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course Phy 241
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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1/2 * 3/4 = 3/8
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(12/5) * (25 / 21)
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12*25 = 300 300/105 = 60/21 = 2.857
5*21 = 105
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@& 60 / 21 reduces further to 20 / 7.
Express fractions as integer / integer.
Decimal approximations are OK when dealing with data, which typically contains uncertainties, but not when doing fraction calculations. OK to add the decimal equilvalent, but it doesn't replace the need for the integer / integer form.*@
(4/3) * 3
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(4/3) (3/1) = 12/3 = 4
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(5/8) * 16
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(5/8)(16/1) = 80/8 = 10
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(5/9) / (3/4)
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(5/9)(4/3) = 20/27
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(13/25) / 2
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(13/25)(1/2) = 13/50
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12 / (2/3)
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(12/1)(3/2) = 36/2 = 18
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(4 / 3^2) * 3
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(4/9)(1/3) = 4/27
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(a/b) * (c/d)
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(a/b)(c/d) = ac/bd
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(a/b) / (c/d)
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(a/b)(d/c) = ad/bc
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(a/b) * c
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(a/b)(c/1) = ac/b
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a / (b / c)
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a(c/b) = ac/b
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(a/b) / c
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(a/b)(1/c) = a/bc
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(a / b) / b
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(a/b)(1/b) = (a/b^2)
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(a / b^2) * b
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(a/b^2)(1/b) = a/b^3
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@& * b doesn't imply 1/b. Your solution would be correct for (a / b^2) / b.*@
(a / b^2) / b
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(a/b^2)(1/b) = a/b^3
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Now do the following calculations:
(m / s) * s
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(m/s)(1/s) = m/s^2
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@& Your solution would correspond to (m/s) / s, but not to (m/s) * s.*@
kg * (m / s^2)
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kg(m/s^2) = kg*m/s^2
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(m/s^2) * s
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(m/s^2) * s = ms/s^2 = m/s
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(m/s^2) * m
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(m/s^2) * m = (m^2/s^2)
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(kg * m / s^2) / (m / s)
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(kg * m/s^2)(s/m) = (kg*m*s/s^2*m) = (kg/s)
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5 m * (1 km / (1000 m) )
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5km*m / 1000m = 1/200 km
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80 ft * (31 cm / ft)
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80 ft (31 cm / ft) = 80ft*cm/ft = 80cm
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@& 80 has to be multiplied by 31; your units are correct*@
20 dollars * (100 cents / dollar)
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20 dollars *(1 dollar / 1 dollar ) = 20 dollars
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@& You've replaced 100 cents with an equivalent expression, so your result is equal to the correct answer. However it isn't in the form of the given calculation.*@
12 pounds * (9.8 Newtons / (2.2 pounds) )
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12 pounds * (9.8 Newtons / 2.2 pounds) = 117.6 pounds * Newtons / 2.2pounds = 53.46 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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F = 5 kg * (3 m/s^2) = 15 kg*m/s^2
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@& You've replaced 100 cents with an equivalent expression, so your result is equal to the correct answer. However it isn't in the form of the given calculation.*@
If F = m a and F = 15 pounds when a = 5 feet / second^2, then what is m?
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F = 15 lbs when a = 5 ft/second^2 so.....
15 = m (5 ft/second^2)
m = 15/(5 ft/secons^2) or 15 * (seconds^2/5ft) = 3seconds^2
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@& 15 should be 15 lbs, and the lbs should be carried through the calculation. The units of your result are not correct.*@
If KE = 1/2 m v^2 with m = 2 kg and v = 4 m/s, then what is KE?
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KE = 1/2 m*v^2
KE = 1/2(2kg)*(4m/s)^2 = 1kg*(4m/s)^2 = (4m*kg/s) ^2
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@& (4 m/s)^2 is 4^2 m^2 / s^2, or 16 m^2 / s^2.*@
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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F = k Q q / r^2
F = 9 GigaNewton m^2 / C^2 (2C) (3C) / 100m^2
F = 9 GigaNewton m^2 / C^2 (6C^2) / 100m^2
F = 9Giganewtons/100
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@& Almost, but you seem to have lost your 6.
Your units look good.*@
@& This looks good overall, but you had a few mistakes. Check my notes and be sure you understand.*@