Help! College level physics question?

Question

This came from my textbook called Physics for Scientist and Engineers, and there are two problems I'm having trouble with (This is my AP Physics summer HW)

1) The consumption of natural gas by a company satisfies the empirical equation V= 1.50t + 0.00800t^2, where V is the volume in millions of cubic feet and t the time in months. Express this eq in units of cubic feet and seconds. Put the proper units on the coefficients. Assume a month is 30.0 days.

2)When a droplet of oil spreads out on a smooth water surface, the resulting "oil slick" is approx. one molecule thick. An oil droplet of mass 9.00 X 10^--7 kg and density 918 kg/m^3 spreads out into a circle of radius 41.8 cm on the water surface. What is the diameter of an oil molecule?

If you got those, thank you very much, but really, i don't expect you to solve those, but i'm desperate, and if there happens a guy who can solve those, i'll be lucky.

Answer 1

1. the conversion factor you need is 2,592,000 secs = 1 month, so just multiply 2592000 to your equation.
V = 1.5*2592000 t + 0.00800 * (2592000^2) t^2
note: square the conversion factor when the unit is squared.

2. you got a cylinder of oil one molecule thick. density = mass / vol of cylinder or d = m/(pi*r^2*h). h is the height / diameter of oil. solving for h = m /(pi*r^2*d).

substitute: h = 9.00x10^-7 / (3.1416*0.418^2*918)

just do the math...

Answer 2

Ok to solve the first problem you'll have to do some dimensional analysis to find the value of T in seconds.

1. (1 month) * (30 days / month) * (24 hours / day) * (60 minute / hour) * (60 seconds / minute) = x seconds per month.

Using this method we can convert the units to seconds and figure out how may seconds are in a month by multiplying all the numbers on the top as the other units are cancelled out except for seconds.

(1 * 30 * 24) * (60 * 60) = x seconds in a month.

(30 * 24) * (3600) = x seconds in a month.

720 * 3600 = x seconds in a month

2,592,000 = x seconds in a month

We now have T for seconds in a month. Now lets convert the coefficients from millions of ft^3 to ft^3.

1.5 million ft^3 changed to scientific notation becomes 1.5 x 10^6 ft^3 and .00800 million becomes 8.00 x 10^3 ft^3

V = (1.5 x 10^6 ft^3) * (2.592 x 10^6 seconds) + (8.00 x 10^3 ft^3)* (2.592 x 10^6 seconds)^2 Final answer.



2. With this one we've got most of what we need to answer it.
We've got the density and mass of the oil drop, and the radius of the slick.

First lets find out the volume of the drop.

D = m/v

So to solve for volume we need to rearrange the equation, we multiply both sides by v first.

D * (v)= m/v *(v)

Dv = m

Now we divide both sides by D to isolate v.

Dv/D = m/D

v = m/D

v = 9.00 X 10^-7 kg / 918 kg/m^3

v = 2.83 x 10^-9 m^3

Now that we have the volume of the droplet we need to find the area of the slick in m^3, so we'll first convert the radius from cm to m.

41.8cm x 1m / 100 cm = .418m = 4.18 x 10^-2 m

Now we need to find the area of the slick, then divide the volume by the area to find the thickness of the oil molecule.

A = pi * r^2

A = pi * (4.18 x 10^-2 m)^2

A = 3.14 * 1.75 x 10^-3 m^2

A = 5.495 x 10^-3 m^2

Now we divide the volume of the oil droplet by the area of the slick to get the thickness of the oil molecule, lets make the thickness be X.

X = V/A

X = 2.83 x 10^-9 m^3 / 5.495 x 10^-3 m^2

X = 5.150 x 10^-7 m Final answer.

Answer 3

If the equation uses t in months, then you need to convert moths to seconds:

1 month = 30 days = 24 hr/day x 30 days = 60min/hr x 24 hr/day x 30 days =60 sec/min x 60min/hr x 24 hr/day x 30 days

1month = 30 x 24 x 3600 seconds

So the conversion is 1/259200 months/sec.

similarly there is 10^6 cu. ft in 1 million cubic feet

So first put results in cu. ft.

V = 1.5x10^6 t +8 x 10^3 t^2 cu ft /month

Now adjust for conversion to seconds:

V = 1.5 x 10^6/(259200)*t + 8x10^3/(259200)^2 t^2

t is now in seconds and V is in cu. ft.

2. Radius of circle is 41.8 cm = 0.418 m. So area is

A = pi*(0.481)^2 m^2 = 0.727 m^2

Let molecule diameter be t. Now based on mass and density, there volume of the oil drop is:

V = density/mass = 9x10^-7/918 m^3 = 9.8x 10^-10 m^3

The volume of the oil doesn't change when it spreads out. So

V =9.8x 10^-10 m^3 = area of circle * t = 0.727 t

So t = 9.8x 10^-10 m^3/0.727m^2 =1.35 x 10^-9 m

Answer 4

1. V1 = millions of cubic feet
V2 = cubic feet
V1 = 1,000,000 V2

t1 = months
t2 = seconds
t1 = 2,592,000

V1= 1.50(t1) + 0.00800(t1)^2
1,000,000V2 = 1.50 (2,592,000t2) + 0.008 (2,592,000t2)^2
1,000,000V2 = 3,888,000t2 + 5.37 x 10^10 t2^2
V2 = 3.89t2 + 5.37 x 10^4 (t2^2)

2. You're given that the mass of all the oil and the density, so from there you can figure out the volume of the all the oil.

V = M / D
V = (9.00 x 10^-7 kg) / (918 kg/m^3)
V = 9.8039 x 10^-10 m^3

Volume also equals (in this case of a cylindrical shape) surface area times height. And in this case height is equal to the thickness, which is one molecule think, or the diameter of an oil molecule.

SA = pi * r^2
SA = pi * (0.418m)^2
SA = 0.5489m^2

V = SA * H
H = V / SA
H = 9.8039 x 10^-10m^3 / 0.5489 m^2
H = 1.79 x 10^-9

Answer 5

It depends on what the next course is about. Different colleges and curriculums have different course matter. My Curriculum had Electricity and Magnetism as the second physics course, and it was a bit tougher than the first. The third was Thermodynamics which was not as tough as the second to me. But as one of the other respondents answered, it depends on your comfort with Math. Also depends on the amount of time you put into it. It is mostly logical thinking.