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Lab 1: Oscillations
(This lesson is designed for a student working remotely.)
Learning Goals: Students will be able to calculate the spring constant k of a spring and develop an understanding of the energy of an oscillating spring.
Develop your understanding:
Open the following simulator and click the lab option:
Become comfortable with the controls by clicking, sliding, using them, and observing what happens in the simulation.
Below are a couple of simulation use tips:
The Movable line has a handle that lets you drag it to different positions.
The ruler and the timer are tools that you drag onto the lab area.
The Pause, Play and Step buttons will help you take screen captures.
The speed buttons can help you observe in slow motion.
If you press the Stop Oscillation button , you will need to grab the mass and move it to make the motion go again.
Part 1: Calculating The Spring Constant k
Place the 100g mass onto the spring. The spring will begin to oscillate up and down. Stop this by clicking on the mass several times or increasing the ‘Damping’ value to ‘Lots’.
Click the ‘Displacement’ and ‘Movable Line’ options on the right. Adjust the movable red line to the tip of the green arrow.
_________ (score out of 6 points) Use the ruler tool (the units are in mm) on the bottom right to measure the extension of the spring with the 100g mass. Convert this mass to a weight (use g=9.8 ms^(-2)) and add this data to table 1. Remember to convert g to kg.
Mass added (g) Weight (N) Extension (mm)
100g
Table 1
Using the slider at the top, change the mass and record 5 more results of weight and extension. Add your results to table 1.
__________(4 points) Plot and insert a graph (either on paper or using Excel) for Force (y-axis) against extension (x-axis). Draw a line of best fit through your points.
__________(5 points) Your data should look like a straight line. The equation for the force of a spring is
F = k x
where:
F = stretching force applied to the spring
k = spring constant
x = extension of the spring
Use your data to calculate the spring constant.
You will use this spring constant later in the lab. Write down the tick mark on the spring constant slider associated with this spring constant.
Part 2: Period of Oscillations
The period of an oscillation is the time it takes the mass to make a complete cycle. This part of the lab is going to explore what physical parameters determine the period of an oscillating mass.
The three physical parameters to explore are:
Mass m (the size of the object oscillating on the spring)
Spring Constant k (related to how stiff the spring is)
Amplitude A (the max distance away from equilibrium the mass reaches)
Gravity g
__________ (2 points for completing)
Complete the predictions below with increase, decrease, or stay the same
If the mass of the object increases, the period will _____________________
If the spring constant increases, the period will ________________________
If the amplitude of the object increases, the period will _________________
If the gravity increases, the period will _________________
Slide the “Gravity” and “Dampening Slides” to zero
Check the “Displacement”, “Mass Equilibrium” and “Period Trace”
Place the known mass on the spring and start with an amplitude of about 30 cm.
You will see a trace of the period as the object goes through a full cycle. Gradually change the mass of the object and answer the following questions
¬¬¬_______ (2 points)
As the mass increases, the period of the object _________________
As the mass decreases, the period of the object _________________
_______ (2 points)
As the spring constant increases, the period of the object _________________
As the spring constant decreases, the period of the object _________________
_______ (2 points)
As the amplitude increases, the period of the object _________________
As the amplitude decreases, the period of the object _________________
_______ (2 points)
As gravity increases, the period of the object _________________
As gravity decreases, the period of the object _________________
_______ (5 points) The equation for period of a mass spring system is T=2π/ω=2π√(m/k). Using the spring constant setting from Part 1, choose a mass and measure the period of oscillation. Compare the measured period to the calculated period with a percent error.
Include an example calculation
Measured Period (s) Calculated Period (s) Percent Error
Part 3: Energy of Oscillations
This part of the lab will cover the concept of conservation of energy for an oscillating mass on a spring. Specifically students will create a Kinetic Energy versus time graph, a Potential Energy versus time graph, and a Total Energy versus time graph.
Slide the “Gravity” and “Dampening Slides” to zero
Check the “Mass Equilibrium” and “Period Trace”
You choose your own initial conditions for mass, amplitude, and spring constant
In order to create an energy graph, we need a way to quantity the bar energy graph. To do so, we will use the ruler. But instead of cm, we will say the units are Joules. For example, in the picture below at this instant in time…
E_total=60 J,KE=46 J,PE_elas=14 J
____________(12 points) Plot and insert a graph of E_total,KE,and PE_elas for one period. Choose enough data points to make the shape the of the graph clear.
