At one point in a pipeline the water's speed is 3.00 m/s and the gauge pressure is 5.00××1044 Pa.

Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

Express your answer in kilopascals.

Optimization of a cylinder container with a height of 4 inches and a radius of 1.25 inches in terms of either volume OR surface area.

Please provide:

(A) Calculation of surface area/volume of the container.

(B) Primary and secondary constraint equations

(C) Derivative of primary equation

(D) Optimized dimensions and how they were determined (number-line analysis to show that the dimensions result in an optimized solution.

(E) Graph of optimization (in terms of volume OR surface area in terms of the radius) marking the optimized value, as well as the actual value based on the actual radius.

(F) Comparison of your results with the container’s actual. In other words, if you chose to optimize the volume, then show: Optimized volume-Actual volume/Actual volume×100% which shows the additional percentage of volume your optimized container holds. If you chose to optimize the surface area, then show: Actual surface area- Optimized surface area/Actual surface area×100 which shows the reduced percentage of surface area your optimized container has.

The activity of a radioactive sample is the number of decays per minute that occur in the sample. We measured this by detecting the radiation entering the Geiger tube window. Explain why our readings were actually only a small fraction of the actual activity. Also, why did that not seem to matter in the determination of Barium-137m’s half-life? Refer to either your A vs. t or your ln A vs. t graph in your explanation.

A model rocket is fired from the ground in a parabolic arc. At the very top of the arc, at a horizontal displacement of 260 m from the launch point, an explosion occurs within the rocket, breaking it into two fragments which separate from each other. One fragment, having 1/3 the mass of the rocket, falls straight down to Earth as if it were at rest at that moment right after the explosion.  Determine the total horizontal displacement from the launch point the other fragment lands.  (The two fragments land simultaneously.)

In the figure, a uniform, upward-pointing electric field E of magnitude 4.50

(a) Calculate the approximate number of protons in an African male elephant of weight 5,000 kg.

(b) Calculate the total negative electric charges in all the electrons in this African elephant (in unit of C).

Hi i really need some help on this question, can you try to explain the steps on this problem?

a) In double-slit interference experiment, path difference Δ = d sin θ. Use ray diagram and words to explain why bright spots located at where Δ = mλ and dark spots located at where Δ=(m+1/2)λ. Here m = 0, ±1, ±2, ±3, etc.

b)Use any resource you can find to study the single-slit diffraction. Explain how the diffraction pattern formed by laser light passing a single narrow slit with width w. Explain where the dark spots would located. (You should find the equation for this.) Use diagram(s) and words to explain why.

c) Explain what Babinet's principle is. Explain how you can measure the thickness of a hair using the principle of diffraction.

Light has many interesting properties. For example, light has reflection which can be understand by the image of an object in a mirror. Can you write down 5 other properties? Explain each property you listed.

How do you describe the ray pattern of light?
What is the value of the speed of light in a vacuum and in any medium?
How is the law of reflection expressed for a wave?
How is the refractive index of a medium defined?
How is Snell's law for light expressed and what is the mathematical expression?

Derive the Boltzmann distribution from first principles (maximizing weight). Why is the Boltzmann distribution so important, explain what it is and how it is used.

A statistical system is composed of N particles with spin 1 2 , immersed in a magnetic field H. The particles are fixed in their positions and possess a magnetic moment µ. The Hamiltonian of such a system is H = −µH X N i=1 σi where σi = ±1

(a) Given that the separation between the spins in the lattice is larger than their de Broglie wavelength, should the spins be treated as distinguishable or indistinguishable particles?

(b) Write down the canonical partition function, QN , for the N particles.

(c) Determine the total energy for this system at an arbitrary temperature, T.

(d) Magnetization is defined as the M = µ(N+ − N−) where N+ and N− are the average number of up and down spins, respectively. Determine M for a given temperature T.

(e) The susceptibility is defined as χ = ∂M ∂H T Find the small magnetic field limit of the susceptibility

An atom of beryllium (m = 8.00 u) splits into two atoms of helium (m = 4.00 u) with the release of 92.2 keV of energy. Suppose the beryllium atom moved in the positive x direction and had a kinetic energy of 44.0 keV. One of the helium atoms is found to be moving in the positive x direction. Find the direction of motion of the second helium, and find the velocity of each of the two helium atoms. Solve this problem in two different ways: by direct application of conservation of momentum and energy; and by applying the results if the original beryllium atom is at rest to a frame of reference moving with the original beryllium atom and then switching to the reference frame in which the beryllium is moving.

(a) by direct application of conservation of momentum and energy

(b) by applying the results if the original beryllium atom is at rest to a frame of reference moving with the original beryllium atom and then switching to the reference frame in which the beryllium is moving

On a frictionless horizontal air table, puck A (with mass 0.253 kg) is moving toward puck B (with mass 0.374 kg) which is initially at rest. After the collision, puck A has velocity 0.119 m/s to the left and puck B has velocity 0.649 m/s to the right. Part A: What was the speed vAi of puck A before the collision? Part B: Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

What characteristics should a medium in which we immerse an object and make it transparent (or invisible) to you? Explain and give at least one example.

Two identical balls, Ball A and Ball B are thrown vertically upward. Ball A is thrown with an initial speed of v, and Ball B is thrown with an initial speed of 2v. Which of the following statement is correct? Ignore air resistance.

A. The maximum heights of the two balls are equal.

B. The maximum height of the second ball is eight times that of the first ball.

C. The maximum height of the second ball is 1.41 times that of the first ball.

D. The maximum height of the second ball is four times that of the first ball.

E. The maximum height of the second ball is two times that of the first ball.