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# Week 6 short assignments 1220

Mizzou

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This 14 page Bundle was uploaded by Dragon Note on Thursday March 24, 2016. The Bundle belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 257 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.

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Date Created: 03/24/16

Short Assignment By 3/2/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 3/2/2016 Due: 11:00am on Wednesday, March 2, 2016 To understand how points are awarded, read therading Policy for this assignment. Problem 23.43 A rectangular coil 23 by 39 has 140 turns. This coil produces a maximum emf of 61 when it rotates with an angular speed of 180 in a magnetic field of strength . Part A Find the value of . Express your answer using two significant figures. ANSWER: = 27 Correct Transformers Learning Goal: To understand the concepts underlying the operation of transformers. One of the advantages of alternating current (ac) over direct current (dc) is the ease with which voltage levels can be increased or decreased. Such a need is always present due to the practical requirements of energy distribution. On the one hand, the voltage supplied to end users must be reasonably low for safety reasons (depending on the country, that voltage may be 110 volts, 220 volts, or some other value of that order). On the other hand, the voltage used in transmitting electric energy must be as high as possible to minimize losses in the transmission lines. A device that uses the principle of electromagnetic induction to increase or decrease the voltage by a certain factor is called a transformer. The main components of a transformer are two coils (windings) that are electrically insulated from each other. The coils are wrapped around the same core, which is typically made of a material with a very large relative permeability to ensure maximum mutual inductance. One coil, called the primary coil, is connected to a voltage source; the other, the secondary coil, delivers the power. The alternating current in the primary coil induces the changing magnetic flux in the core that creates the emf in the secondary coil. The magnitude of the emf induced in the secondary coil can be controlled by the design of the transformer. The key factor is the number of turns in each coil. Consider an ideal transformer, that is, one in which the coils have no ohmic resistance and the magnetic flux is the same for each turn of both the primary and secondary coils. If the number of turns in the primary coil is and that in the secondary coil is , then the emfs induced in the coils can be written as , and therefore, . If the coils have zero resistance (as we have assumed), then for each coil the terminal voltage will be equal to the induced emf. We can then write . Note that if , then . In this case we have a step-up transformer. Conversely, if , then , and we are dealing with a step-down transformer. Without energy losses, the power in the primary and secondary coils is the same: . Short Assignment By 3/2/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... In answering the questions below, consider the transformer ideal unless otherwise noted. Part A The primary coil of a transformer contains 100 turns; the secondary has 200 turns. The primary coil is connected to a size-AA battery that supplies a constant voltage of 1.5 volts. What voltage would be measured across the secondary coil? ANSWER: Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/29/2016 Due: 11:00am on Monday, February 29, 2016 To understand how points are awarded, read theding Policy for this assignment. Motional EMF in a Conducting Rod In the figure, a conducting rod of length \texttip{L}{L} = 32.0 {\rm cm} moves in a magnetic field \texttip{\vec{B}}{\vec{B}} of magnitude 0.430 {\rm T} directed into the plane of the figure. The rod moves with speed \texttip{v}{v} = 6.00 {\rm m/s} in the direction shown. Part A When the charges in the rod are in equilibrium, which point, a or b, has an excess of positive charge? ANSWER: a b Correct The force \texttip{\vec{F}}{F_vec} on a charge \texttip{q}{q} moving with velocity \texttip{\vec{v}}{v_vec} in a magnetic field \texttip{\vec{B}}{B_vec} is given by \vec{F}=q \vec{v} \times \vec{B}. The magnitude of the force is given by F=\vert q \vert vB\sin\phi where \vert q \vert is the magnitude of the charge, \texttip{v}{v} and \texttip{B}{B} are the magnitudes of the velocity and magnetic field and \texttip{\phi }{phi} is the angle measured from the direction of \texttip{\vec{v}}{v_vec} to the direction of \texttip{\vec{B}}{B_vec}. When \texttip{\vec{v}}{v_vec} is perpendicular to \texttip{\vec{B}}{B_vec}, \phi = 90^{\circ} and \sin \phi = 1. You can use the right-hand rule to determine the direction in which the electrons in the rod are forced to move. Part B What is the direction of the electric field in the rod? Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: from a to b from b to a Correct Keep in mind that the electric field exists due to the separation of the positive and negative charges caused by the magnetic force. Also, recall that electric field lines start on positive charges and end on negative charges. Part C When the charges in the rod are in equilibrium, what is the magnitude \texttip{E}{E} of the electric field within the rod? Express your answer in volts per meter to at least three significant figures. Hint 1. How to approach the problem Use the fact that at equilibrium, the electric and magnetic forces on a test charge in the rod must be equal and opposite to each other. Hint 2. Formula for the force on a charge moving in a magnetic field The force \texttip{\vec{F}}{F_vec} on a charge \texttip{q}{q} moving with velocity \texttip{\vec{v}}{v_vec} in a magnetic field \texttip{\vec{B}}{B_vec} is given by \vec{F}=q \vec{v} \times \vec{B}. The magnitude of the force is given by F=\vert q \vert vB\sin\phi where \vert q \vert is the magnitude of the charge, \texttip{v}{v} and \texttip{B}{B} are the magnitudes of the velocity and magnetic field and \texttip{\phi }{phi} is the angle measured from the direction of \texttip{\vec{v}} {v_vec} to the direction of \texttip{\vec{B}}{B_vec}. When \texttip{\vec{v}}{v_vec} is perpendicular to \texttip{\vec{B}}{B_vec}, \phi = 90^{\circ} and \sin \phi = 1. Hint 3. Formula for the force acting on a charge in an electric field The force \texttip{\vec{F}}{F_vec} on a charge \texttip{q}{q} in an electric field \texttip{\vec{E}}{E_vec} is \vec{F} = q \vec{E}. Hint 4. Units Recall that the SI unit of a magnetic field is the tesla, velocity is measured in meters per second, and electric field is measured in volts per meter. ANSWER: \texttip{E}{E} = 2.58 \rm V/m Correct Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part D Which point, a or b, has a higher potential? Hint 1. Electric field and potential Recall that a positive charge in an electric field tends to move from a higher potential to a lower potential, just as objects in a gravitational field fall from greater to lower height. ANSWER: a b Points a and b have the same potential. Correct Part E What is the magnitude \texttip{V_{ba}}{V_ba} of the potential difference between the ends of the rod? Express your answer in volts to at least three significant figures. Hint 1. Formula for the potential difference The formula for the potential difference \texttip{V}{V} caused by a uniform electric field \texttip{E}{E} over a length \ell is V = E\ell. ANSWER: \texttip{V_{ba}}{V_ba} = 0.826 \rm V Correct Part F What is the magnitude \cal E of the motional emf induced in the rod? Express your answer in volts to at least three significant figures. Hint 1. Definition of motional emf Motional emf is the potential difference generated by moving a conducting rod through a magnetic field. The motional emf is measured between the two ends of the rod. ANSWER: Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... \cal E = 0.826 \rm V Correct Induced Current in a Metal Loop Conceptual Question For each of the actions depicted below, a magnet and/or metal loop moves with velocity \texttip{\vec{v}}{v_vec} (\texttip{\vec{v}}{v_vec} is constant and has the same magnitude in all parts). Determine whether a current is induced in the metal loop. If so, indicate the direction of the current in the loop, either clockwise or counterclockwise when seen from the right of the loop. The axis of the magnet is lined up with the center of the loop. Part A For the action depicted in the figure, indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). Hint 1. Magnetic flux Magnetic flux is the product of the component of magnetic field perpendicular to a given area and the area itself. Conceptually, it is proportional to the number of magnetic field lines passing through a given area. Hint 2. Induction and changing flux Whenever magnetic flux through an area changes, an electromotive force (emf) is created around the area. This induced emf has a direction such that if a conductor is present, current will flow to create a secondary magnetic field that opposes the change in the original magnetic flux. Basically, the induced current will "try" to maintain the initial value of the magnetic flux. Hint 3. How to find the direction of the magnetic field produced by a loop To determine the direction of the magnetic field produced by a current in a loop, use the right-hand rule: curl the fingers of your right hand in the direction of the current; your thumb will point in the direction of the magnetic field produced by the loop. Hint 4. Find the initial magnetic field through the loop Does the magnetic field that passes through the loop due to the magnet point to the left or the right? Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: right left Hint 5. Find the change in magnetic flux As the magnet is brought toward the loop, does the magnetic flux through the loop increase, decrease, or stay the same? ANSWER: increases decreases stays the same Hint 6. Induced magnetic field Since the magnetic flux is increasing with the field directed to the left, current will flow in the loop to create a magnetic field oriented to the right to oppose this increase in flux. Now, to create a field directed to the right, determine the direction in which current must flow through the loop. ANSWER: clockwise counterclockwise zero Correct Part B For the action depicted in the figure, indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Find the initial magnetic field through the loop Does the magnetic field that passes through the loop due to the magnet point to the left or the right? ANSWER: right left Hint 2. Find the change in magnetic flux As the magnet is moved away from the loop, does the magnetic flux through the loop increase, decrease, or stay the same? ANSWER: increases decreases stays the same Hint 3. Induced magnetic field Since the magnetic flux is decreasing, with the field directed to the right, current will flow in the loop to create a magnetic field oriented to the right to replace this decrease in flux. Now, to create a field directed to the right, determine the direction in which current must flow through the loop. ANSWER: clockwise counterclockwise zero Correct Part C For the action depicted in the figure, indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Find the initial magnetic field through the loop Does the magnetic field that passes through the loop due to the magnet point to the left or the right? ANSWER: right left Hint 2. Find the change in magnetic flux Does the magnetic flux through the loop increase, decrease, or stay the same? ANSWER: increases decreases stays the same ANSWER: clockwise counterclockwise zero Correct Part D For the action depicted in the figure, indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: clockwise counterclockwise zero Correct Part E For the action depicted in the figure, indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). Hint 1. Find the change in magnetic flux As the loop is moved away from the magnet, does the magnetic flux through the loop increase, decrease, or stay the same? ANSWER: increases decreases stays the same ANSWER: Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/29/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... clockwise counterclockwise zero Correct Score Summary: Your score on this assignment is 100%. You received 3 out of a possible total of 3 points. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment by 3/4/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment by 3/4/2016 Due: 11:00am on Friday, March 4, 2016 To understand how points are awarded, read therading Policy for this assignment. Geometry and Reflections Learning Goal: To learn and practice the geometry skills necessary for complex reflection setups. The law of reflection has the very simple form , where is the angle between the normal and the incident ray and is the angle between the normal and the reflected ray. Although the law itself is easy to use, many realistic situations involve successive reflections from multiple surfaces. The law of reflection does not become any more complicated in such cases, but the geometry of the rays does become complicated. Consider the case of light shining onto a mirror, which is attached to another mirror at some angle , as shown in the figure . In this problem, we will find the angle at which light leaves the arrangement of two mirrors. Part A If the light strikes the first mirror at an an, what is the reflected angle ? Express your answer in terms of . ANSWER: = Correct Part B Now, find the angle (shown in the new figure ) in terms of . You can easily find in terms of , then just substitute your expression from Part A. Express your answer in degrees in terms of . Notice that the degrees symbol is already listed for you, so just use the number "23" to indicate 23 degrees. Short Assignment by 3/4/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Relationship between and and are complementary angles. ANSWER: = Correct Part C Now, find the angle shown in the figure in terms of and . Express your answer in degrees in terms of and . Hint 1. Angles in a triangle The sum of the angles in a triangle is . ANSWER: = Correct Short Assignment by 3/4/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part D Find the angle shown in the figure in terms of and . You will need to assume that , as it appears in the picture. Express your answer in degrees in terms of and . Hint 1. Relationship between and and are complementary angles. Hint 2. How to find in terms of You can find in terms of by using the law of reflection. ANSWER: = Correct Virtually any reflection problem, no matter how intimidating it may seem, can be broken down into simple parts by considering each individual reflection carefully. Score Summary: Your score on this assignment is 100%. You received 1 out of a possible total of 1 points.

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