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

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.

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

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

Ryan starts jogging home at the rate of 6km/hr. After reaching Harbor Front, he begins jogging back home. Because of fatigue, his speed for the return trip decreases to 4.5km/h and takes 1 hour longer. Determine the total distance that Ryan jogged.

Please see attached file for full problem description.
1. The thickness h of a puddle of water on a waxy surface depends on the density ρ of the liquid, the surface tension γ (SI units: N/m) and another physically which is gravity, g. Use dimensional analysis to find a relationship between the thickness and the other 3 vari

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.
(a) At what rate is his distance from second base decreasing when he is halfway to first base?
(b) At what rate is his distance from third base increasing at the same moment?

A fisherman notices that wave crests pass the bow of his anchored boat every 4.0seconds. He measures the distance between two crests to be 9.0 m. How fast are the waves traveling?
**please explain this in the simplest, least confusing way....thank you so much :)

A uniform rope of mass m and length L hangs from a ceiling.
(a) Show that the speed of a transverse wave in the rope is a function of y, the distance from the
lower end, and is given by v = Sqrt(gy).
(b) Show that the time it takes a transverse wave to travel the length of the rope is given by t =
2sqrt(L/g). (Hint: calculat