A very long straight wire carries 3.0 A current. A small, 4.0 cm by 5.0 cm square wire loop carrying 2.0 A current is placed next to a long wire such that the 4.0 cm long side is parallel to it and one side is 2.0 cm away. What is the magnitude of the force experienced by the square loop?

A very long straight wire carries 3.0 A current. A small, 4.0 cm by 5.0 cm square wire loop carrying 2.0 A current is placed next to a long wire such that the 4.0 cm long side is parallel to it and one side is 2.0 cm away. What is the magnitude of the force experienced by the square loop?

info@checkyourstudy.com A very long straight wire carries 3.0 A current. … Read More...
The frame below supports the IEA sign that weight 600 Ib. The sign is connected to the frame by cables at joints E and D . (a) Determine the support reactions at A and F . (b) Determine all the force acting on member CEF.

The frame below supports the IEA sign that weight 600 Ib. The sign is connected to the frame by cables at joints E and D . (a) Determine the support reactions at A and F . (b) Determine all the force acting on member CEF.

The frame below supports the IEA sign that weight 600 … Read More...
For the 50-kg package, find (a) the force in cable OC and the force in each spring OA and spring OB. Then find (b) the stretch in each spring. Both springs have an unstretched length of 2 m and a spring constant of k = 500 N/m. (Hint: Fsp = k(x))

For the 50-kg package, find (a) the force in cable OC and the force in each spring OA and spring OB. Then find (b) the stretch in each spring. Both springs have an unstretched length of 2 m and a spring constant of k = 500 N/m. (Hint: Fsp = k(x))

