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course Phy 241
8/31 11:30 am
Adapted from spiral outline: units, percent difference, etc.
Instructions:
Copy this document into a text editor, such as notepad.
Insert your answers between lines marked **** and #$&*. Do not insert anything into the lines so marked.
Do not eliminate anything that appears in this document. Insert as indicated, but otherwise do not make any changes to what you see here.
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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(20/7)
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(4/3) * 3
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4
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(5/8) * 16
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10
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(5/9) / (3/4)
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(5/12)
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(13/25) / 2
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(13/50)
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12 / (2/3)
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18
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(4 / 3^2) * 3
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(4/3)
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(a/b) * (c/d)
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((ac)/(bd))
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(a/b) / (c/d)
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((ad)/(bc))
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(a/b) * c
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(ac)/b
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a / (b / c)
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(ac)/b
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(a/b) / c
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a/(bc)
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(a / b) / b
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(a/b^2)
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(a / b^2) * b
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(a/b)
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(a / b^2) / b
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(a/b^3)
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Now do the following calculations:
(m / s) * s
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m
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kg * (m / s^2)
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(kg*m)/(s^2)
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(m/s^2) * s
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(m/s)
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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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5m
@& m appears in numerator and denominator. As the calculation is posed, you're left with 5/1000 km = 1/200 km.
This is of course equal to 5 m, but the calculation yields 1 / 200 km.*@
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80 ft * (31 cm / ft)
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2,480 cm
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20 dollars * (100 cents / dollar)
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20,000 cents
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@& 2 000, not 20 000
I don't always count zeros correctly myself, as you well know.*@
12 pounds * (9.8 Newtons / (2.2 pounds) )
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53 and 5/11 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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(5 kg)*(3 m/s^2)
15 kg*m/s^2
15 N
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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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(15 lbs)/(5ft/s^2)
3 lbs*s^2/ft
3 (slug*ft/s^2)*s^2/ft
3 slugs
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If KE = 1/2 m v^2 with m = 2 kg and v = 4 m/s, then what is KE?
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(1/2)(2 kg)((4 m/s)^2)
16 kg*m^2/s^2
16 J
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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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(9 GigaNewton m^2/c^2)(2 c)(3 c)/((10 m)^2)
.54 GigaNewtons
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"
@& Excellent. Even including unit correspondences (e.g., slugs, Joules etc.).
Check my notes. *@