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course phy 121
8/29 9
Adapted from spiral outline: units, percent difference, etc.
Instructions:
1. Copy this document into a text editor, such as notepad.
2. Insert your answers between lines marked **** and #$&*. Do not insert anything into the lines so marked.
3. Do not eliminate anything that appears in this document. Insert as indicated, but otherwise do not make any changes to what you see here.
4. Submit a copy of your completed document using the Submit Work Form at http://vhcc2.vhcc.edu/dsmith/submit_work.htm .
Do the following calculations with fractions. This should take you 5 minutes or less: Do not use a calculator. You can do all the numerical calculations if you know the multiplication facts for single-digit numbers.
Each answer should be typed as a sequence of numbers, letters, slashes , asterisks and parentheses. If you have questions then please show some of the steps of your work, and you will ordinarily be asked to do so. For this document, however, just the answers will be sufficient. On these questions, I'll usually be able to figure out what you've done from your answers.
(1/2) * (3/4)
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(3/8)
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(12/5) * (25 / 21)
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(300/105)
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@& Good, but this reduces to lower terms.*@
(4/3) * 3
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(12/3)
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(5/8) * 16
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(80/8)
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(5/9) / (3/4)
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(1.67/2.25)
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@& 1.67 is an approximation, not an exact value. The correct result is 15 / 12.*@
(13/25) / 2
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(6.5/25)
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@& Your expression is equal to this, but a fraction is expressed in the form integer / integer.*@
12 / (2/3)
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(6/.333)
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@& Your expression is equal to this, but a fraction is expressed in the form integer / integer.*@
(4 / 3^2) * 3
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(12/9)
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@& Good, but note that this reduces to 4/3.*@
(a/b) * (c/d)
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(ac/bd)
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(a/b) / (c/d)
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(a/c)/(b/d)
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@& This isn't a simple fraction. A simple fraction is one quantity / another quantity, in the form numerator / denominator. You can have only one numerator and one denominator.*@
(a/b) * c
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(ac/b)
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a / (b / c)
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(a/b)/(1/c)
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@& This is right so far. Good.
But you need one more step to put this into the form of a simple fraction.
You willl get a / (b c)*@
(a/b) / c
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(a/c)/b
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@& This is right so far, but you need one more step to get a / (b c).*@
(a / b) / b
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(a/b)/b
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@& This isn't a simple fraction.*@
(a / b^2) * b
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(ab)/b^2
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@& Good, but this reduces. *@
(a / b^2) / b
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(a/b)/b^2
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@& This is equivalent to the given expression, but it isn't a simple fraction.*@
Now do the following calculations:
(m / s) * s
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(ms)/s=m
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kg * (m / s^2)
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(Kg*m)/s^2
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@& Good, but you need one more step to reduce this.*@
(m/s^2) * s
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(ms)/s^2
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(m/s^2) * m
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M^2/s^2
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(kg * m / s^2) / (m / s)
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Kg/s
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5 m * (1 km / (1000 m) )
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5/1000 km
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80 ft * (31 cm / ft)
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320 cm
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@& Good units, but 80 * 31 = 2480, not 320.*@
20 dollars * (100 cents / dollar)
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2000 cents
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12 pounds * (9.8 Newtons / (2.2 pounds) )
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53.45 newtons
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Now answer the following:
Work out and show units in every step:
If F = m a, then if m = 5 kg and a = 3 m/s^2, what is the value of F?
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75kg/s^2
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If F = m a and F = 15 pounds when a = 5 feet / second^2, then what is m?
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M=3
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@& You did the right thing, but with units that would be 3 pounds / (ft / second^2) = 3 pounds * second^2 / ft.*@
If KE = 1/2 m v^2 with m = 2 kg and v = 4 m/s, then what is KE?
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16kg/m/s
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@& 16 is right.
But note that when you square 4 m/s every part of the expression is squared, including the m and the s.*@
If F = k Q q / r^2 with k = 9 GigaNewton m^2 / C^2, Q = 2 C and q = 3 C with r = 10 m, then what is F?
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5.4 giganewtons
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"
@& You did really well with the formulas. You had a couple of errors, so be sure to see my note, but you're very much on the right track.
You came up a step short on simplifying a lot of the other expressions, but you were usually on the right track.
Check all my notes. You're going to do well with units.*@