A 2 kg ball, moving to the right at a velocity of 2 m/s on a frictionless table, has an elastic head-on collision with a stationary 5 kg ball. What is the total kinetic energy before the collision? What is the total kinetic energy after the collision?

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Unit IV problem solving worksheet

This assignment will allow you to demonstrate the following objectives:

  1. Apply the concept of momentum conservations to daily life.

4.1 Relate impulse-momentum theorem to Newton’s second law.

4.2 Show the relationship between linear momentum conservation and Newton’s third law.

4.3 Apply momentum conservation to rotational kinematics.

 

5.Identify the total mechanical energy conservation.

5.1 Interpret total kinetic energy conservation in elastic collision.

 

Instructions: Solve the problems below. Each question is worth 10 points. You must show your work with as much detail as possible. Answer the questions directly in this template. Before doing so, it is highly recommended that you thoroughly review the Unit IV Lesson in the study guide.

 

  1. A boy exerts an average force of 100 N on a shopping cart for 0.5 seconds. What is the impulse? Hint: See Sample Question 1 in the Unit IV Lesson.

 

  1. In an effort to participate in a science fair, Alice designed a toy car engine that can generate a total impulse of 100 Ns. The mass of the toy car is 2 kg. What is the final speed that her toy car attains when moved from rest? Ignore frictional forces. Hint: See Sample Question 2 in the Unit IV Lesson.

 

  1. Curious George observed an interesting event in an international toy exhibition. Two toy cars were moving forward in a monorail. Toy car #1, weighing 10 kg, was ahead of toy car #2, weighing 20 kg, in the beginning, but they collided and joined together. The initial velocity of toy car #1 is 10 m/s and that of toy car #2 is 20 m/s. What is the final velocity of both of these cars after they are connected? Assume that there is no friction in this system. Hint: See Sample Question 3 in the Unit IV Lesson and Example 5 on page 181 to 182 in the textbook.

 

  1. In an isolated system, a 2kg ball with an initial velocity of 3 m/s hits a 5 kg ball that is initially at rest. What is the total kinetic energy before the collision? If the total kinetic energy after the collision is the same as that before the collision, is this an elastic collision or inelastic collision? Hint: See Sample Question 4 in the Unit IV Lesson and Example 7 on page 185 in the textbook.

 

  1. Consider an inelastic collision between a green ball and an orange ball. The mass m of the green ball is 1 kg and the mass M of the orange ball is 3 kg. Before the collision, the orange ball was at rest and the initial velocity of the green ball was 5 m/s. After the collision, they were combined as one object as shown in the following. What is the final velocity V? Hint: Use the momentum conservation law.

 

  1. A wheel spins counterclockwise through three revolutions for 2 seconds. What is the average angular velocity of the wheel?   Hint: See Example 3 on page 204 in the textbook.

 

  1. The fan blades of a jet engine in an airplane rotate counterclockwise with an initial angular velocity of 100 rad/s. As the airplane takes off, the angular velocity of the blades reaches 400 rad/s in 10 seconds. Calculate the average angular acceleration. Hint: See Example 4 on page 205 in the textbook.

 

  1. A new car takes 10 seconds to accelerate from rest to 30 m/s. Its mass is 1500 kg. What is the net average force that acts on the car? Hint: Use the equation (7.3) on page 176 in the textbook.

 

  1. A 2 kg ball, moving to the right at a velocity of 2 m/s on a frictionless table, has an elastic head-on collision with a stationary 5 kg ball. What is the total kinetic energy before the collision? What is the total kinetic energy after the collision?

 

  1. Starting from rest, Amy and Jane push off against each other on the smooth frictionless ice rink. The mass of Amy is 50 kg and that of Jane is 60 kg. Amy moves to the right (positive direction) with a velocity of 3 m/s. What is the recoil velocity of Jane?   Hint: See Example 6 on page 182 in the textbook.

Describe all possible flight hazards that could be encountered by the pilot of a small general aviation (Skybrary) aircraft during take-off, landing, and along the flight path between two small airports in the Rocky Mountains of Colorado during clear, windy weather conditions.

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Module 4 A&S Question

In this activity, you will take your learning to the next level by applying and synthesizing (A&S) concepts explored in this module. Instructions Choose one question option (1 or 2) to answer. Place your chosen question and the formulated answer* within a separate document.
Integrate information from the module lessons to develop and support your answers.
Your answer will be scored on completeness, correctness, clarity, and conciseness, and the degree of synthesis and application of the related concepts, not on how many words they contain. More is not necessarily better! This is NOT an essay assignment.
Save your assignment using a naming convention that includes your first and last name and the activity number (or description). Do not add punctuation or special characters.
This activity is due by the last day of the module.
Read through all sections before proceeding to the next page, and refer back whenever necessary.

