Download Title: Springs, Spring Constants, and Changes in Potential Energy

Physics--Chapter 12: Vibrations and Waves
Springs Lab
Title: Springs, Spring Constants, and Changes in Potential Energy
Date:
Partner(s):
Background Information:
The law of conservation of energy states that the total energy in an isolated system remains
constant at all times. If there is no friction, this energy will remain mechanical energy. That is it
can be exchanged between one form of potential energy and another, or it can be exchanged
between kinetic and potential energy. Suppose a spring is hung vertically with a mass attached to
its lower end. The force exerted on the spring by the mass will cause the spring to stretch and the
mass will come to rest at its equilibrium position. If the mass is lifted a few centimeters above its
equilibrium position and dropped, it will oscillate with simple harmonic motion. At the top and
bottom of its motion the mass will be momentarily at rest and thus have zero kinetic energy.
Choosing the lowest point in the oscillation as the reference level for gravitational potential
energy, the total mechanical energy at this point will all be in the form of elastic potential energy
of the spring. Similarly, at the top of the oscillation, the total mechanical energy will again be all
in the form of gravitational potential energy.
Objectives:
In this lab you will study the conservation of energy in a mass hanging from a spring. You will
compare the change in gravitational potential energy of the system with the change in elastic
potential energy as the mass oscillates between its two extreme positions. You will determine a
spring constant for the spring, and verify this by timing oscillations of the spring-mass system.
Procedure:
Needed Materials: long spring hanging from ceiling, short spring supported by ring stand, clamp,
and cross bar at the lab tables, meterstick, various masses, 50-g mass holder, stopwatch
To Do for each spring:
Spring Constant Determination Data:
1. Use a meter stick to measure the height of the bottom of the vertically hanging spring and
record it in the data table. This is the zero displacement. Note that no masses or the holder
are attached to the spring at this point.
2. Add the mass holder to the spring, measure the height and record it in the data table.
Determine displacement and enter this in the data table.
3. Experiment with the amount of mass that can be added to achieve a noticeable stretch, result
in good oscillation, not touch the table or floor, and not overstretch the spring.
4. Add even-increment masses (i.e. 100 g per trial) to the holder based on your experimenting
in #3, measuring the height after each. Record total mass on the spring for each trial and the
corresponding height. Note that the mass value is increasing and the height value is
decreasing.
5. Continue to add masses, measure the heights and record until you have collected 10 data
points. Fill in displacement data as well.
Conservation of Energy and Period Data:
1. Leave the final mass from the previous section attached to the spring.
2. Lift the mass so that the spring is in its unextended position. This needs to be verified from
your height data so that your oscillation time can be accurate.
Physics--Chapter 12: Vibrations and Waves
Springs Lab
3. Drop the mass, measure its lowest height with the meter stick and record the data in the table.
Repeat three times to verify this measurement.
4. Time one period of oscillation and note in data summary.
5. Repeat this procedure three times.
* If you started with the long spring, repeat both procedures with the short spring. If you started
with the short spring, repeat with the long spring.
Data Summary:
Determination of Spring Constant Data
height (m)
displacement (m)
long
short
long
short
mass (kg)
long
short
Trial
mass (kg)
long
short
Conservation of Energy Data
unextended height
lowest height (m)
(m)
long
short
long
short
force (N)
long
short
Δh (m)
long
short
1
2
3
Average Δh:
Trial
Oscillation Data
time (s)
long
short
1
2
3
Average:
Results:
Spring Constant Determination:
1. Calculate the force on the spring for each mass and record in the data table.
2. Make a graph of force vs. displacement using your graphing calculator for each spring.
Record the linear equation and the correlation values of your graphs in your notebook. Also,
sketch each of these graphs in your notebook.
Physics--Chapter 12: Vibrations and Waves
Springs Lab
3. What is the experimentally determined spring constant for the long spring? For the short
spring?
Conservation of Energy and Period Determination:
1. Calculate the difference between the unextended height and the lowest height for each of the
three trials and record the data.
2. Calculate the average difference between the unextended height and the lowest height and
record on the value in the data table.
3. Calculate the gravitational potential energy of the spring when the mass is at the highest
spring position for the long spring. Repeat for the short spring.
4. What would be the elastic potential energy of both springs in this position?
5. What would be the kinetic energy of both springs in this position?
6. What would be the total mechanical energy of both springs in this position?
7. Calculate the elastic potential energy of the spring when the mass is at the lowest spring
position for the long spring. Repeat for the short spring.
8. What would be the gravitational potential energy of both springs at this position?
9. What would be the kinetic energy of both springs in this position?
10. What would be the total mechanical energy of both springs in this position?
11. Using the time for one period of oscillation, verify the spring constant value for each spring
by calculation.
Conclusion: (what did you learn? from what in the lab did you learn this? real world example?)
Discussion of Error:
1. According to the law of conservation of energy, the total mechanical energy at the highest
and lowest points should be the same. Determine the percent difference between your values
for both the long and short spring. How can you account for any difference between the
values?
2. Calculate a percent difference for the two values obtained for the spring constant for each
spring. Which method do you think is more accurate? Why?
Suggestions for Improvement: (always make reasonable suggestions!)