HW01 - Concepts of Motion

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 1/21 HW01 - Concepts of Motion Due: 11:59pm on Tuesday, September 20, 2022 To understand how points are awarded, read the Grading Policy for this assignment. Problem 1.2 - Enhanced - with Hints and Feedback You are watching a jet ski race. A racer speeds up from rest to 70 in just a few seconds, then continues at a constant speed. Part A Select the correct basic motion diagram of the jet ski, using images from the video, from 10 before reaching top speed until 10 afterward. Hint 1. How to approach the problem Recall the definition of a motion diagram and how to determine velocities from the length of displacement vectors in the diagram. Displacement vectors are increasing in length if an object is speeding up, and decreasing in length if an object is slowing down. ANSWER: Correct Problem 1.6 - Enhanced - with Hints and Feedback You drop a soccer ball from your third-story balcony. Part A

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 2/21 Use the particle model to draw a motion diagram showing the ball's position and average velocity vectors from the time you release the ball until the instant it touches the ground. Hint 1. How to approach the problem Determine how the speed of the soccer ball changes in time. Then recall that in a motion diagram displacement vectors are increasing in length if an object is speeding up, and decreasing in length if an object is slowing down. ANSWER: Correct

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 3/21 Motion of Two Rockets Learning Goal: To learn to use images of an object in motion to determine position, velocity, and acceleration. Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a time-exposure image where a stroboscope has illuminated the rockets at the uniform time intervals indicated. Part A At what time(s) do the rockets have the same velocity? Hint 1. How to determine the velocity The diagram shows position, not velocity. You can't find instantaneous velocity from this diagram, but you can determine the average velocity between two times and : . Note that no position values are given in the diagram; you will need to estimate these based on the distance between successive positions of the rockets. ANSWER: Correct at time only at time only at times and at some instant in time between and at no time shown in the figure

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 4/21 Part B At what time(s) do the rockets have the same x position? ANSWER: Correct Part C At what time(s) do the two rockets have the same acceleration? Hint 1. How to determine the acceleration The velocity is related to the spacing between images in a stroboscopic diagram. Since acceleration is the rate at which velocity changes, the acceleration is related to the how much this spacing changes from one interval to the next. ANSWER: Correct Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________. ANSWER: at time only at time only at times and at some instant in time between and at no time shown in the figure at time only at time only at times and at some instant in time between and at no time shown in the figure

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 5/21 Correct Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________. ANSWER: Correct Part F At what time(s) is rocket A ahead of rocket B? Hint 1. Use the diagram You can answer this question by looking at the diagram and identifying the time(s) when rocket A is to the right of rocket B. ANSWER: Correct Problem 1.52 - Enhanced - with Hints and Feedback and nonzero acceleration velocity position time and nonzero acceleration velocity position time before only after only before and after between and at no time(s) shown in the figure

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 6/21 Part A Select the correct motion diagram with added acceleration vector. A partial motion diagram is shown in the figure above. Hint 1. How to approach the problem Use the definition of a motion diagram and the spacing of the object's positions to determine whether the object is speeding up or slowing down for each part of the path. Recall in which of these cases the acceleration and velocity vectors point in the same and in opposite directions. ANSWER:

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 7/21 Correct Part B Select the correct physics problem for which this is the correct motion diagram. Hint 1. How to approach the problem Determine whether the object accelerates or decelerates for each part of the path. Recall that the magnitude of the velocity vector corresponds to its length.

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 8/21 ANSWER: Correct Part C Select the correct pictorial representation for your problem. Hint 1. How to approach the problem Use the directions of accelerations you determined in part A and the values of the initial and final speeds from the previous part. ANSWER: Jeremy has perfected the art of steady acceleration and deceleration. From a speed of 60 he brakes his car to rest in 10 with a constant magnitude of deceleration. Then he turns into an adjoining street. Starting from rest, Jeremy accelerates with exactly the same magnitude as his earlier magnitude of deceleration and reaches the same speed of 60 over the same distance in exactly the same time. Find the car's acceleration or deceleration. Jeremy has perfected the art of steady acceleration and deceleration. From a speed of 10 he increases the speed of his car to 60 with a constant magnitude of acceleration. Then he turns into an adjoining street. Starting from 60 , Jeremy continues the journey with exactly the same speed. Find the car's acceleration or deceleration. Jeremy has perfected the art of steady acceleration and deceleration. From a speed of 10 he increases the speed of his car to 60 with a constant magnitude of acceleration. Then he turns into an adjoining street. Starting from 60 , Jeremy slows down with exactly the same magnitude as his earlier magnitude of acceleration and reaches the same speed of 10 over the same distance in exactly the same time. Find the car's acceleration or deceleration. Jeremy has perfected the art of steady acceleration and deceleration. From a speed of 60 he brakes his car to rest in 10 with a constant magnitude of deceleration. Then he turns into an adjoining street. Starting from rest, Jeremy continues the journey and reaches the speed of 30 over the same distance in exactly the same time. Find the car's acceleration or deceleration.

