#$&*
course PHY 201
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)
20/7
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(4/3) * 3
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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1/18
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@& This is 18, not 1/18.
12 / (2/3) = 12 * 3/2, not 1/12 * 2/3.*@
(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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b/ac
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@& This is a * (c / b), not 1/a * (b/c).*@
(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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Ab/b^2
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@& RIght, but this then reduces to a / b.*@
(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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Ms/s
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@& s in denominator divides s in numerator so this simplifies to just m.*@
kg * (m / s^2)
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Kg*m/s^2
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(m/s^2) * s
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Ms/s^2
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@& s in denominator divides s in numerator so this simplifies to just m / 2.*@
(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/s^2*m
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@& This still needs to be simplified. You get kg / s.*@
5 m * (1 km / (1000 m) )
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5*m*km/1000 m
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@& m divide out giving you (5 / 1000) km, or (1/200) km.*@
80 ft * (31 cm / ft)
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80 ft * 31 cm
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@& ft divide out. You get 2480 cm.*@
20 dollars * (100 cents / dollar)
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20 dollars * 100 cents
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@& dollars divide out, leaving you just 2000 cents.*@
12 pounds * (9.8 Newtons / (2.2 pounds) )
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12 pounds * 9.8 N per 2.2 pounds
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@& pound per pound means pound / pound, which divides out*@
@& The numbers would be 12 * 9.8 / 2.2, around 50.
So the result is around 50 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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5 kg * 3 m/s^2
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@& ... which multiplies out to 15 kg m/s^2.*@
If F = m a and F = 15 pounds when a = 5 feet / second^2, then what is m?
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15 lbs=m*5 ft/sec^2
m=3 lbs * ft per sec^2
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@& Almost. That would be 3 lbs / (ft / sec^2) = 3 lbs * sec^2 / ft.*@
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 kg * 16 m/s
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@& (4 m/s)^2 = 16 m^2 / s^2.
The result would be 16 kg 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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54gNm^2/c^4/ 100 m
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@& (10 m)^2 = 100 m^2. So you have m^2 in both numerator and denominator.
You'll have C^2 in the numerator as well as in the denominator, so that unit will also divide out.
You'll be left with just .54 gN.*@
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@& Check my notes and be careful of the details, and you'll be fine on this.*@