A couple of problem, who can solve it?

[Ocean5]

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Hi every one,

There are a couple of problems, I can't find the final answer.

1) The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft2) and has a height of 481 ft (Fig. P1.24). If the volume of a pyramid is given by the expression V = (1/3)bh, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.




2) Newton's law of universal gravitation is represented by the following formula, were F is the gravitational force, M and m are masses, and r is a length.

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Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G? (Use m, kg, and s as appropriate.)

 

[Streetwolf]

1) The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft2) and has a height of 481 ft (Fig. P1.24). If the volume of a pyramid is given by the expression V = (1/3)bh, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.

Okay so the base is 566,280 ft^2. Convert feet to meters by doing 1ft(12in/ft)(2.54cm/in)(1m/100cm) = 0.3048 meters. Now convert ft^2 to m^2 by doing 566,280 ft^2 * (0.3048 m / 1 ft)^2 = 172,602.144 m^2.

I find it easier to set up the relationship between units in a fraction and THEN square the whole thing (or cube or raise to w/e power you need to raise it to). So I knew there are 0.3048 meters in 1 foot. So if you take that fraction and square it, you get the relationship between m^2 and ft^2.

And you need the height which is 481 ft (0.3048 m / 1 ft) = 146.6088 m. So then you plug the two numbers into V = 1/3 b * h and get this answer:

25,304,993.21 m^3.

Alternatively you could have done (1/3 * 566,280 ft^2 * 481 ft) = 6,984,120 ft^3 * (0.3048 m / 1 ft)^3 = 25,304,993.21 m^3.

2) Newton's law of universal gravitation is represented by the following formula, were F is the gravitational force, M and m are masses, and r is a length.

​

Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G? (Use m, kg, and s as appropriate.)

Force = kg*(m/s^2)

F = GMm/r^2

So G = Fr^2/Mm.

r has units of meters and M and m have units of kg.

So just put in the units:

G = (kg*(m/s^2))*(m)^2 / (kg)^2
G = kg*m^3 / kg^2*s^2
G = m^3/kg*s^2

So G has units of m^3 / kg*s^2.

 

[Ocean5]

Okay so the base is 43,560 ft^2. Convert feet to meters by doing 1ft(12in/ft)(2.54cm/in)(1m/100cm) = 0.3048 meters. Now convert ft^2 to m^2 by doing 43,560 ft^2 * (0.3048 m / 1 ft)^2 = 4,046.86 m^2.

I find it easier to set up the relationship between units in a fraction and THEN square the whole thing (or cube or raise to w/e power you need to raise it to). So I knew there are 0.3048 meters in 1 foot. So if you take that fraction and square it, you get the relationship between m^2 and ft^2.

And you need the height which is 481 ft (0.3048 m / 1 ft) = 146.6088 m. So then you plug the two numbers into V = 1/3 b * h and get this answer:

197,768 m^3.

Alternatively you could have done (1/3 * 43,560 ft^2 * 481 ft) = 6,984,120 ft^3 * (0.3048 m / 1 ft)^3 = 197,768 m^3.



Force = kg*(m/s^2)

F = GMm/r^2

So G = Fr^2/Mm.

r has units of meters and M and m have units of kg.

So just put in the units:

G = (kg*(m/s^2))*(m)^2 / (kg)^2
G = kg*m^3 / kg^2*s^2
G = m^3/kg*s^2

So G has units of m^3 / kg*s^2.

Hi Streetwolf,

Thank you very much for your response. Actually, I wanted to post something about this problems, since I've been working on them for 2 hrs maybe.
Ya I know it is crazy, but I was wondering why I don't get the riht answer. Then I came up with the right ones, but still the second one is foggy to me. Don't get me wrong your second (unit cal) is correct. I got the same thing , but it wasn't what my class wanted it. Infact they wanted the dimentional version of those units. I lost points anyways. BUT YOUR UNITS ARE CORRECT! Converting them to dimention we'll get: L^3/ M.sec^2.
I really think they asked it in a wrong way.

The second one is: V= BH/3
13 . 43560 ft^2 . 481 ft = 90793560 ft^3

Now since 1m = 3.281 ft, so we'll have

90793560 ft^3 . 1m^3/ 35.32 ft^3= 2570599.094 m^3

Thank god this one was correct. Thank you again for your post. Nest time I should post them few days befor emy exam!

 

[Streetwolf]

The question asked for SI units. I used SI units. The words 'length' (L) and 'mass' (M) are NOT SI units. Either your teacher is a ******* or your book is completely messed up.

The volume problem - I must have missed the 13 acres part. So yeah my answer is off by a bit. I'll fix it.

And that would be a stupid mistake =]

 

[Ocean5]

The question asked for SI units. I used SI units. The words 'length' (L) and 'mass' (M) are NOT SI units. Either your teacher is a ******* or your book is completely messed up.

The volume problem - I must have missed the 13 acres part. So yeah my answer is off by a bit. I'll fix it.

And that would be a stupid mistake =]

You are good, that is the important thing! Yes, you are right, asking in unit and having students to answer in dimention is ridiculous. I lost point on it.