Question Option 1
Question Option 2
Describe all possible flight hazards that could be encountered by the pilot of a small general aviation (Skybrary) aircraft during take-off, landing, and along the flight path between two small airports in the Rocky Mountains of Colorado during clear, windy weather conditions.

Hint: Review Weather and Flying in Module 4 Lesson 2.
Proceed to the Question Option 2 section.

 

In this activity, you will take your learning to the next level by applying and synthesizing (A&S) concepts explored in this module. Instructions Choose one question option (1 or 2) to answer. Place your chosen question and the formulated answer* within a separate document.
Integrate information from the module lessons to develop and support your answers.
Your answer will be scored on completeness, correctness, clarity, and conciseness, and the degree of synthesis and application of the related concepts, not on how many words they contain. More is not necessarily better! This is NOT an essay assignment.
Save your assignment using a naming convention that includes your first and last name and the activity number (or description). Do not add punctuation or special characters.
This activity is due by the last day of the module.
Read through all sections before proceeding to the next page, and refer back whenever necessary.

Question Option 1
Question Option 2

Describe all possible flight hazards that could be encountered by the pilot of a small general aviation (Skybrary) rr aircraft that:
A. takes off or lands during the time frame of the passage of a cold front at the airfield

B. flies directly through a cold front

Hint: Review Weather and Flying in Module 4 Lesson 2.

look at a simulated wave on a string – a transverse wave. Set the frequency of the wave and then measure the wavelength and speed. Use these to try to answer the question: “Does wave speed really equal frequency times wavelength?”.

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Physics Lab: Waves on a String

Introduction

Waves are a familiar part of everyday life. You have probably seen water waves and waves on a string. You hear sound waves and see light waves.

Waves have a wavelength, λ, a frequency, f, and a speed, v. These three quantities are related by:

v = fλ

In this lab you will look at a simulated wave on a string – a transverse wave. You will set the frequency of the wave and then measure the wavelength and speed. We will use these to try to answer the question: “Does wave speed really equal frequency times wavelength?”.

Write your own problem that requires you to add vectors that are parallel to each other and going in the same direction. Solve the problem and include both the algebraic solution and a diagram for your solution. Write your own vector problem that requires you to add vectors that are parallel to each other but going in opposite directions. Solve the problem and include both the algebraic solution and a diagram for your solution.

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Physics

Part A:

1. A homing pigeon flies 25 m/s when there is no wind. On the day of the worldwide homing pigeon races, you get a favorable tail wind of 7 m/s. How fast does your homing pigeon fly?

2. On the way home, your pigeon must fly against the 7 m/s wind. How fast does the pigeon fly on the way home?

3. You are boating up a river. Your boat provides enough power to go 15 m/s on still water but the river has a current of 11 m/s in the opposite direction. How fast are you going in relation to the land?
4. An airplane takes off going 85 km/hour at an angle of 35 degrees above the horizon. Break this vector into x and y components.

5. Add the following vectors and find the resultant vector—both magnitude and direction. Vector 1: 23 Newtons @ 17 degrees and Vector 2: 57 Newtons @ 9 degrees.

Step1: Sketch each of the vectors and label with speed and direction.

Step 2: Find the 0-components of each vector and add them together. Step 3: Find the y-component of each vector and add them together. Step 4: Use the new x and y components to create a new right angled triangle in which the hypotenuse is the Resultant vector.

Step : Use the pythagorean theorem to find the magnitude of the resultant vector. Step 6: Use SOH-CAH-TOA to find the angle of the resultant vector. Step 7: Write your final answer in one complete statement that inlcudes both magnitude and direction.

 

Part B:

Real World Problems (15 points each) The map below shows the flight path for someone traveling from Washington DC and passing above Indianapolis, Indiana; Lincoln, Nebraska (hometown of the University of Nebraska High School!) and landing in San Francisco. For the sake of clarity, we will assume that the plane is flying due West the entire trip. The plane’s engines put out enough power to fly at 545 mph if there is no wind (but they could put out more if needed).

Washington, D.C. No,th Carolina Vhst Virginia OkIlhOTA klunsas South N. Meaxo Cato.. Mississipq – Alab Lourvana Georgia
1. Show all your work including both a diagram and algebraic solution. When the plane crosses over Indianapolis, the wind speed at flight altitude is 45 mph @ 45 degrees South of East. If the plane does not make any corrective action, the wind will both slow it down and knock it off course. Calculate the new velocity vector (both magnitude and direction) for the plane?