 
Chapter 03 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Components and Structure of the Atom Learning Goal: To specify the basic components of the atom and describe our modern conception of its structure. Part A The atom consists of three types of subatomic particles: protons, neutrons, and electrons. The electron is by far the lightest of the three, while the much heavier proton and neutron have masses very similar to each other. Two of the types of particles carry an electrical charge, while the third is neutral. Label the subatomic particles and appropriate charges by their relative locations. Identify the subatomic particles by dragging the appropriate labels to their respective targets. Hint 1. Which subatomic particles carry electric charge? Of the three subatomic particles, two carry equal but opposite charges. Select the two correct statements that match the subatomic particle with the appropriate charge. Check all that apply. ANSWER: Hint 2. Which subatomic particles are not found in the nucleus? Protons and electrons carry equal but opposite charges. Atomic nuclei are positively charged and are not composed of negatively charged particles. Which types of subatomic particles cannot be located within the nucleus? Select any that apply. ANSWER: ANSWER: The electron carries a positive charge. The proton carries a positive charge. The neutron carries a positive charge. The proton carries a negative charge. The electron carries a negative charge. The neutron carries a negative charge. neutrons electrons protons Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 14 5/21/2014 8:02 PM Correct This image represents the classical model of the atom proposed by Niels Bohr. Although this model has changed slightly as the result of modern scientific discoveries, it does help in understanding the relative locations of the subatomic particles in the atom. Notice that the protons and neutrons are bound in the nucleus, while the electrons are located in the space surrounding the nucleus. Part B Of the three types of subatomic particles, only neutrons do not carry charge. Protons carry a positive charge, and electrons carry a negative charge. Protons and neutrons are bound in the nucleus, while electrons orbit the nucleus. When the number of each type of subatomic particle in an atom changes, the characteristics defining the atom also change. Match the appropriate phrases with the type of subatomic particle that completes the defining characteristic. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. Hint 1. What type of subatomic particle is lost or gained when an ion forms? For any atom of a given element to go from being neutral ( ) to being ionized ( ), what type of subatomic particle must be lost or gained? Select all that apply. ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 14 5/21/2014 8:02 PM Hint 2. What type of subatomic particle identifies an element? When identifying the element classification of a particular atom, which type of subatomic particle is used? ANSWER: ANSWER: Correct The number of each type of subatomic particle plays an important role in the characteristics of the atom. The general element classification (hydrogen, carbon, oxygen, etc.) is governed by the number of protons in the nucleus. If the number of protons changes in an atom, so does the type of element. The electrons are the only type of subatomic particle not in the nucleus. They orbit around the nucleus, bound by the electromagnetic force. When electrons are lost or gained by a neutral atom, the charge balance shifts, resulting in the atom becoming an ion. Ions can be either positive when electrons are lost or negative when electrons are gained. Part C In the classical view of the atom, Bohr pictured electrons orbiting the positively charged nucleus similar to how the planets orbit the Sun. While this picture was not entirely correct, it provides a good framework in which to make calculations about the energies of electrons. Different from the predictions of Newtonian mechanics, which allows any energy to be possible, Bohr described the electron orbits (now called orbitals) as having specific energies. Rank the following electron energy states according to their electron energies. Rank from highest to lowest energies. Hint 1. What are the definitions of orbital, ground state, and excited state? Define orbital, ground state, and excited state. loss of an electron loss of a proton loss of a neutron gain of an electron gain of a proton gain of a neutron electron proton neutron Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 14 5/21/2014 8:02 PM Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. ANSWER: Hint 2. How does the state change when an electron absorbs energy? Electrons can absorb energy either from light radiation or from collisions with other atoms. If an electron is in the first excited energy state and absorbs enough energy to go to the next higher energy state, into what state will the electron transition? ANSWER: ANSWER: the ground state the second excited state the third excited state Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 14 5/21/2014 8:02 PM Correct Excited states refer to the energy of an electron. The higher the state, the higher the energy of the electron. The electron energies of each orbital are fixed. The energy required for an electron to transition between each orbital is an exact value, corresponding to the difference between the orbital energies. Any energy more or less than these precise differences cannot be used by the electron to make a transition; only the energies equal to the full values can induce a transition. Part D The Bohr model accounted for most of the general characteristics of the atom. However, the modern model based on quantum mechanics explains that, although the energy of each orbital is fixed, the orbital radius is actually an average distance. The result is a “cloud” where the electron is