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Chapter 1 Homework
Due: 9:00am on Tuesday, September 1, 2009
Note: To understand how points are awarded, read your instructor's Grading Policy.
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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
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,
, the units of mass are
Hint A.1
, and the units of distance are
and
are the masses of the bodies,
is the distance between them, and
. For this equation to have consistent units, the units of
is the gravitational constant. In SI units, the units or force are
must be which of the following?
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 B.1
How to approach the problem
Hint not displayed
ANSWER:
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.
Measurements in SI Units
Familiarity with SI units will aid your study of physics and all other sciences.
Part A
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 50
ANSWER:
.
100
200
300
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Correct
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 5
is about 50
. Ten
(1
) is about the width of this adult's little finger and 10
6.4
. The distance from elbow to fingertips on the average adult
is about the width of the average hand.
Part B
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
ANSWER:
.
80
500
1200
Correct
Something that weighs 1
has a mass of about
. This is a useful conversion to keep in mind!
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 625.8
?
Express your answer in centimeters to three significant figures.
ANSWER:
1590
Correct
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
Hint B.1
= 1.696×104
. Find its range in miles. Use the facts that
and
.
Convert yards to feet
Hint not displayed
Express your answer in miles to three significant figures.
ANSWER:
= 9.64
Correct
1.696×104
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
and
Hint C.1
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
.
Convert miles to meters
Hint not displayed
Hint C.2
Convert hours to seconds
Hint not displayed
Express your answer in meters per second to three significant figures.
ANSWER:
= 0.447
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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 1.23
Convert the following to SI units:
Part A
9.79
ANSWER:
9.79
9.79×10−6
9.79×10−6
Correct
Part B
3.42 km
ANSWER:
3420 mm
3420 m
3.42 m
Correct
Part C
47.0 cm/ms
ANSWER:
470 cm/min
47.0 km/ms
470 m/s
Correct
Part D
60.0 km/hour
ANSWER:
16.7 m/s
60.0 m/min
16.7 mm/hour
60.0 mm/min
Correct
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.
Part A
Aluminum,
ANSWER:
2700
Correct
Part B
Alcohol,
ANSWER:
810
Correct
Conceptual Question 1.8
Part A
Determine the sign (positive or negative) of the position for the particle in the figure in the textbook.
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Negative
Positive
Correct
Part B
Determine the sign (positive or negative) of the velocity for the particle in the figure.
ANSWER:
Positive
Negative
Correct
Part C
Determine the sign (positive or negative) of the acceleration for the particle in the figure.
ANSWER:
Negative
Positive
Correct
Motion of Two Rockets
Learning Goal: To learn to use images of an object in motion to determine 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 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.
ANSWER:
at time
only
at time
only
at times
and
at some instant in time between
and
at no time shown in the figure
Correct
Part B
At what time(s) do the rockets have the same x position?
ANSWER:
at time
only
at time
only
at times
and
at some instant in time between
and
at no time shown in the figure
Correct
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Part C
At what time(s) do the two rockets have the same acceleration?
Hint C.1
How to determine the acceleration
Hint not displayed
ANSWER:
at time
only
at time
only
at times
and
at some instant in time between
and
at no time shown in the figure
Correct
Part D
The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________.
ANSWER:
and nonzero acceleration
velocity
displacement
time
Correct
Part E
The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________.
ANSWER:
and nonzero acceleration
velocity
displacement
time
Correct
Part F
At what time(s) is rocket A ahead of rocket B?
Hint F.1
Use the diagram
Hint not displayed
ANSWER:
before
after
before
between
only
only
and after
and
at no time(s) shown in the figure
Correct
Significant Figures
Part A
To seven significant figures, the mass of a proton is
. Which of the following choices demonstrates correct rounding?
Check all that apply.
ANSWER:
Correct
The number
is incorrect because when we round to four significant figures we get 1.673, not 1.672. Similarly,
is incorrect because when we round to six significant figures we
get 1.67262, not 1.67263.
Part B
To eight significant figures, Avogadro's constant is
. Which of the following choices demonstrates correct rounding?
Check all that apply.
ANSWER:
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Correct
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 39.68 out of a possible total of 40 points.
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