Foundations of Algebra and Geometry
Chapter 4 Answers
Equations
Sir Issac Newton was a famous physicist long before Einstein was born.
He came up with equations to describe the forces in the world we can see.
Learn more about Newton's
Laws at this Web site.
Part A, Using Formulas
1. Using the information found at the Newton's Laws Web site, answer the following questions.
a. What is Newton's Second Law?
[F = ma]b. Suppose the value of a, the acceleration (measured in meters per second2), is 10, and the value of m, the mass (measured in kg), is 2. What is F, the force applied (measured in Newtons)?
[F = (2)(10) = 20 kg · meters per second2]c. If an acceleration of 10 meters per second2 is applied to an object with a mass (m) of 4 kg, what is the force that is applied?
[F = (4)(10) = 40 Newtons]d. If an acceleration of 10 meters per second2 is applied to an object with a mass (m) of 5 kg, what is the force that is applied?
[F = (5)(10) = 50 Newtons]
2. Based on your answers to 1, approximately how much force do
you think would need to be applied to an object with a mass of 10 kg to
achieve an acceleration of 10 meters per second2?
[F = (10)(10) = 100 kg · meters per second2]
Part B, Using Number Sense
3. Using your number sense, answer the following questions.
a. If F = 16 Newtons and m = 4 kg, what is a?
[16 = 4a --> a = 4 meters per second2]b. If F = 84 Newtons and m = 12 kg, what is a?
[84 = 12a --> a = 6 meters per second2]
Part A, Understanding Equality
1. Because distances in space are so large, scientists often write distances in light-years or in parsecs rather than in miles. Go to the MegaConverter Web site to find out how far some astronomical distances are. Click on "Use the Selector List" then select "Astro Distance" and use the pull-down menus.
a. How far is 1 light-year in miles?
[5,878,639,427,505 miles]b. How far is 1 parsec in light-years?
[3.26 light years]
2. Using the information found at the Cambridge X-ray Astronomy Group Web site, answer the following questions.
a. Find out how far away scientists can distinguish supernovae and x-ray stars. [50 kiloparsecs]
b. Use your answer from 1b to write your answer from a in light-years.
Hint: 1 kiloparsec = 1000 parsecs.
[(50,000)(3.26) = 163,000 light years]c. Use your answer from 1c to write your answer from a in miles.
[9.5821823 · 1017]
3. Does the distance depend on the form in which you write it? That is,
is the distance the same if you write it in miles or light-years or parsecs?
Explain.
[The distance is the same regardless of the unit
of measure being used.]
Part B, Isolating the Variable
4. Using the information found at the Cambridge X-ray Astronomy Group Web site, answer the following questions.
a. Write an equation that relates the Earth's distance from the center of our galaxy to the radius of the galaxy.
[distance = 80% of radius]b. Substitute for the variables and solve your equation from a for distance.
[distance = 8 kiloparsecs]c. Write an equation that expresses the distance of the Earth from a star at the edge of our galaxy.
[distance = 8 kiloparsecs + 10 kiloparsecs]d. Solve your equation from c for distance.
[distance = 18 kiloparsecs]
Part D, Solving Two-Step Equations
5. The three fuel cells aboard the Space Shuttle weigh a total of 790 pounds which includes the 10 pound casing. Write and solve an equation to determine the weight of one fuel cell. [3f + 10 = 790; f = 260 lbs]