____________(8 points) Using your graphs, answer the following questions
At what location of the object is KE a maximum?
At what location of the object is KE zero?
At what location of the object is PE_elas a maximum?
At what location of the object is PE_elas zero?
Part 4: Dampening
This part of the lab will explore what happens to the energy graphs when dampening is included in the simulation.
Slide the “Gravity” to zero
Slide the “Dampening” to the lowest non-zero setting
___________(8 points) Write down your observations and explanations for what happens to the kinetic energy, elastic potential energy, thermal energy, and total energy
___________(2 points) Mechanical energy is defined as the kinetic energy plus the potential energy
ME=KE+PE_elas
Draw what the mechanical energy versus time graph would look like from the beginning of the motion when the object is located at its maximum amplitude to when the dampening has brought the object to a stop.
Lab 2: Standing Waves
(This lesson is designed for a student working remotely.)
Learning Goals
Observe how waves are reflected from a boundary
Observe how waves interfere on a string
Calculate the wave speed of a transverse wave on a string
Predict and test frequencies for a multiple standing waves.
Develop your understanding:
Open the simulation and play with the controls for the different set up options
This controls the type of wave sent down the left side of the string
This controls the boundary on the right side of the string
These are the controls. They will be different depending on what type of wave is sent down the string. Dampening and Tension in the string are the only two constants for all wave types. It is also where you can access measuring tools such as a ruler.
Part 1: Reflected Waves at Boundaries
Consider a single wave pulse shot down the string. At the boundary the string is fixed, nailed down, it doesn’t move. This is called an open boundary.
________ (1 completion point) Predict what the wave will look like when it is reflected.
In the upper left, choose “Pulse”
In the upper right, choose “Fixed End”
Slide “Dampening” to “None”
Slide “Tension” to “High”
Click the green pulse button on the oscillator
¬¬¬¬________(2 points) Describe the reflected wave. If you have the draw tool available, draw it on the picture provided.
________(2 points) Describe the reflected wave when it hits the left side of the string where the pulse was started.
Consider a single wave pulse shot down the string. At the boundary the string is free to move. This is called a closed boundary.
________ (1 completion point) Predict what the wave will look like when it is reflected.
In the upper left, click “Restart”
In the upper left, choose “Pulse”
In the upper right, choose “Loose End”
Slide “Dampening” to “None”
Slide “Tension” to “High”
Click the green pulse button on the oscillator
¬¬¬¬________(2 points) Describe the reflected wave. If you have the draw tool available, draw it on the picture provided.
________(2 points) Describe the reflected wave when it hits the left side of the string where the pulse was started.
Part 2: Wave Superposition
What is going to happen when we fire down more than one pulse? When two pulses are in the same location at the same time, they interfere. That is they add together by superposition. Typically wave interference is divided into two types: constructive and destructive.
________ (1 completion point) Predict what will happen as more waves are pulsed on the string.
In the upper left, click “Restart”
In the upper left, choose “Pulse”
In the upper right, choose “Fixed End”
Slide “Dampening” to “None”
Slide “Tension” to “High”
Click the green pulse button on the oscillator to send down one wave pulse
Gradually increase the number of pulses on the wave. Do not quickly click the button 5 times. Allow time to observe what happens as the number of wave pulses increases.
________(2 points) How would you describe the type of interference with two waves?
________(2 points) How would you describe the type of interference with many waves?
Part 3: Calculating Wave Speed
In Part 3, students will calculate the wave speed based on the tension and amplitude of a wave. Wave speed will be calculated two ways.
The first will be calculating the time it takes for the crest of the wave to travels from one position (Fig. 1) to another position (Fig. 2). Students will use the ruler and timer to calculate the speed of the wave as it travels.
The second will be by calculating the wave speed with the equation v=λf. The wavelength is the distance is takes for the wave to repeat itself (Fig 3). The frequency is controlled by the control panel.
Figure 3
Part 3a: Tension and Wave Speed
In the upper left, click “Restart”
In the upper left, choose “Oscillate”
In the upper right, choose “No End”
Slide “Dampening” to “None”
Select an Amplitude and Frequency. You may want to play with different values until you observe a wave you like.
Use the ruler and timer to collect data (table is provided in step h). A step by step method is not provided for how data is to be collected. Students will need to work with the simulation to develop the step by step process.
_____________ (6 points) Include screen shots below similar to figures 1 through 3 with the ruler and timer as an example of your data collection. Label which tension the screenshot corresponds to.