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 9/21 Known Find Known Find Known Find Known Find

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 10/21 Correct What x vs. t Graphs Can Tell You To describe the motion of a particle along a straight line, it is often convenient to draw a graph representing the position of the particle at different times. This type of graph is usually referred to as an vs. graph. To draw such a graph, choose an axis system in which time is plotted on the horizontal axis and position on the vertical axis. Then, indicate the values of at various times . Mathematically, this corresponds to plotting the variable as a function of . An example of a graph of position as a function of time for a particle traveling along a straight line is shown below. Note that an vs. graph like this does not represent the path of the particle in space. Now let's study the graph shown in the figure in more detail. Refer to this graph to answer Parts A, B, and C. Part A What is the overall displacement of the particle? Express your answer in meters. Hint 1. Definition of displacement The displacement of the particle is given by the difference between the initial position at and the position at . In symbols, . Hint 2. How to read an x vs. t graph Remember that in an vs. graph, time is plotted on the horizontal axis and position on the vertical axis. For example, in the plot shown in the figure, at . ANSWER: Correct In this example, the magnitude of the displacement is also equal to the total distance traveled by the particle (30 ). = 30

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 11/21 Part B What is the average velocity of the particle over the time interval ? Express your answer in meters per second. Hint 1. Definition and graphical interpretation of average velocity The average velocity of a particle that undergoes a displacement along a straight line in a time interval is defined as . In an vs. graph, then, the average velocity equals the slope of the line connecting the initial and final positions. Hint 2. Slope of a line The slope of a line from point A, with coordinates , to point B, with coordinates , is equal to the "rise" over the "run," or . ANSWER: Correct The average velocity of a particle between two positions is equal to the slope of the line connecting the two corresponding points in an vs. graph. Part C What is the instantaneous velocity of the particle at ? Express your answer in meters per second. Hint 1. Graphical interpretation of instantaneous velocity The velocity of a particle at any given instant of time or at any point in its path is called instantaneous velocity. In an vs. graph of the particle's motion, you can determine the instantaneous velocity of the particle at any point in the curve. The instantaneous velocity at any point is equal to the slope of the line tangent to the curve at that point. ANSWER: Correct The instantaneous velocity of a particle at any point on its vs. graph is the slope of the line tangent to the curve at that point. Since in the case at hand the curve is a straight line, the tangent line is the curve itself. Physically, this means that the instantaneous velocity of the particle is constant over the entire time interval of motion. This is true for any motion where distance increases linearly with time. = 0.600 = 0.600

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 12/21 Another common graphical representation of motion along a straight line is the vs. graph , that is, the graph of (instantaneous) velocity as a function of time. In this graph, time is plotted on the horizontal axis and velocity on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only one nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion. Part D Which of the graphs shown is the correct vs. plot for the motion described in the previous parts? Hint 1. How to approach the problem Recall your results found in the previous parts, namely the fact that the instantaneous velocity of the particle is constant. Which graph represents a variable that always has the same constant value at any time? ANSWER: Correct Whenever a particle moves with constant nonzero velocity, its vs. graph is a straight line with a nonzero slope, and its vs. curve is a horizontal line. Part E Graph A Graph B Graph C Graph D

