. Record on the DATA TABLE the value
spring constant and should
calculated here and the percentage difference between this and the value from Part I. Before proceeding you
 difference in units between the two values. Convince yourself that each value is
should take note of apparent
expressed in proper units.
b. We now discuss the significance of the mass intercept mo. Note that on the graph this is the point at which
the period would go to zero. The mass does not vanish at the same point because the applied mass ma was
being plotted and no account was being taken of the pan or the mass of the spring. By extrapolating
backward to the T 2 = 0 point we find the theoretical amount of the mass that would have to be removed in
order to make the period go to zero. This value of mo must then include the mass of the pan and some portion
of the mass of the spring. Using the triple beam balance, determine the mass of the pan (including the double
bar). Subtract this from the value of mo determined from the graph. The reminder must be due to the spring
itself. Record this as the partial mass of the spring on the DATA TABLE. Theoretical calculations indicate
that this should be 1/3 of the mass of the spring. Using the triple beam balance, determine the mass of the
spring and record it on the DATA TABLE. Calculate 1/3 of this mass value and find the percent difference
between this and the partial mass of the spring obtained before.
The Jolly Balance
DATA TABLE
Name (Partner A): __________________________________________
Date: ____________
Name (Partner B): __________________________________________
Course/Lab Section: __________
Name (Lab Instructor): ______________________________________
Part I
x
(cm)
Part II
x
(cm)
ma
(g)
(m)
F
(N)
(kg)
T
(s)
T2
(s2)
0
5
10
15
20
25
30
35
40
45
50
From Part I:
k = ____________ N/m
From Part II:
K = ___________ kg/s2,
k = ____________ kg/s2
% difference between the two values of k : _________ %
mo (from Graph III): ____________ kg
Mass of spring _________ g = _________ kg
Mass of pan _________ g = _________ kg
1/3 of mass of spring _________ kg
Partial mass of spring __________ kg
% difference between the partial masses of the spring = ________%
SHOW ALL YOUR WORK.