Dimensional Analysis: Distance, Density, Speed, Value

Please use Dimensional analysis technique and show the work.

1-Approximately how many dollars worth of pennies would you need to place side by side to cover a total distance of one mile?

2-The speed limit on many Australian highways is 100.0 kilometers per hour. Convert this to miles per hour.

3-What is the volume in milliliters of 1.00 pint of heavy cream?

4-The average density of whole milk is 1.034 grams per milliliter. What is the density of whole milk in pounds per gallon?

5-If oxygen molecule is moving at 4.78 x 10 e4 centimeters per second, what is its speed in miles per hour?

6-Light in a vacuum travels at a speed of 3.00 x 10 e8 m/s. If Pluto was 3.6 billion miles ( 3.6 x 10 e 9 mi) from the sun, how many minutes would it take sunlight to reach Pluto?

7-A recent television commercial advertised the sale of gold coins that were actually buffalo nickels clad in 12 mg of nearly 100% of gold. For the unbelievable low price of only $ 9.95 you can own one of these treasured pieces of gold normally sold for over $50.00! Calculate the actual value of the coin (i.e. the value of the gold present, plus the face value of the coin- ignoring any added historical numismatic value that a buffalo nickel may warrant.) The market price of gold is given in troy ounces where 1 troy ounce+ 31.1g.

Solution Summary

A dimensional analysis, distance, density, speed and values are examined in the solution.

Questions:
1. If the sun which is 93,000,000 miles away away from Earth was to go out, how long would it take for us to know that this had happened? Light travels at a speed of 3 x 10^8 meters/second.
2. What would the density be (in g/cm^3) of a block that is 4 cm by 15 cm by 12 cm, and has a mass of 4.3 kg?
3. An ob

We would like to know the nature of the drag forces experienced by a sphere as it passes through a fluid. The sphere has a low speed. Therefore, the drag force is highly dependent on the viscosity of the fluid. The fluid density is to be neglected.
a) Use dimensional analysis to develop a model for drag force: F (MLT^-2) as a

Determine the specific gravity of spherical particles, D=(1/200 in), which drop through air at 33degrees F at a speed U of 0.3 ft/s. The drag force on a small sphere in laminar motion is given by 3(pi)(mu)DU.
This problem is in Fluid Mechanics by Victor Streeter.

Which of the following sets of equations represent possible cases of two-dimensional flow with constant density?
a) u=x+y; v=x-y
b) u=x+2y; v=x^2-y^2
c) u=4x+y; v=x-(y^2)
d) u=x*t+2y; v=x^2-y*(t^2)
e) u=x*t^2 ; v=x*y*t+y^2

Using dimensional analysis, which one of the following equations is
(a -> m/^2, v -> m/s, x -> m , t -> s)
a. x = v/t
b. v = 2ax
t2 = x/a
c. x2 = 2av
d. x = at

Consider the normal modes of a vibration under uniform tension of a stretched string consisting of two sections of unequal mass density, so that the wave speed differs from one section to the next.
a. What conditions must be satisfied by the string displacement at the junction of the two sections?
b. Suppose that the mass de

You travel from point A to point B and back again. You travel back and forth using the identical path. Your average speed going from A to B is v1 and your average speed from B to A is v2. In term of v1 and v2 only, what is your average speed for the entire trip back and forth?

Two cars lost in a blinding snowstorm are traveling across a large field, each thinking they are on the road, as shown in the figure on the left. They collide. If the distance x is 124 meters and the red car is travelling at 12.7 mph, how fast to the nearest hundredth of a mph was the blue car travelling? 10.37 mph? How do I fig

Suppose that a particle, starting at the origin, has an equal chance of moving to the left or right by a distance ∆x in a time interval of ∆t.
(a) Let n>0 be an integer, and let m be an integer, such that -n≤m≤n and n-m is even. By computing the number of ways that the particle can move a net distance