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 13/21 Shown in the figure is the vs. curve selected in the previous part. What is the area of the shaded region under the curve? Express your answer in meters. Hint 1. How to approach the problem The shaded region under the vs. curve is a rectangle whose horizontal and vertical sides lie on the axis and the axis, respectively. Since the area of a rectangle is the product of its sides, in this case the area of the shaded region is the product of a certain quantity expressed in seconds and another quantity expressed in meters per second. The area itself, then, will be in meters. ANSWER: Correct Compare this result with what you found in Part A. As you can see, the area of the region under the vs. curve equals the overall displacement of the particle. This is true for any velocity curve and any time interval: The area of the region that extends over a time interval under the vs. curve is always equal to the displacement over . Dimensions of Physical Quantities Learning Goal: To introduce the idea of physical dimensions and to learn how to find them. Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension -- length . Part A In classical mechanics there are three base dimensions. Length is one of them. What are the other two? Hint 1. MKS system The current system of units is called the International System (abbreviated SI from the French Système International). In the past this system was called the mks system for its base units: meter, kilogram, and second. What are the dimensions of these quantities? = 30

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 14/21 ANSWER: Correct There are three dimensions used in mechanics: length ( ), mass ( ), and time ( ). A combination of these three dimensions suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity), it always obeys an equation that permits it to be expressed in terms of the units used for these three dimensions. One then derives a unit to measure the new physical quantity from that equation, and often its unit is given a special name. Such new dimensions are called derived dimensions and the units they are measured in are called derived units. For example, area has derived dimensions . (Note that "dimensions of variable " is symbolized as .) You can find these dimensions by looking at the formula for the area of a square , where is the length of a side of the square. Clearly . Plugging this into the equation gives . Part B Find the dimensions of volume. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for volume You have likely learned many formulas for the volume of various shapes in geometry. Any of these equations will give you the dimensions for volume. You can find the dimensions most easily from the volume of a cube , where is the length of the edge of the cube. ANSWER: Correct Part C Find the dimensions of speed. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for speed Speed is defined in terms of distance and time as . acceleration and mass acceleration and time acceleration and charge mass and time mass and charge time and charge =

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 15/21 Therefore, . Hint 2. Familiar units for speed You are probably accustomed to hearing speeds in miles per hour (or possibly kilometers per hour). Think about the dimensions for miles and hours. If you divide the dimensions for miles by the dimensions for hours, you will have the dimensions for speed. ANSWER: Correct The dimensions of a quantity are not changed by addition or subtraction of another quantity with the same dimensions. This means that , which comes from subtracting two speeds, has the same dimensions as speed. It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both quantities to the same set of units before you actually compute the sum. You can use this rule to check your answers to any physics problem you work. If the answer involves the sum or difference of two quantities with different dimensions, then it must be incorrect. This rule also ensures that the dimensions of any physical quantity will never involve sums or differences of the base dimensions. (As in the preceeding example, is not a valid dimension for a physical quantitiy.) A valid dimension will only involve the product or ratio of powers of the base dimensions (e.g. ). Part D Find the dimensions of acceleration. Express your answer as powers of length ( ), mass ( ), and time ( ). Hint 1. Equation for acceleration In physics, acceleration is defined as the change in velocity in a certain time. This is shown by the equation . The is a symbol that means "the change in." ANSWER: Correct Consistency of Units In physics, every physical quantity is measured with respect to a unit . Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics. Part A = =

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 16/21 Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation , where is the magnitude of the gravitational attraction on either body, and are the masses of the bodies, is the distance between them, and is the gravitational constant. In SI units, the units of force are , the units of mass are , and the units of distance are . For this equation to have consistent units, the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER: Correct Part B One consequence of Einstein's theory of special relativity is that mass is a form of energy. This mass-energy relationship is perhaps the most famous of all physics equations: , where is mass, is the speed of the light, and is the energy. In SI units, the units of speed are . For the preceding equation to have consistent units (the same units on both sides of the equation), the units of must be which of the following? Hint 1. How to approach the problem To solve this problem, we start with the equation . For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for . ANSWER:

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 17/21 Correct To solve the types of problems typified by these examples, we start with the given equation. For each symbol whose units we know, we replace the symbol with those units. For example, we replace with . We now solve this equation for the units of the unknown variable. Converting Units: The Magic of 1 Learning Goal: To learn how to change units of physical quantities. Quantities with physical dimensions like length or time must be measured with respect to a unit , a standard for quantities with this dimension. For example, length can be measured in units of meters or feet, time in seconds or years, and velocity in meters per second. When solving problems in physics, it is necessary to use a consistent system of units such as the International System (abbreviated SI, for the French Système International) or the more cumbersome English system. In the SI system, which is the preferred system in physics, mass is measured in kilograms, time in seconds, and length in meters. The necessity of using consistent units in a problem often forces you to convert some units from the given system into the system that you want to use for the problem. The key to unit conversion is to multiply (or divide) by a ratio of different units that equals one. This works because multiplying any quantity by one doesn't change it. To illustrate with length, if you know that , you can write . To convert inches to centimeters, you can multiply the number of inches times this fraction (since it equals one), cancel the inch unit in the denominator with the inch unit in the given length, and come up with a value for the length in centimeters. To convert centimeters to inches, you can divide by this ratio and cancel the centimeters. For all parts, notice that the units are already written after the answer box; don't try to write them in your answer also. Part A How many centimeters are there in a length 60.2 ? Express your answer in centimeters to three significant figures. ANSWER: Correct 153

