Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that were in Archimedes' bathwater that day, because water doesn't get created or destroyed on a large scale. It follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. In the more than two thousand years since his discovery, the water molecules from Archimedes' bathwater have been through this cycle enough times that they are probably about evenly distributed throughout all the water on the earth. When you buy a can of soda, about how many molecules from that famous bathtub of Archimedes are there in that can?

Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3 times 10^5, enter 5. If your estimated answer is 8.7 times 10^5, you should enter 6 (rounding up to the next power of 10).

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Suppose that the water that was in Archimedes' bathwater is indeed evenly distributed throughout all the water on the earth. If you denote by N the total number of water molecules on earth, and by N_arch the number of water molecules that were in Archimedes' bathwater, then the fraction of water molecules in some arbitrary sample of water that had been in Archimedes' bath is:

f = N_arch/N

If you multiply the numerator and the denominator by the mass of a single ...

A force is applied to the end of a 2ft long uniform board weighing 50lbs, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30 degrees, the magnitude of the applied force F is...
a. 28.9lb
b. 50lb
c. 100lb
d. 57.7 lb

A 509 kg uniform solid sphere has a radius of 0.409 m. Find the magnitude of the gravitational force exerted by the sphere on a 50.9 g particle located
(a) 1.48 m from the center of the sphere
_______ N
(b) at the surface of the sphere
_______ N
(c) 0.206 m from the center of the sphere
_______ N

The acceleration of point G has a magnitude of 15m/s^2 and is in the x direction. Point G is the center of the dis. The radius of the disk is R=0.5m and the instant shown theta=45 degrees and the angular speed of the disk is 7rad/s. Determine the magnitude of the angular acceleration of the disk.
See attached file for more inf

The oscillation frequencies of a diatomic molecule are typically 10^12hz-10^14Hz. Derive in order of magnitude estimate for the harmonic oscillator constant K for such molecules.
I need to know how to do this for a test tomorrow. So detailed solutions please.

Vector b has magnitude 7.1 and direction 14 degrees below the +x-axis.
Vector c has x-component cx = -1.8 and y-component cy=6.7.
Compute:
A) the x and y components of b;
B) the magnitude and directions of c;
C) the magnitude and direction of c + b(resultant)?

3. (TCO B) You have been requested to provide a contingency estimate for a project involving the manufacturing of a new television. You are provided with the following component and labor estimates, together with the type of estimate:
Description Estimated base cost Type of estimate
Plasma S

An electron e= 1.6*10^-19C, m= 9.1*10^-31kg is accelerated through a potential difference of 2kV. It then passes into a magnetic field perpendicular to its path, where it moves in a circular arc of diameter 0.36m.
1.) What is the magnitude of the velocity of the electron in a magnetic field?
2.) What is the magnitude of t

Please provide formulas and step by step instructions on how to solve.
A Vector F has a magnitude of 20 and is directed vertically downward. Find is components Fx and Fy in each of the coordinate frames.
Please see attached.

Please do not include your response in a .pdf format, but Word documents are okay. Thanks!
Here is the actual problem:
A 1000 kg car pushes a 2000 kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N.
(a) What is the magnit

An 85-kg jogger is heading due east at a speed of 2.0 m/s. A 55-kg jogger is heading 32° north of east at a speed of 3.0 m/s. Find the magnitude and direction of the sum of the momenta of the two joggers.