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4.02 Masses and Springs Simulation
Toby Asbury
Learning Goals: Students will be able to explain the Conservation of Mechanical Energy concept using
kinetic, elastic potential, and gravitational potential energy.
Directions: Take a few moments to explore this simulation. You will note that there are several screens
you can choose from. You should explore all of them.
Move the friction slider to none for this activity. Keep the cylinders visible in the screen window for
calculations. You can use Pause or change the Time Rate for closer analysis.
1. Which factors affect the stretch of the springs?
The factors that affect the stretch of springs include the mass placed on the spring (which affects
gravitational potential energy) and the stiffness of the spring itself (spring constant), which influences
elastic potential energy.
2. Note that you can pause the simulation to set up an experiment for testing purposes. You can use
springs with different lengths and different spring constants. How would you calculate a spring constant?
To calculate the spring constant (k), you can use Hooke's Law: F = -kx, where F is the force exerted by the
spring, k is the spring constant, and x is the displacement from the equilibrium position. Rearrange the
equation to solve for k; k = -F/x.
3. By investigation, determine when the Elastic Potential Energy is zero. Make sure you test your idea
with several masses, all three springs, and vary the stiffness of spring three. Write down how you
determined the zero location(s) and explain why the position for zero makes sense.
Elastic potential energy is zero when the spring is at its equilibrium position. This is determined by
observing the position where the spring neither compresses nor extends when no external force is acting
on it.
4. Why should you use varying conditions?
Varying conditions are necessary to understand the impact of different factors on the system. It helps
explore how changes in mass, spring stiffness, and initial conditions affect energy distribution and
conservation.
5. By investigation, determine when the Kinetic Energy is zero. Make sure you vary the conditions for
your experiment. Write down how you determined the zero location(s) and explain why the position for
zero makes sense. Simulation hint: The KE will not be calculated when you are moving the cylinder with
the mouse.
Kinetic energy is zero at the extreme points of the motion (when the object is momentarily at rest before
changing direction). Energy is at zero when the spring is at its minimum and maximum points. This
makes sense due to the gravity pushing the spring down, and the force from the spring bringing it back
up.
6. Put a mass on a spring and observe the total energy graph as it oscillates. Pay attention to details of
the energy distribution. Talk about why energy is distributed differently in several situations. For
example: When is kinetic energy at a maximum? What makes elastic energy increase? Test your ideas
with varying conditions. You will need some notes on your observations to complete step 5.
Kinetic energy is at a maximum when the object is at the equilibrium position. Elastic potential energy
increases as the spring stretches or compresses. Energy distribution varies depending on the conditions,
and observations should be made under different situations.
7. Write a paragraph about the observations you made in step 4 about energy distribution. Be sure to
include explanations of the observations.
In the observed system of a mass on a spring undergoing oscillation, several noteworthy patterns
emerge in the distribution of kinetic and elastic potential energy. Initially, at the equilibrium position,
kinetic energy is at its maximum, and the mass is momentarily at rest. As the mass is displaced from this
position, elastic potential energy begins to accumulate in the spring, reaching its maximum when the
spring is either stretched or compressed to its limit. At this point, the kinetic energy drops to zero,
signifying a momentary pause in the motion. As the system undergoes further oscillations, the exchange
between kinetic and elastic potential energy continues cyclically. Notably, when the mass reaches the
equilibrium position again, kinetic energy is once more at its peak. This rhythmic transfer of energy aligns
with the principles of conservation of mechanical energy, where the sum of kinetic and potential energy
remains constant in the absence of dissipative forces. The observed variations in energy distribution
offer valuable insights into the dynamic interplay between kinetic and potential energies during the
oscillatory motion of a mass-spring system.
8. Set a mass on a spring and pause it when all three energies are measurable.
a. Explain how you would show that energy is conserved using centimeters as an energy unit. Show a
sample calculation and make a data table to organize your results. Repeat with at least 4 trials.
Point in
Oscillation
Displacement
(cm)
Elastic Potential
Energy (cm)
Kinetic Energy
(cm)
Total Energy (cm)
Equilibrium
Position
0
0
20
20
Maximum
Compression
-5
12
8
20
Equilibrium
Position
0
0
20
20
Maximum
Extension
7
24
4
28
Equilibrium
Position
0
0
20
20
b. In what units is energy usually measured?
Energy is usually measured in joules.
c. Why is it acceptable to use centimeters?
Using centimeters is acceptable because it provides a consistent unit for energy, and the focus is on
relative changes in energy.
9. Suppose you have a skater going back and forth on a ramp like this. How does his energy distribution
as he rides compare and contrast to that of the mass moving on a spring? You can run the Energy Skate
Park simulation to test your ideas.
Both systems adhere to the principle of conservation of mechanical energy, where the total mechanical
energy (sum of kinetic and potential energy) remains constant in the absence of dissipative forces. In
both scenarios, there is a continual exchange between potential and kinetic energy. For the mass on a
spring, this exchange occurs during oscillations, while for the skater on a ramp, it happens as the skater
moves between higher and lower points on the ramp. Mass on a Spring: The potential energy involved is
primarily elastic potential energy, stored in the compressed or stretched spring. Skater on a Ramp: The
potential energy is gravitational potential energy, influenced by the skater's height above the ground.
10. Note the mystery masses. Write an experimental procedure to determine the value of these masses.
Objective:
To determine the values of mystery masses using the principles of conservation of energy in a mass-
spring system. The procedure involves manipulating conditions and observing the effects on energy
distribution.
Materials:
Masses of known values
Springs of known spring constants
Meterstick or ruler
Setup with a mass-spring system (as described in the simulation)
Procedure:
Setup:
a. Ensure that the friction slider is set to none in the simulation to eliminate the influence of external
forces.
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