2. Show all your work including both a diagram and algebraic solution. When crossing over Lincoln, Nebraska, the plane runs into a headwind of 25 mph due East. If the plane does not make any corrective action, it will slow down and arrive in San Francisco late. How fast would the plane have to fly in order to maintain its intended speed and not lose any time?

3. Show all your work including both a diagram and algebraic solution. When the plane crosses the border to Utah, it encounters a cross wind of 15 mph 5 degrees West of North. What speed and direction must the plane head in to keep going due West at 545 mph?

 

Part C:

1. Write your own problem that requires you to add vectors that are parallel to each other and going in the same direction. Solve the problem and include both the algebraic solution and a diagram for your solution.

2. Write your own vector problem that requires you to add vectors that are parallel to each other but going in opposite directions. Solve the problem and include both the algebraic solution and a diagram for your solution.

3. Write your own vector problem that requires you to break at least two vectors into components, add them together and find the resultant vector. Solve the problem and include both the algebraic solution and a diagram for your solution.

Of the four main forces acting on aircraft, name the one that can be altered, in the process of proper flight planning, to reduce the impact of high density altitude flying conditions. Explain why a combination of high, hot, and humid conditions creates high density altitude flying conditions.

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Density Altitude

Now, synthesize and apply the information you reviewed on the concept of density altitude to address the following:

1. Using terms that an average person could easily understand and by applying related concepts and terms, present a practical definition of density altitude.

2. Fill in the blank: If the value of density altitude is relatively high, the air density is relatively

3. Of the four main forces acting on aircraft, name the ones that are reduced by high density altitude flying conditions.

4. Of the four main forces acting on aircraft, name the one that can be altered, in the process of proper flight planning, to reduce the impact of high density altitude flying conditions.

5. Explain why a combination of high, hot, and humid conditions creates high density altitude flying conditions. Your explanation should involve a discussion of how air temperature, pressure, humidity affect air density and thus the density altitude. 6. Apply your understanding of density altitude to answer the following scenario-based question:

A general aviation pilot in training is scheduled to do repeated touch and go’s (landing and taking off again without coming to a full stop) in a Cessna 172 at Bob Adams Field in Steamboat Springs, Colorado (elevation 6882 feet) on a mid-afternoon in early August. Explain why the aircraft’s ability to take off, land, and climb during the touch and go’s will be negatively impacted. Include an image within your document that visualizes the explanation.

Submission Instructions

  • • Formulate your answers within a document. DO NOT include the question statements.
  • • Integrate information from the resources to develop and support your answers.
  • • Each answer will be scored on the completeness, correctness, clarity, conciseness, and the degree of synthesis and application of the related concepts, not on how many words the answer contains. More is not necessarily better!
  • • Save your assignment using a naming convention that includes your first and last name and the activity number (or description). Do not add punctuation or special characters.

Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the vertical position and velocity of the ball. Enter your values in your data table. Identify the point on each graph where the ball was at the top of its path. Determine the time, vertical position, and velocity. Enter your values in your data table.

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Lab Energy of the Tossed Ball

Procedure:

  1. Measure and record the mass of the ball you plan to use in this experiment.
  2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it.
  3. Hold the ball directly above the Motion Detector. Have your partner click to begin data collection. Toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector catch the ball before it hits the detector.

Note:  Use two hands, be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it moves vertically above the detector. Verify that the position vs. time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. When you have good data on the screen, proceed to the Analysis section.

  1. Click on the Examine button, , and move the mouse across the position or velocity graphs of the motion of the ball to answer these questions.
  • Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the vertical position and velocity of the ball. Enter your values in your data table. (after release)
  • Identify the point on each graph where the ball was at the top of its path. Determine the time, vertical position, and velocity. Enter your values in your data table. (top path)
  • Find a time where the ball was moving downward, just before it was caught. Measure and record the vertical position and velocity of the ball at that time. (before catch)
  • Collect two more times on the way up and on the way down for a total of seven data points.
  • For each of the seven points in your data table, calculate:

Gravitational Potential Energy: Ug =mgy  ;          Kinetic Energy: K = 1/2mv2 ; and

Total Energy: TE = Ug+KE

Conduct your own physical experiment using the scientific method. Research the scientific method and give a 1 page written description of each step.

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Week 2

Conduct your own physical experiment using the scientific method. Research the scientific method and give a 1 page written description of each step. You will then document your process with photos and/or video. Results will also be shared by uploading such media (or the links) of your process to the discussion board in this module. Save and submit the media in this exercise along with your 1-2 page written description.

