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1 1 of 6 9/5/2009 6:13 PM Chapter 1 Homework Due: 9:00am on Tuesday, September 1, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View] 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. 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 or 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 A.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. One consequence of Einstein's theory of special relativity is that mass is a form of energy. This massenergy 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 B.1 How to approach the problem 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. Familiarity with SI units will aid your study of physics and all other sciences. Measurements in SI Units What is the approximate height of the average adult in centimeters? Hint A.1 Converting between feet and centimeters The distance from your elbow to your fingertips is typically about
2 2 of 6 9/5/2009 6:13 PM If you're not familiar with metric units of length, you can use your body to develop intuition for them. The average height of an adult is The distance from elbow to fingertips on the average adult is about 50. Ten (1 ) is about the width of this adult's little finger and 10 is about the width of the average hand. Approximately what is the mass of the average adult in kilograms? Hint B.1 Converting between pounds and kilograms Something that weighs 1 has a mass of about Something that weighs 1 has a mass of about. This is a useful conversion to keep in mind! Learning Goal: To learn how to change units of physical quantities. Converting Units: The Magic of 1 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. How many centimeters are there in a length 625.8? Express your answer in centimeters to three significant figures 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. Suppose that a particular artillery piece has a range = Find its range in miles. Use the facts that and. Hint B.1 Convert yards to feet Express your answer in miles to three significant figures = 9.64 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 ( ). What is the speed of a car going and. 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 Hint C.1 Hint C.2 Convert miles to meters Convert hours to seconds Express your answer in meters per second to three significant figures. = 0.447
3 3 of 6 9/5/2009 6:13 PM Notice that by equating the two values for, you get remembering this relationship in the future, you can reduce this task to a single conversion.. It might be valuable to remember this, as you may frequently need to convert from miles per hour into more useful SI units. By Convert the following to SI units: Problem km 3420 mm 3420 m 3.42 m 47.0 cm/ms 470 cm/min 47.0 km/ms 470 m/s Part D 60.0 km/hour 16.7 m/s 60.0 m/min 16.7 mm/hour 60.0 mm/min Problem 1.54 The quantity called mass density is the mass per unit volume of a substance. Express the following mass densities in SI units. Aluminum, 2700 Alcohol, 810 Conceptual Question 1.8 Determine the sign (positive or negative) of the position for the particle in the figure in the textbook.
4 4 of 6 9/5/2009 6:13 PM Negative Positive Determine the sign (positive or negative) of the velocity for the particle in the figure. Positive Negative Determine the sign (positive or negative) of the acceleration for the particle in the figure. Negative Positive Learning Goal: To learn to use images of an object in motion to determine velocity and acceleration. Motion of Two Rockets Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a timeexposure image where a stroboscope has illuminated the rockets at the uniform time intervals indicated. At what time(s) do the rockets have the same velocity? Hint A.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. at time only at time only at times and at some instant in time between at no time shown in the figure and At what time(s) do the rockets have the same x position? at time only at time only at times and at some instant in time between at no time shown in the figure and
5 5 of 6 9/5/2009 6:13 PM At what time(s) do the two rockets have the same acceleration? Hint C.1 How to determine the acceleration at time only at time only at times and at some instant in time between at no time shown in the figure and Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant). and nonzero acceleration velocity displacement time Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant). and nonzero acceleration velocity displacement time Part F At what time(s) is rocket A ahead of rocket B? Hint F.1 Use the diagram before only after only before and after between and at no time(s) shown in the figure Significant Figures To seven significant figures, the mass of a proton is. Which of the following choices demonstrates correct rounding? Check all that apply. The number is incorrect because when we round to four significant figures we get 1.673, not Similarly, is incorrect because when we round to six significant figures we get , not To eight significant figures, Avogadro's constant is. Which of the following choices demonstrates correct rounding? Check all that apply.
6 6 of 6 9/5/2009 6:13 PM All these options are correct; they represent different levels of precision, even though the numerical value is the same. Score Summary: Your score on this assignment is 99.2%. You received out of a possible total of 40 points.
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