most likely to be located. The following is an image of an atom of hydrogen, consisting of one proton, zero neutrons, and one electron. When an electron is excited to different energy levels, the radius from the nucleus also changes. Rank the following electron energy states according to the average distance of the electron from the nucleus. Rank from largest to smallest distances. Hint 1. What is the relationship between electron orbital distance and electron energy? Rank the following general electron energies from largest to smallest electron orbital distances. Rank from largest to smallest orbital distances. ANSWER: ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 14 5/21/2014 8:02 PM Correct Excited states refer to the energy state of an electron. The higher the state, the higher the energy and the greater the distance of the electron from the nucleus. Due to the attractive force between the negatively charged electron and the positively charged nucleus, the electron requires greater energies to overcome this attraction and achieve orbits at greater distances. Concept Review: The pH Scale Can you classify solutions as acidic, neutral, or basic? Part A Decide whether each label describes a solution that is acidic, neutral, or basic, and then drag it into the appropriate bin. ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 14 5/21/2014 8:02 PM Correct Activity: Carbohydrates Click here to complete this activity. Then answer the questions. Part A Glycogen is _____. ANSWER: Correct Animals store energy in the form of glycogen. a polysaccharide found in animals a source of saturated fat a polysaccharide found in plant cell walls the form in which plants store sugars a transport protein that carries oxygen Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 14 5/21/2014 8:02 PM Part B glucose + glucose —> _____ by _____. ANSWER: Correct Maltose is the disaccharide formed when two glucose molecules are linked by dehydration synthesis. Part C Which of these is a source of lactose? ANSWER: Correct Lactose is the sugar found in milk. Part D Which of these is a polysaccharide? ANSWER: Correct Cellulose is a carbohydrate composed of many monomers. Part E _____ is the most abundant organic compound on Earth. ANSWER: maltose + water … dehydration synthesis lactose + water … hydrolysis starch + water … dehydration synthesis sucrose + water … dehydration synthesis cellulose + water … hydrolysis potatoes sugar beets sugar cane starch milk sucrose lactose glucose galactose cellulose Cellulose Lactose Starch Glucose Glycogen Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 14 5/21/2014 8:02 PM Correct Cellulose, a component of plant cell walls, is the most abundant organic compound found on earth. Activity: Protein Structure Click here to complete this activity. Then answer the questions. Part A Proteins are polymers of _____. ANSWER: Correct Proteins are polymers of amino acids. Part B What type of bond joins the monomers in a protein’s primary structure? ANSWER: Correct The amino acids of a protein are linked by peptide bonds. Part C Which of these illustrates the secondary structure of a protein? ANSWER: nucleotides CH2O units glycerol hydrocarbons amino acids ionic hydrogen hydrophobic S—S peptide Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 14 5/21/2014 8:02 PM Correct Alpha helices and beta pleated sheets are characteristic of a protein’s secondary structure. Part D The secondary structure of a protein results from _____. ANSWER: Correct Electronegative oxygen and nitrogen atoms leave hydrogen atoms with partial positive charges. Part E Tertiary structure is NOT directly dependent on _____. ANSWER: bonds between sulfur atoms peptide bonds hydrogen bonds hydrophobic interactions ionic bonds hydrophobic interactions ionic bonds hydrogen bonds peptide bonds bonds between sulfur atoms Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 10 of 14 5/21/2014 8:02 PM Correct Peptide bonds link together the amino acids of a protein’s primary structure. Activity: Lipids Click here to complete this activity. Then answer the questions. Part A Which of these is NOT a lipid? ANSWER: Correct RNA is a nucleic acid Part B This figure is an example of a(n) _____. ANSWER: Correct The fatty acid tails lack double bonds. steroids phospholipid RNA cholesterol wax steroid unsaturated fat nucleic acid protein saturated fat Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 11 of 14 5/21/2014 8:02 PM Part C Which of these is a phospholipid? ANSWER: Correct Phospholipids are composed of a phosphate group, a glycerol, and fatty acids. Part D Which of these is rich in unsaturated fats? ANSWER: Correct Olive oil is a plant oil, and most plant oils are rich in unsaturated fats. Part E beef fat lard butter olive oil a fat that is solid at room temperature Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 12 of 14 5/21/2014 8:02 PM A function of cholesterol that does not harm health is its role _____. ANSWER: Correct Cholesterol is an important component of animal cell membranes. Concept Review: Types of Macromolecules Can you identify characteristics of proteins, nucleic acids, and carbohydrates? Part A Decide whether each label describes proteins, nucleic acids, or carbohydrates, and then drag it into the appropriate bin. ANSWER: Correct Concept Review: Earth’s Interior Layers Can you identify characteristics of Earth’s interior layers? Part A Drag the labels to the appropriate targets. ANSWER: as a component of animal cell membranes in calcium and phosphate metabolism All of cholesterol’s effects cause the body harm. as the most abundant male sex hormone as the primary female sex hormone Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 13 of 14 5/21/2014 8:02 PM Correct Score Summary: Your score on this assignment is 99.6%. You received 31.87 out of a possible total of 32 points. Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 14 of 14 5/21/2014 8:02 PM

