#$&*
course Phy 201
8/30/11 10:57pmIt's weird doinog these calculations on the computer instead of on paper. I hope I didn't make any mistakes because of a stray finger.
Adapted from spiral outline: units, percent difference, etc.
Instructions:
Copy this document into a text editor, such as notepad.
Insert your answers between lines marked **** and #$&*. 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) =
(1*3) / (2*4) = 3/8
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(12/5) * (25 / 21)
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(12/50) * (25/21) =
(12*25) / (5*21) =
300 / 105 =
60/21 = 20/7
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(4/3) * 3
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(4/3) * 3 =
(4/3) * (3/1) =
(4*3) / (3*1) =
12/3= 4
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(5/8) * 16
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(5/8) * 16 =
(5/8) * (16/1) =
(5*16) / (8*1) =
80/8 = 10
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(5/9) / (3/4)
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(5/9) / (3/4) =
(5/9) * (4/3) =
(5*4) / (9*3) = 20/27
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(13/25) / 2
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(13/25) / 2 =
(13/25) / (2/1) =
(13/25) * (1/2) =
(13*1) / (25*2) = 13/50
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12 / (2/3)
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12 / (2/3) =
(12/1) / (2/3) =
(12/1) * (3/2) =
(12*3) / (1*2) =
36/2 = 18
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(4 / 3^2) * 3
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(4 / 3^2) * 3 =
(4 / 9) * (3/1) =
(4*3) / (9*1) =
12/9 = 4/3
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(a/b) * (c/d)
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(a/b) * (c/d) =
(a*c) / (b*d) = (ac)/(bd)
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(a/b) / (c/d)
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(a/b) / (c/d) =
(a/b) * (d/c) =
(a*d) / (b*c) = (ad)/(bc)
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(a/b) * c
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(a/b) * c =
(a/b) * (c/1) =
(a*c) / (b*1) = (ac)/b
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a / (b / c)
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a / (b/c) =
(a/1) / (b/c) =
(a/1) * (c/b) = (a*c) / (1*b) = (ac)/b
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(a/b) / c
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(a/b) / c =
(a/b) / (c/1) =
(a/b) * (1/c) =
(a*1) / (b*c) = a/(bc)
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(a / b) / b
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(a/b) / b =
(a/b) / (b/1) =
(a/b) * (1/b) =
(a*1) / (b*b) = a/(b^2)
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(a / b^2) * b
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(a / b^2) * b =
(a / b^2) * (b / 1) =
(a * b) / (b^2 *1) =
(ab) / (b^2) = a/b
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(a / b^2) / b
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(a / b^2) / b =
(a / b^2) / (b / 1) =
(a / b^2) * (1/b) =
(a * 1) / (b^2 * b) = a/(b^3)
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Now do the following calculations:
(m / s) * s
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(m / s) * s =
(m / s) * (s / 1) =
(m * s) / (s * 1) =
(m * s) / s = m
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kg * (m / s^2)
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kg * (m / s^2) =
(kg / 1) * (m / s^2) =
(kg * m) / (1 * s^2) = (kg*m) / (s^2)
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(m/s^2) * s
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(m / s^2) * s =
(m / s^2) * (s / 1) =
(m * s) / (s^2 * 1) =
(m * s) / (s^2) = m/s
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(m/s^2) * m
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(m / s^2) * m =
(m / s^2) * (m / 1) =
(m * m) / (s^2 * 1) = (m^2) / (s^2)
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(kg * m / s^2) / (m / s)
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(kg * m / s^2) / (m / s) =
(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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5m * (1km / 1000m) =
(5m / 1m) * (1km / 1000m) =
(5m * 1km) / (1m * 1000m) =
(5 m*km) / (1000m) = (m*km) / 200m
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@& m km / m = km, so your answer is (1/200) km.*@
80 ft * (31 cm / ft)
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80ft * (30cm / ft) =
(80ft / 1ft) * (30cm / ft) =
(80ft * 30cm) / (ft / ft) = 240 ft*cm
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@& One more zero. 2400, not 240 (actually the second number is 31 so it's 2480).
You did get messed up on the ft.
80ft * (30cm / ft) is correct (ignoring the distinction between 30 and 31).
The units of that are
ft * (cm / ft) = ft * cm / ft. The feet divide out, leaving cm.
You appear to have introduced an extra ft that wasn't there, in your step
(80ft / 1ft) * (30cm / ft).
*@
20 dollars * (100 cents / dollar)
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(20 dollars / 1 dollar) * (100 cents / 1 dollar) =
(20 dollars * 100 cents) / (1 dollar * 1 dollar) = 2000 dollars*cents
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@& You threw in an extra dollar unit.
That resulted in
(20 dollars * 100 cents) / (1 dollar * 1 dollar), which would be 2000 cents * dollar / dollar^2 = 2000 cents / dollar
However the correct unit is just dollars * cents / dollar = cents.
20 dollars is therefore the same as 2 000 cents.
*@
12 pounds * (9.8 Newtons / (2.2 pounds) )
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12 pounds * (9.8 Newtons / 2.2 pounds)
(12 pounds / 1 pound) * (9.8 Newtons / 2.2 pounds)
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@& You've got an extra pound in there.
Your numbers need to be calculated.
You end up with around 50 Newtons. The pounds that were originally there divided out.
*@
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 = m*a
F = 5kg * 3m/s^2
F = 15 (kg*m)/(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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F = m*a
15 pounds = m * 5ft/sec^2
m = (15 pounds) / (5ft/sec^2)
m = 3 pounds/(ft/sec^2)
Note: are complex fractions allowed (above)
: if not then here's a simple fraction below
m = 3 pounds*(sec^2/ft)
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@& Good. I think this is the first one I've seen that got everything completely right.*@
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) ((4 m/s)^2)
KE = (1/2) (2kg) (4m/s) (4m/s)
KE = 16 kg (m^2/s^2)
KE = 16 ((kg*m^2)/(s^2))
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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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F = k Q q / r^2
F = (9(m^2 / c^2)) (2 c) (3 c) (10m^2)
@& You lost your GigaNewton.*@
@& The r^2 is in the denominator. You lost your / sign.*@
F = ((9 / 1) * (m^2 / c^2)) (2c) (3c) (10m^2)
F = ((9 * m^2) / (1 * C^2)) (2c * 3c) (10m^2)
F = (9m^2 / c^2) (6c) (10m^2)
@& 2 C * 3 C = 6 C^2, not 6 C.*@
F = (54m^2c / c^2) (10m^2)
F = 540m^4c / c^2
F = 540m^4 / c
@& You made a few errors here. I inserted notes at the appropriate places.*@
#$&*"
@& You inserted units on a few problems that weren't there, and had some other errors.
I believe you'll understand my notes, and you're going to do fine on units.*@