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course Phy 241
August 30 at 11:12 pm
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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1/2
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(12/5) * (25 / 21)
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300 /105
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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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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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8
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@& 12 * (2/3) = 8, but 12 / (2/3) is not 8.
What's the rule for dividing fractions?
How does it apply to this question?*@
(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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ab/bc
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@& You might have a typo. Should be a d / (b c), not ab / (b c).
Be sure you understand why.*@
(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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1/200 km
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80 ft * (31 cm / ft)
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2400 cm
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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 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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1. F = (5kg)(3 m/s^2)
2. F = 15kg(m)/s^2
Is this correct? Having both the top multiplied and having 15kg(m)? Because of the past problems like (a)(b/c) = (ab/c)?
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@& You are correct. Very good.*@
If F = m a and F = 15 pounds when a = 5 feet / second^2, then what is m?
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1. (15 pounds) = (m)(5 feet/second^2)
2. (15 pounds)/(5 feet/second^2)
3. (15 pounds) * (second^2/5 feet)
4. m = (15 pounds)(second^2)/(5 feet)
@& Very good, but still one step to go.
Divide the 15 by the 5 to get 3.
You end up with
3 pounds * second^2 / feet.*@
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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. KE = (1/2)(2 kg)(4 m/s)^2
2. KE = (1/2)(2 kg)(16 m^2/s^2)
3. KE = (kg)(16 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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1. F = (9 GigaNewton m^2/C^2)(2C)(3C)/(10)^2
2. F = (9 GigaNewton m^2/C^2)(6C)/(100)
I am not sure what I have to do next on this one. Could you please tell me the next step? Or if I was doing it correctly.
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@& It's not 10^2, it's (10 m)^2.
2 C * 3 C = 6 C^2, not 6 C.
So you get
F = (9 GigaNewton m^2/C^2)(6C^2)/(100 m^2)
Still needs to be simplified. Make sure you see how this all comes out to just
.54 GigaNewtons*@
@&
You've done very well here. A few errors, but easily enough corrected.
You'll be in very good shape on the units aspect of the course.*@