Chapter 03 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Components and Structure of the Atom Learning Goal: To specify the basic components of the atom and describe our modern conception of its structure. Part A The atom consists of three types of subatomic particles: protons, neutrons, and electrons. The electron is by far the lightest of the three, while the much heavier proton and neutron have masses very similar to each other. Two of the types of particles carry an electrical charge, while the third is neutral. Label the subatomic particles and appropriate charges by their relative locations. Identify the subatomic particles by dragging the appropriate labels to their respective targets. Hint 1. Which subatomic particles carry electric charge? Of the three subatomic particles, two carry equal but opposite charges. Select the two correct statements that match the subatomic particle with the appropriate charge. Check all that apply. ANSWER: Hint 2. Which subatomic particles are not found in the nucleus? Protons and electrons carry equal but opposite charges. Atomic nuclei are positively charged and are not composed of negatively charged particles. Which types of subatomic particles cannot be located within the nucleus? Select any that apply. ANSWER: ANSWER: The electron carries a positive charge. The proton carries a positive charge. The neutron carries a positive charge. The proton carries a negative charge. The electron carries a negative charge. The neutron carries a negative charge. neutrons electrons protons Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 14 5/21/2014 8:02 PM Correct This image represents the classical model of the atom proposed by Niels Bohr. Although this model has changed slightly as the result of modern scientific discoveries, it does help in understanding the relative locations of the subatomic particles in the atom. Notice that the protons and neutrons are bound in the nucleus, while the electrons are located in the space surrounding the nucleus. Part B Of the three types of subatomic particles, only neutrons do not carry charge. Protons carry a positive charge, and electrons carry a negative charge. Protons and neutrons are bound in the nucleus, while electrons orbit the nucleus. When the number of each type of subatomic particle in an atom changes, the characteristics defining the atom also change. Match the appropriate phrases with the type of subatomic particle that completes the defining characteristic. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. Hint 1. What type of subatomic particle is lost or gained when an ion forms? For any atom of a given element to go from being neutral ( ) to being ionized ( ), what type of subatomic particle must be lost or gained? Select all that apply. ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 14 5/21/2014 8:02 PM Hint 2. What type of subatomic particle identifies an element? When identifying the element classification of a particular atom, which type of subatomic particle is used? ANSWER: ANSWER: Correct The number of each type of subatomic particle plays an important role in the characteristics of the atom. The general element classification (hydrogen, carbon, oxygen, etc.) is governed by the number of protons in the nucleus. If the number of protons changes in an atom, so does the type of element. The electrons are the only type of subatomic particle not in the nucleus. They orbit around the nucleus, bound by the electromagnetic force. When electrons are lost or gained by a neutral atom, the charge balance shifts, resulting in the atom becoming an ion. Ions can be either positive when electrons are lost or negative when electrons are gained. Part C In the classical view of the atom, Bohr pictured electrons orbiting the positively charged nucleus similar to how the planets orbit the Sun. While this picture was not entirely correct, it provides a good framework in which to make calculations about the energies of electrons. Different from the predictions of Newtonian mechanics, which allows any energy to be possible, Bohr described the electron orbits (now called orbitals) as having specific energies. Rank the following electron energy states according to their electron energies. Rank from highest to lowest energies. Hint 1. What are the definitions of orbital, ground state, and excited state? Define orbital, ground state, and excited state. loss of an electron loss of a proton loss of a neutron gain of an electron gain of a proton gain of a neutron electron proton neutron Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 14 5/21/2014 8:02 PM Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. ANSWER: Hint 2. How does the state change when an electron absorbs energy? Electrons can absorb energy either from light radiation or from collisions with other atoms. If an electron is in the first excited energy state and absorbs enough energy to go to the next higher energy state, into what state will the electron transition? ANSWER: ANSWER: the ground state the second excited state the third excited state Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 14 5/21/2014 8:02 PM Correct Excited states refer to the energy of an electron. The higher the state, the higher the energy of the electron. The electron energies of each orbital are fixed. The energy required for an electron to transition between each orbital is an exact value, corresponding to the difference between the orbital energies. Any energy more or less than these precise differences cannot be used by the electron to make a transition; only the energies equal to the full values can induce a transition. Part D The Bohr model accounted for most of the general characteristics of the atom. However, the modern model based on quantum mechanics explains that, although the energy of each orbital is fixed, the orbital radius is actually an average distance. The result is a “cloud” where the electron is most likely to be located. The following is an image of an atom of hydrogen, consisting of one proton, zero neutrons, and one electron. When an electron is excited to different energy levels, the radius from the nucleus also changes. Rank the following electron energy states according to the average distance of the electron from the nucleus. Rank from largest to smallest