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 18/21 Sometimes you will need to change units twice to get the final unit that you want. Suppose that you know how to convert from centimeters to inches and from inches to feet. By doing both, in order, you can convert from centimeters to feet. Part B Suppose that a particular artillery piece has a range = 9440 . Find its range in miles. Use the facts that and . Express your answer in miles to three significant figures. Hint 1. Convert yards to feet The first step in this problem is to convert from yards to feet, because you know how to then convert feet into miles. Convert 9440 into feet. Use . Express your answer in feet to three significant figures. ANSWER: ANSWER: Correct Often speed is given in miles per hour ( ), but in physics you will almost always work in SI units. Therefore, you must convert to meters per second ( ). Part C What is the speed of a car going in SI units? Notice that you will need to change from miles to meters and from hours to seconds. You can do each conversion separately. Use the facts that and . Express your answer in meters per second to four significant figures. Hint 1. Convert miles to meters In converting into meters per second, you will need to multiply by . When you do this, the miles will cancel to leave you with a value in meters per hour. You can then finish the conversion. What is in meters per hour? Express your answer in meters per hour to four significant figures. ANSWER: 2.83×10 4 = 5.36 = 1609

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10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 19/21 Hint 2. Convert hours to seconds Which of the following would you multiply by to convert it into meters per second ( )? ANSWER: ANSWER: Correct Notice that by equating the two values for , you get . It might be valuable to remember this, as you may frequently need to convert from miles per hour into more useful SI units. By remembering this relationship in the future, you can reduce this task to a single conversion. Problem 1.25 - Enhanced - with Hints and Feedback Convert the following to basic SI units: Part A 79 Express your answer with the appropriate units. Hint 1. How to approach the problem Use the table of frequently used conversions between SI units and English units. You can use the number of inches in one meter or the number of centimeters in one inch. Do not forget to convert centimeters to meters. ANSWER: Correct Part B 4.05×10 6 = 0.4469 = 2.0

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 20/21 Express your answer with the appropriate units. Hint 1. How to approach the problem Convert years to days first. Continue to convert to smaller units gradually. ANSWER: Correct Part C 69 Express your answer with the appropriate units. Hint 1. How to approach the problem You have to convert both feet and days to basic SI units. To convert feet, you can use inches or miles in an intermediate calculation. ANSWER: Correct Part D 5.7×10 4 Express your answer with the appropriate units. Hint 1. How to approach the problem Use the table of frequently used conversions between SI units and English units to convert miles to basic SI units. Note that the conversion factor in the table is for miles. How should you change it to get miles squared? ANSWER: Correct Problem 1.57 - Enhanced - with Hints and Feedback = 1.28×10 14 = 2.4×10 −4 = 1.5×10 11

10/3/22, 1:49 PM HW01 - Concepts of Motion https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072418 21/21 The quantity called mass density is the mass per unit volume of a substance. What are the mass densities in basic SI units of the following objects? Part A A 227 solid with a mass of 0.0179 . Express your answer with the appropriate units and with the appropriate number of significant figures. Hint 1. How to approach the problem Derive the expression for the calculation of mass density from its definition in the introduction. Convert the given quantities to SI units to get the answer in basic SI units. ANSWER: Correct Part B 97 of liquid with a mass of 79 . Express your answer with the appropriate units and with the appropriate number of significant figures. Hint 1. How to approach the problem Derive the expression for the calculation of mass density from its definition in the introduction. Convert the given quantities to SI units to get the answer in basic SI units. ANSWER: Correct Score Summary: Your score on this assignment is 97.2%. You received 11.67 out of a possible total of 12 points. = 78.9 = 810

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