_____________ (10 points) Complete the data table below
Amplitude (m) Frequency (Hz)
Tension Distance
(m) Time
(s) v_meas
(m/s) λ
(m) f
(Hz) v_calc
(m/s) % difference
Low
Medium
High
_____________ (2 points) Make a statement on how wave speed depends on tension.
Part 3b: Amplitude and Wave Speed
In the upper left, click “Restart”
In the upper left, choose “Oscillate”
In the upper right, choose “No End”
Slide “Dampening” to “None”
Select a Tension and Frequency. You may want to play with different values until you observe a wave you like.
Use the ruler and timer to collect data (table is provided in step h). A step by step method is not provided for how data is to be collected. Students will need to work with the simulation to develop the step by step process.
_____________ (10 points) Complete the data table below. Students need to choose a range of amplitudes to test
Tension Frequency (Hz)
Amplitude
(m) Distance
(m) Time
(s) v_meas
(m/s) λ
(m) f
(Hz) v_calc
(m/s) % difference
_____________ (2 points) Make a statement on how wave speed depends on amplitude.
Part 4: Understanding Standing Waves
Most waves on a string will interfere to create a chaotic pattern. There are only a few select frequencies that will create waves that only have constructive interference. The wave has to perfectly fit between the endpoints (or end nodes)
Let’s draw a series of standing waves with a table of information
m = the number harmonic (this is called the mode or harmonic)
λ = wavelength in terms of L
# nodes (n) = number of locations with Amplitude = 0
# antinodes (a) = number of locations with Amplitude = max
Here is m=1
m = 1
λ= 2L
n = 2
a = 1
m = 2
λ=
n = 3
a = 2
_______(1 point) Here is m=2, complete the table on the right
_______(5 points) Draw the fourth harmonic and complete the table on the right
m =
λ=
n =
a =
_____(1 point) Does the number harmonic match with the number of nodes or antiodes?
_____(5 points) Write down the m = 1, m = 2, and m = 4 harmonic wavelengths. Generate a formula to predict the wavelength λ in terms of L and m for any harmonic? Student should end up with a formula with m,L,and 2. Test it out for the 3 examples above.
λ_1= λ_m=
λ_2=
λ_4=
_____(5 points) The control panel only lets the user control the frequency of the generator. Therefore, we have to solve for the frequency of the m^th standing wave. Using the result from b) and the wave speed equation v=λf, solve for the frequency for any harmonic m. Students should end up with an equation with the variables v,m,L and the number 2
Part 5: Creating Standing Waves
In the upper left, click “Restart”
In the upper left, choose “Oscillate”
In the upper right, choose “Fixed End”
Slide “Dampening” to “None”
Set the Amplitude to 0.01 cm
From Part 3a) or 3b) choose a combination of Tension and Frequency to create a standing wave.
_____________ (9 points) Create 3 different standing waves using the results from Part 4: c). Insert screenshots of the standing waves. You may have to let the simulation run for a minute or two. If a pattern does not appear, the frequency is incorrect.
_____________(4 points) What is the highest harmonic you could fit on the string?
Lab 3: Bending Light
This lesson is designed for a student working remotely
When a light ray strikes a smooth interface separating two transparent materials (like air, glass, or water), the wave is partly reflected and partly refracted (or transmitted) into the second material. For an example of this, imagine you are outside looking at a restaurant window. You can probably see both the inside of the restaurant (from the refracted light) and some of the street behind you (from the reflected light). Similarly, a person in the restaurant can see some of the street scene, as well as a reflection of the other people in the restaurant. This lab will explore the relationship between how light is reflected and refracted.
Learning Goals
Understand the relationship between how light is reflected and refracted
Describe what happens to light when it shines on a medium.
Explain light direction changes at the interface between two media and what determines the angle.
Describe the effect of varying wavelength on the angle of refraction.
Explain why a prism creates a rainbow.
Apply Snell’s law to a laser beam incident on the interface between media.
Part 1: Qualitatively How is Light Bent?
Explore the More Tools module and become acquainted with how the simulation functions and how to use the tools. Ignore the Time measuring tool. Make some general observations. Note: The Wave function did not work on Firefox when I tried it.
Select “Ray” in the top left. This part will focus on the ray model of light and what happens at the interface (where the air meets the water)
______(5 points) The dashed black line where the light strikes the water is called the normal line. Light tends to either get closer (bend towards or the angle decreases) the normal line or go further away (bend away or the angle increases) from the normal line. Complete the table below with different combinations of air, water and glass to come up with a general conclusion. Be sure to test with several incident angles and colors.