What’s in common and what are the differences among different parts of the EM spectrum? What makes them harmful or not harmful to human body? Which part do wifi, cellphone, or microwave radiation belong to? Are they harmful to human body?

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Does wifi, cellphone or microwave radiation affect our health? and Why?

Along with this document, there are 5 research papers included in the Final Project folder on Blackboard that you are required to read and refer to when writing your own research paper. More specifically, these 5 research papers should serve the following purposes as you prepare, draft and edit your final research paper:
As your literature review sources. “A literature review surveys books, scholarly articles, and any other sources relevant to a particular issue, area of research, or theory, and by so doing, provides a description, summary, and critical evaluation of these works in relation to the research problem being investigated. Literature reviews are designed to provide an overview of sources you have explored while researching a particular topic and to demonstrate to your readers how your research fits within a larger field of study.” (https://libguides.usc.edu/writingguide/literaturereview)
As templates or sample papers as you write your own;
As your references (you can read more research papers and list them as your references besides these 5 given, but not less).

NOTE that we have 0 tolerance for plagiarism in this course. You may cite the papers but are not allowed to copy and paste sentences or paragraphs into your own paper.

In this paper, you are also required to give a clear introduction to Electromagnetic Waves (EM waves), including:
Different parts of the EM spectrum
What’s in common and what are the differences among different parts of the EM spectrum?
What makes them harmful or not harmful to human body?
Which part do wifi, cellphone, or microwave radiation belong to? Are they harmful to human body? If yes, what makes them harmful? If no, please explain. What evidence do you have to support your claim/hypothesis?

What was the ultraviolet catastrophe? (1 point) Explain what is meant by quantized light. Explain why observations of blackbody radiation provide evidence for the quantization of light. Write 2 – 3 sentences explaining how quantum mechanics describes light and matter. How does the interference pattern of electrons support the idea that matter can behave as a wave?

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Unit test

Question 1: Nuclear Structure (10 points)
a. Protons and neutrons make up the nucleus of an atom. Write 3 – 4 sentences describing the electrostatic force between each pair of particles (proton-proton, proton-neutron, neutron-neutron) and the strong nuclear force between each pair of particles. (5 points)

  1. Write 3 – 4 sentences predicting the changes in electrostatic force, strong nuclear force, and the stability of a nucleus if the number of neutrons is increased. (3 points)
  2. Write 2 – 3 sentences describing Einstein’s explanation for why the total starting mass is greater than the total ending mass after a nuclear reaction. (2 points)

 

Question 2: Radioactivity (7 points)
a. Write 2 – 3 sentences describing the mass number, charge, and penetrating ability of alpha particles. (3 points)

 

  1. Write the symbol for the nucleus that completes the nuclear equation:   (2 points)
  2. Write the symbol for the nucleus that completes the nuclear equation:   (2 points)

 

Question 3: Half-life (4 points)
a. The half-life of iron-61 is 6 minutes. If a sample originally contains 8 g of the isotope, how much remains after 18 minutes? Write 2 – 3 sentences explaining your reasoning. (2 points)

 

  1. The ratio of carbon-14 to nitrogen-14 in an artifact is 1:3. In other words, ¼ of the original carbon-14 remains. Given that the half-life of carbon-14 is 5730 years, how old is the artifact? Write 2 – 3 sentences explaining your reasoning. (2 points)

 

Question 4: Fission and Fusion (9 points)

a. Write 2 – 3 sentences describing what happens to a uranium nucleus during nuclear fission. (2 points)

 

  1. Write 2 – 3 sentences explaining why nuclear fusion cannot be used in power plants, yet can still be the original source of the electric energy used in homes. (4 points)
  2. Write 3 – 4 sentences evaluating the use of nuclear fission to generate electric energy. Provide at least one point in favor of and two points against using fission. (3 points)

 

Question 5: Quantization (8 points)

a. What is a blackbody radiator? (1 point)

 

  1. What was the ultraviolet catastrophe? (1 point)
  2. Explain what is meant by quantized light. (1 point)
  3. Explain why observations of blackbody radiation provide evidence for the quantization of light. (2 points)
  4. Write 2 – 3 sentences explaining how quantum mechanics describes light and matter. How does the interference pattern of electrons support the idea that matter can behave as a wave? (3 points)

 

Question 6: Relativity (6 points)

a. How does the speed of light in a vacuum change when observed from two different frames of reference? (2 points)

 

  1. Which frames of reference can be studied using special relativity? (2 points)
  2. A stationary observer measures an object that is traveling at nearly the speed of light. Describe how the length of this object compares with the length of an identical object that the observer is holding. Write 1 or 2 sentences explaining your reasoning. (2 points)

