Lab 11 Energy Conservation and Springs (1)
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Florida International University *
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Aerospace Engineering
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Apr 3, 2024
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Conservation of Mechanical Energy using Masses and Springs simulation https://phet.colorado.edu/en/simulation/masses-and-springs Learning Goals: Students will be able to explain the Conservation of Mechanical Energy concept using kinetic, elastic potential, and gravitational potential energy. Directions: 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.
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. Zero location is the location where the mass sits while the spring is not moving over time (at equilibrium). This makes sense since when the mass is at rest. 2.
Why did I have you use varying conditions? By varying the conditions, it proves that disregarding the conditions the zero location will always be when it is at equilibrium.
3.
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. We can see from our analysis that the kinetic energy is 0 when the elastic potential energy is at its maximum, which occurs when the object's displacement is at its maximum. We discovered the site of the mass's momentary rest, and the distance between this point and the equilibrium location gave us the location of maximal elastic potential energy. Also, the mass comes to a halt for a brief while at this point, implying that KE is at its lowest, which is really 0. There are two points where KE is 0, which makes sense since one is where the KE becomes elastic PE for the compressed spring and the other is when the KE becomes elastic PE for the extended spring. 4.
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 the energy is distributed differently for several situations. For example: When is kinetic energy at a maximum? What makes the elastic energy increase? Test your ideas with varying conditions. You will need some notes on your observations to complete step 5. According to my findings, the total energy of free oscillation always decreases with time owing to damping. In terms of energy distribution, because energy is wasted in damping, the body has KE, and the system has elastic PE at any given time. With a few exceptions, the total energy partitioning continues to exchange between these two: KE is usually positive, although PE might be negative. Because damping reduces total energy, the amplitude of oscillation diminishes over time, as does the velocity of oscillation. Stiffer springs oscillate faster.
5.
Write a paragraph about the observations you made in step 4 about energy distribution. Be sure to include explanations of the observations. The potential energy stored in the spring is at its peak when it is at its greatest compression or extension. This is because the spring is in its most deformed state, ready to apply maximum force upon restoring the mass to its equilibrium position. In
Conservation of Mechanical Energy using Masses and Springs simulation https://phet.colorado.edu/en/simulation/masses-and-springs contrast, when the mass approaches equilibrium, its velocity is at its greatest, resulting in maximum kinetic energy. However, when the mass travels away from equilibrium, its velocity and kinetic energy drop. The laws of energy conservation explain these results, since the total of kinetic and potential energy remains constant during the oscillation cycle, with energy continually converting between these two forms as the mass-spring system moves in a periodic manner.
6.
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. To demonstrate the conservation of energy in a mass-spring system and use centimeters as an energy unit, you can measure the height of the mass at different points during its oscillation and calculate the potential energy and kinetic energy at each of these points. Trial Height (cm) Height (m) PE (J) KE (J) TE (J) 1 10 cm 0.10 m 0.0981 0.04905 0.14715 2 15 cm 0.15 m 0.14715 0.073575 0.220725 3 20 cm 0.20 m 0.1962 0.0981 0.2943 4 25 cm 0.25 m 0.24525 0.122625 0.367875 b.
In what units is energy usually measured? Energy is usually measured in joules (J) in the International System of Units (SI). c.
Why is it acceptable to use centimeters? Converting height from centimeters to meters is simple (just divide by 100), and this method is appropriate for educational or small-scale investigations. While the SI unit for energy is joules (J), measuring height in centimeters simplifies computations and gives a clear illustration of energy conservation in a simplified environment. 7.
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 Shate Park simulation to test your ideas.
When the skater reaches the top of the ramp, its potential energy is at its peak since its velocity is zero. The potential energy here is gravitational potential energy (gravitational potential energy = mgh) from the zero potential surface (in our instance, the ground). When compared to a spring-mass system, the spring has a large potential energy due to the spring being in an extreme position (spring potential energy is provided by 12 kx
2
, where k = spring constant and x = displacement from equilibrium position). Because the mass's velocity is 0 at this moment, the kinetic energy is also zero. Similarly, when the skater travels upward from the lowest to the highest position, its kinetic energy grows as its potential energy increases, and when it reaches the second highest point, it has the maximum potential energy once more. Similarly, the mass on the spring oscillates between two extreme points where the elongation of the spring x is greatest and hence attains the greatest potential energy. It has the greatest kinetic energy when the elongation of the spring is zero, and hence the potential energy is likewise zero. The total energy is likewise constant in this case.
Conservation of Mechanical Energy using Masses and Springs simulation https://phet.colorado.edu/en/simulation/masses-and-springs 2h h 8.
The main difference between kinetic energy, KE, and gravitational potential energy, PE
g, is that
a.
KE depends on position and PE
g depends on motion.
b.
KE depends on motion and PE
g depends on position.
c.
Although both energies depend on motion, only KE depends on position. d.
Although both energies depend on position, only PE
g depends on motion.
9.
Joe raised a box is above the ground. If he lifts the same box twice as high, it has a.
four times the potential energy b.
twice the potential energy c.
there is no change in potential energy. 10.
As any object free falls, the gravitational potential energy a.
vanishes b.
is immediately converted to kinetic energy. c.
is converted into kinetic energy gradually until it reaches the ground. 11.
A small mass, starting at rest, slides without friction down a rail to a loop-de-loop as shown. The maximum height of the loop is the same as the initial height of the mass. Will the ball make it to the top of the loop? a.
Yes, the ball will make it to the top of the loop. b. No, the ball will not make it to the top. Use the figures below to answer the following questions. A spring is hanging from a fixed wire as in the first picture on the left. Then a mass is hung on the spring and allowed to oscillate freely (with no friction present)
. Answers A-D show different positions of the mass as it was oscillating. The dotted lines are on the drawing to help you see the change in position relative to the spring with no mass. A.
Spring with no mass attached B. Mass at maximum height C. Mass at minimum height D.
5.
For each of the questions, select all the letters that apply. a.
Where does the spring have maximum elastic potential energy? C b.
Where is the gravitational potential energy the least? C c.
Where is the kinetic energy zero? D d.
Where is the elastic potential energy zero? D
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Conservation of Mechanical Energy using Masses and Springs simulation https://phet.colorado.edu/en/simulation/masses-and-springs