Index of Refraction for Incident Ray (n_top) Index of Refraction for Transmitted Ray (n_bot) Does the n value increase or decrease? How does Light Bend?
______(4 points) What determines how the light bends? Write a summary description of what happens to light when it goes from one medium to another. Use the following vocabulary words in your summary: index of refraction, incident angle, reflected angle, and refracted angle, color, etc.
______(1 point) Does light bend toward or away from the normal when the index of refraction is the same for the incident ray and transmitted ray? Test it out for multiple materials
______(2 points) Total internal reflection is a state when light is not longer transmitted but only reflected. By adjusting the index of refraction for the incident and transmitted ray, determine the relationship (greater than, equal to, less than) of n_incident and n_transmitted that can result in total internal reflection. Provide a screenshot of one example of total internal reflection.
Part 2: Relating How Light is Bent to Wave Speed.
Consider your own motion while you walk through air or swim in water. There is a difference in the resistance to your motion through air as opposed to water. If swimming in air was possible, it would be easier to swim in air than water. The same happens for light. The wave speed of light will be different for different mediums. In fact, the index of material is calculated by the ratio of the speed of light c to the speed of light in the material.
n=c/v
Select the “wave” option in the top left. This part will focus on the wave model of light. Every color band represents a wave crest (top of the wave). Every dark band represents a wave trough (bottom of the wave)
Record the following steps in the table provided
Select a color you want to observe
______(1 point) Use the “Speed” tool to measure the speed of the light in air, glass, and water. Provide a screenshot of one measurement.
______(1 point) Calculate the index of refraction and compare it to the index of refraction in the simulation. Provide a sample calculation.
______(1 point) Use the measure tool to calculate the index of refraction for the Mystery A and Mystery B materials. Provide a sample calculation
______(6 points)
Color
Material Wave Speed (m/s) n_calculated % error
Air
Glass
Water
Mystery A
Mystery B
Part 3: Law of Reflection
Light is always reflected at the interface. This section will relate the angle of incidence to the angle of reflection. Below is an example of how the data will be measured. Notice how the 0° is located at the top of the protractor. The protractor will measure the incident and reflected angles from the normal line.
Select “Ray” in the top left
Insert the protractor to take measurements
Use the “Intensity” tool to measure the intensity of the reflected light.
______(5 points) Select 5 angles to measure the incident angle, transmitted angle, and reflected ray intensity and record data in the table provided.
Incident Angle (degrees) Reflected Angle (degrees) Reflected Ray Intensity
______(1 point) Insert a screenshot of one of your data points.
______(1 point) Comment on the relationship between the incident and reflected angle.
______(1 point) Comment on how the reflected ray intensity changes with the incident angle.
Part 4: Snell’s Law
Snell’s Law (n_1 sin〖θ_1 〗=n_2 sin〖θ_2 〗) is the relationship between the incident ray and transmitted ray. It includes both the index of refraction and the angle. The subscript 1 and 2 represent materials 1 and 2. If you want to associate 1 with incident and 2 with transmitted, you may. Remember that the angles are still always measured from the normal line.
______(9 points) Use Snell’s Law to predict the angle of refraction for 3 scenarios.
Place your data in the table below
Provide a calculation for each scenario
Provide a screenshot for each scenario
Scenario n_1 θ_1 n_2 Calculated θ_2 Measured θ_2 % error
1
2
3
______(6 points) Use Snell’s Law to calculate the index of refraction for material Mystery A and Mystery B
Place your data in the table below
Provide a calculation for each material
Provide a screenshot for each material
Compare the measured value of the index of refractions for the mystery materials to what was calculated in Part 2.
Material n_1 θ_1 θ_2 Calculated n_2 Measured n_2 % Difference
Mystery A
Mystery B
Part 5: Total Internal Reflection
Part 1: f) discussed total internal reflection qualitatively. Quantitatively, total internal reflection occurs after the incident ray has reached its critical angle. The critical angle is the angle of incidence that results in an angle of transmission that is 90°. That is the transmitted ray is just skimming the interface surface and you do not observe any more transmission.
______(6 points) Use Snell’s Law to calculate the critical angle for 2 scenarios
Place your data in the table below
Provide a calculation for each material
Provide a screenshot for each material
n_1 n_2 Calculated θ_2 Measured θ_2 % Error