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course Phy 201
8/26/11 9:30
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) = (60/21)
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(4/3) * 3
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(12/3) = (4/1) = 4
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(5/8) * 16
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(80/8) = (10/1) = 10
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(5/9) / (3/4)
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(20/27)
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(13/25) / 2
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(13/50)
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12 / (2/3)
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(36/2) = (18/1) = 18
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(4 / 3^2) * 3
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(4/9) * 3 = (12/9) = (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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(a/b) * (d/c) = (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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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*b) = (a/b^2)
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(a / b^2) * b
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(a/b^3)
@& This would be
(a / b^2) * (1 / b) = a / b^3.*@
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(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^2)
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@& This would be (m/s) * (s/1) = m * s / s = m.*@
kg * (m / s^2)
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(kgm/s^2)
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(m/s^2) * s
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(m/s^3)
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@& This would be (m/s^2) * (s/1) = m * s^2 / s = m/s.*@
(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* m^/s^3)
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@& This would be
(kg m/2 / s) * (m / s) = (kg m * m) / (s^2)*@
5 m * (1 km / (1000 m) )
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(1km/5000m)
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@& This would be
(5 m * km) / (1000 m) = 1/200 km.*@
80 ft * (31 cm / ft)
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(2480 cm/ft^2)
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@& ft * cm / ft = cm, so the result is 2480 cm.*@
20 dollars * (100 cents / dollar)
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(20000 dollars/cents)
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@& cents is not in any denominator
dollars is in a numerator and in a denominator
dollars * cents / dollars = cents * dollars / dollars = cents * (dollars / dollars) = cents.*@
12 pounds * (9.8 Newtons / (2.2 pounds) )
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12 pounds * (4.45 Newton pounds) = 2.69 Newton pounds
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@& (2.2 pounds) is a denominator. So pounds is part of a denominator.
The units would be
pounds * Newtons / pounds = Newtons.*@
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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(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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(15 = 5 * m) = 15/5 = 3 pounds feet/second^2
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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 * m * v^2) =
@& You need to use units in all steps.
(1/2 * 2 * 4^2) should have been written
(1/2 * 2 kg * (4 m/s)^2)
This gives you units kg * (m/s)^2 = kg m^2 / s^2.*@
= 16kg m/s
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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 * 2 * 3 / 10^2) = 54/100 = 27/50 GigaNewton m^2 / C^4 / m
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@& You didn't have any units in
(9 * 2 * 3 / 10^2) = 54/100
That would be
(9 GigaNewton mY2 / C^2) * (2 C) * (3 C) / (10 m)^2
and the units would come out in GigaNewtons.
My guess is that most people aren't going to get this one, which is fairly complicated (but not bad once you have a little more practice).*@
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@& Good work. You did have a few mistakes, especially on the formulas, where you need to use units at every step. See my notes. You're going to be fine with this, given just a little more practice.*@
@& We will be going over these in class as well, but not until Wednesday after they are due. In the meantime let me know if you have any questions.*@