 

Question 7: Cosmology (6 points)

a. Write 2 – 3 sentences identifying the most widely accepted theory for the formation of the universe. In your description, be sure to include how the universe began and what is happening to the size of the universe today. (2 points)

 

  1. Write 2 – 3 sentences explaining redshift and what it led scientists to conclude about the universe. (2 points)
  2. Scientists have proposed three models of the universe: flat, open, and closed. Each of these describes a different future for the universe. Write 2 – 3 sentences identifying the model that is most widely accepted and describing the future of the universe according to that model. (2 points)

How does the total mass before a nuclear reaction compare with the total mass after a nuclear reaction? How does Einstein’s equation address this difference? Complete the table below to review the main types of radiation.

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Modern Physics

Question 1 (8 points)

a. Fill in the blanks in the following paragraph to correctly describe the nucleus of an atom. (2 points)                        and                         are the two types of nucleons that make up a nucleus. The                         force exists between                         in the nucleus because of their charge. Because it is repulsive, this force tends to make a nucleus                         . However, the                         force acts between protons, between neutrons, and between protons and neutrons. This force helps to make a nucleus                         , because it is always attractive.

 

  1. How does the total mass before a nuclear reaction compare with the total mass after a nuclear reaction? How does Einstein’s equation address this difference? (1 point)

 

  1. Complete the table below to review the main types of radiation. (2 points)
Radiation Symbol Mass
number		 Charge       

Penetrating

      

ability
Alpha particle        
Negative beta
particle (electron)		        
Positive beta
particle (positron)		        
Gamma ray        
  1. Write the symbol for the nucleus that completes each nuclear equation. (1 point each)

Question 2 (4 points)

a. What happens to a radioactive isotope over the course of 1 half-life? (1 point)

 

  1. How does the half-life of an isotope relate to the stability of its nucleus? (1 point)
  2. Complete the following table to show how to determine the amounts of parent and daughter nuclei and the time passed with each half-life. (2 points)
Number of
half-lives		 Fraction of
original
isotope
remaining		 Fraction of
original
isotope
changed to
daughter
isotope		 Ratio of
parent
isotope to
daughter
isotope		       

      

Time

      

      
0 1 0 1:0 0
1     20 days
2   1:3  
3        

Question 3 (3 points)

a. Review nuclear fission and nuclear fusion by placing X’s in the appropriate boxes. (2 points)

  Nuclear
fission		 Nuclear
fusion
Converts matter into energy    
Occurs in nuclear power plants    
Splits a nucleus    
Produces radioactive waste    
Uses hydrogen    
Occurs in the Sun    
Uses uranium    
Creates limited fuel    
Creates abundant fuel    
  1. What conditions are required for nuclear fusion that prevent it from being used to generate electric energy? (1 point)

 

Question 4 (4 points)

a. In quantum mechanics, what does wave-particle duality describe? (1 point)

 

  1. What does the term quantized light mean? (1 point)

 

  1. Fill in the blanks in the following paragraph to correctly identify phenomena that help provide evidence for the particle nature of light. (2 points)

    A(n) _______________ absorbs energy and then emits electromagnetic radiation based on its _______________. Classical physics predicted that at a high enough temperature, _______________ light would be emitted. Instead, white light was emitted, resulting in the ultraviolet _______________. The photoelectric effect occurs when light shining on a metal creates a(n) _______________. However, only light of a certain minimum _______________ causes electrons to flow. Gas atoms excited by an electric current emit bands of colors of light in a(n) _______________. Each narrow band of light is associated with _______________ of a specific energy.

Question 5 (3 points)

a. In what frames of reference does special relativity apply? (1 point)

 

  1. In what frames of reference must general relativity be used? (1 point)

 

  1. Describe what happens to time and length at speeds close to the speed of light. (1 point)

 

Question 6 (3 points)

a. Describe the big bang theory. (1 point)

 

  1. Match each model of the universe with the future it predicts. (1 point)

    A. Closed
    B. Flat
    C. Open

    _____ The universe will stop expanding but will not collapse.

    _____ The universe will continue to expand forever.

    _____ The universe will stop expanding and then collapse back to its point of origin.

c. Match each observation to the conclusion it supports in the big bang theory. (1 point)

A. Light from other galaxies is shifted toward the red end of the spectrum.
B. Cosmic background radiation appears uniform across the sky.
C. The amount of helium in the universe matches predictions.

_____ Nucleosynthesis of light elements occurred shortly after the expansion of the original ball of energy.

_____ The universe is expanding.

_____ The universe began from a single point.