distances. Hint 1. What is the relationship between electron orbital distance and electron energy? Rank the following general electron energies from largest to smallest electron orbital distances. Rank from largest to smallest orbital distances. ANSWER: ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 14 5/21/2014 8:02 PM Correct Excited states refer to the energy state of an electron. The higher the state, the higher the energy and the greater the distance of the electron from the nucleus. Due to the attractive force between the negatively charged electron and the positively charged nucleus, the electron requires greater energies to overcome this attraction and achieve orbits at greater distances. Concept Review: The pH Scale Can you classify solutions as acidic, neutral, or basic? Part A Decide whether each label describes a solution that is acidic, neutral, or basic, and then drag it into the appropriate bin. ANSWER: Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 14 5/21/2014 8:02 PM Correct Activity: Carbohydrates Click here to complete this activity. Then answer the questions. Part A Glycogen is _____. ANSWER: Correct Animals store energy in the form of glycogen. a polysaccharide found in animals a source of saturated fat a polysaccharide found in plant cell walls the form in which plants store sugars a transport protein that carries oxygen Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 14 5/21/2014 8:02 PM Part B glucose + glucose —> _____ by _____. ANSWER: Correct Maltose is the disaccharide formed when two glucose molecules are linked by dehydration synthesis. Part C Which of these is a source of lactose? ANSWER: Correct Lactose is the sugar found in milk. Part D Which of these is a polysaccharide? ANSWER: Correct Cellulose is a carbohydrate composed of many monomers. Part E _____ is the most abundant organic compound on Earth. ANSWER: maltose + water … dehydration synthesis lactose + water … hydrolysis starch + water … dehydration synthesis sucrose + water … dehydration synthesis cellulose + water … hydrolysis potatoes sugar beets sugar cane starch milk sucrose lactose glucose galactose cellulose Cellulose Lactose Starch Glucose Glycogen Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 14 5/21/2014 8:02 PM Correct Cellulose, a component of plant cell walls, is the most abundant organic compound found on earth. Activity: Protein Structure Click here to complete this activity. Then answer the questions. Part A Proteins are polymers of _____. ANSWER: Correct Proteins are polymers of amino acids. Part B What type of bond joins the monomers in a protein’s primary structure? ANSWER: Correct The amino acids of a protein are linked by peptide bonds. Part C Which of these illustrates the secondary structure of a protein? ANSWER: nucleotides CH2O units glycerol hydrocarbons amino acids ionic hydrogen hydrophobic S—S peptide Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 14 5/21/2014 8:02 PM Correct Alpha helices and beta pleated sheets are characteristic of a protein’s secondary structure. Part D The secondary structure of a protein results from _____. ANSWER: Correct Electronegative oxygen and nitrogen atoms leave hydrogen atoms with partial positive charges. Part E Tertiary structure is NOT directly dependent on _____. ANSWER: bonds between sulfur atoms peptide bonds hydrogen bonds hydrophobic interactions ionic bonds hydrophobic interactions ionic bonds hydrogen bonds peptide bonds bonds between sulfur atoms Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 10 of 14 5/21/2014 8:02 PM Correct Peptide bonds link together the amino acids of a protein’s primary structure. Activity: Lipids Click here to complete this activity. Then answer the questions. Part A Which of these is NOT a lipid? ANSWER: Correct RNA is a nucleic acid Part B This figure is an example of a(n) _____. ANSWER: Correct The fatty acid tails lack double bonds. steroids phospholipid RNA cholesterol wax steroid unsaturated fat nucleic acid protein saturated fat Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 11 of 14 5/21/2014 8:02 PM Part C Which of these is a phospholipid? ANSWER: Correct Phospholipids are composed of a phosphate group, a glycerol, and fatty acids. Part D Which of these is rich in unsaturated fats? ANSWER: Correct Olive oil is a plant oil, and most plant oils are rich in unsaturated fats. Part E beef fat lard butter olive oil a fat that is solid at room temperature Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 12 of 14 5/21/2014 8:02 PM A function of cholesterol that does not harm health is its role _____. ANSWER: Correct Cholesterol is an important component of animal cell membranes. Concept Review: Types of Macromolecules Can you identify characteristics of proteins, nucleic acids, and carbohydrates? Part A Decide whether each label describes proteins, nucleic acids, or carbohydrates, and then drag it into the appropriate bin. ANSWER: Correct Concept Review: Earth’s Interior Layers Can you identify characteristics of Earth’s interior layers? Part A Drag the labels to the appropriate targets. ANSWER: as a component of animal cell membranes in calcium and phosphate metabolism All of cholesterol’s effects cause the body harm. as the most abundant male sex hormone as the primary female sex hormone Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 13 of 14 5/21/2014 8:02 PM Correct Score Summary: Your score on this assignment is 99.6%. You received 31.87 out of a possible total of 32 points. Chapter 03 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 14 of 14 5/21/2014 8:02 PM

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8.[ Book Section 8.2] Two infinitely long parallel wires are separated by a distance of 10cm. If the wires carry 25A in opposite directions, calculate the force on the wires. (Side note: Watch the video for a demo of the forces between shorter wires: https://youtu.be/X4dXXnUMHbQ?t=14m)

8.[ Book Section 8.2] Two infinitely long parallel wires are separated by a distance of 10cm. If the wires carry 25A in opposite directions, calculate the force on the wires. (Side note: Watch the video for a demo of the forces between shorter wires: https://youtu.be/X4dXXnUMHbQ?t=14m)

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

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