(Go go gadget problem solver!) Joe, Bill, and Fred are playing a game with marbles at the top of an uncarpeted (wooden) staircase. They decide to try to roll their marbles off the top step and see how many steps the marble will skip before hitting. The faster they roll the marbles, the farther down the staircase the marble will go before hitting a step. Suppose one of these marbles leaves the floor at the top of the staircase at 2.54m/s. Each stair is 20.0cm tall and 20.0cm deep. Which stair will the marble hit first? Clearly label your answer on a picture/sketch. [Hint, you don

A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.8 m/s at ground level. The engines then fire, and the rocket accelerates upward at 4.20 m/s2 until it reaches an altitude of 980 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of ?9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.)

(a) For what time interval is the rocket in motion above the ground? s

(b) What is its maximum altitude? km

(c) What is its velocity just before it hits the ground? m/s

An ideal gas with ?=1.4 occupies 3.0L at 300 K and 100kPapressure and is compressed adiabatically until its volume is 2.0 L. It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to state A.

Part A

Find the net work done on the gas.

Express your answer using two significant figures.

Part B

Find the minimum volume reached.

Express your answer using two significant figures.

A jet with mass m = 10⁵ kg jet accelerates down the runway for takeoff at 1.8 m/s².

1) What is the net horizontal force on the airplane as it accelerates for takeoff?

2) What is the net vertical force on the airplane as it accelerates for takeoff?

3) Once off the ground, the plane climbs upward for 20 seconds. During this time, the vertical speed increases from zero to 29 m/s, while the horizontal speed increases from 80 m/s to 92 m/s.

4)What is the net vertical force on the airplane as it climbs upward?

5) After reaching cruising altitude, the plane levels off, keeping the horizontal speed constant, but smoothly reducing the vertical speed to zero, in 16 seconds.

What is the net horizontal force on the airplane as it levels off?

6)What is the net vertical force on the airplane as it levels off?

A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire) as shown in the figure(Figure 1) . The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (say 0.90 g) is to be felt?

An alpha particle with kinetic energy 15.0MeV makes a collision with lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude L=p0b, where p0 is the magnitude of the initial momentum of the alpha particle and b=1.30

3.

Two 2.20-?C point charges are located on the x axis. One is at x = 1.57 m, and the other at x = -1.57 m. Determine the magnitude of the electric field on the y axis at y = 0.530 m. Answer in units of N/C.

4.Three identical point charges of charge q = 7.3 ?C are placed at the vertices (corners) of an equilateral triangle. If the side of triangle is a = 5.2m, what is the magnitude, in N/C, of the electric field at the point P in one of the sides of the triangle midway between two of the charges?

5.Four charges are placed at the corners of a square. If q₁ = 44.0 x 10^-9 C, q₂ = -24.0 x 10^-9 C, q₃ = 26.0 x 10^-9 C, q₄ = -46.0 x 10^-9 C and the side of the square is a = 0.32 m. What would be the magnitude of the electrical field in the middle of the square? Answer in units of N/C.

Two in-phase loudspeakers are located at (x,y)coordinates (?3.0m,+2.0m) and (?3.0m,?2.0m). They emit identical sound waves with a 2.0 m wavelength and amplitude a.

Determine the amplitude of the sound at the five positions on the y-axis (x=0)

a)with y=0.5m

b)with y=1.0m

c)with y=1.5m

d)with y=2.0m

The usual way to model a vibrating membrane is by using the wave equation. Is it possible to do that from "within"? Probably the answer is yes, but where can I see it done explicitly. What I mean is can we model the membrane as a two dimensional Riemannian manifold without any specific embedding in R3 plus equations involving the metric (or form, tensors etc.) such that at any time it is isometric to the surface given by the graph of the function satisfying the wave equation at that time. Higher dimensional generalizations are also interesting.   

I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.

Problem 4.49

Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15 ?   . The sand enters a pipe h = 3.2m below the end of the conveyer belt, as shown in the figure (Figure 1) .

Part A

What is the horizontal distance d between the conveyer belt and the pipe?

Express your answer to two significant figures and include the appropriate units.

If our universe comes from a flux compactification of string theory over 6 dimensions with a nonzero flux, then it can't be continually deformed to another compactification with zero flux as the total flux is a topological invariant. The cosmological constant of our universe is positive, which in string theory means it is a metastable state. The stable vacuum for a flux compactification in string theory is a BPS compactification with negative cosmological constant.

What if our metastable observable universe is actually embedded in a larger stable anti de Sitter background? An inflating metastable or slowly rolling or chaotically inflating patch of this asymptotically AdS universe inflates to our observable universe. By the AdS/CFT correspondence, our universe can be described by a superconformal field theory in 2+1D with no gravity.

Is there any flaw in my reasoning?

As I hope is obvious to everyone reading this, the universe contains more matter than antimatter, presumably because of some slight asymmetry in the amounts of the two generated during the Big Bang. This raises the question of whether there are any processes short of the Big Bang that produce more matter than antimatter. That is, is there any known process where a particle collider (or whatever) would convert some energy into matter not through the production of particle-antiparticle pairs but through some process that produced more matter than antimatter? This doesn't need to be restricted to current accelerators-- if there's some mechanism for this that requires impractically high energies, but is based on solid theories (i.e., the Standard Model or straightforward extensions thereof), that would be interesting, too.

I'm fairly certain that the answer is "no," because I know that the matter-antimatter asymmetry is related to CP violation, and I also know that existing measurements of CP violation are not enough to explain the asymmetry. If there were a known way to slam protons together and make more quarks than antiquarks, I wouldn't expect this to still be a mystery. My particle physics knowledge is far from comprehensive, though, so it can't hurt to ask.

(I was briefly confused into thinking that there was such an experiment a while back, but it turned out to just be sloppiness about marking the antiquarks on the part of the people writing about it...)

(This is another question prompted by the book-in-progress, on relativity, this time a single word: I wrote that matter created from energy in particle physics experiments is "generally" in the form of particle-antiparticle pairs. Then I started wondering whether that qualifier was really needed, and thus this question.)

Stop me if i'm wrong but displacement is, for example, when you enter a bathtub the water level rises around you.

What happens when displacement isnt possible?

I'll give an example. I have two blocks off steel, one at the top of a chamber and one at the bottom. there is a gap between the two blocks that is filled with water. There is NO gap between the two blocks and the side of the chamber (the water cannot escape)

What happens when the two block come together, in effect squashing the water? where does the water go?

Very unintuitive observation:

I pour myself a Guinness and the bubbles in my glass seem to move down toward the bottom of the glass instead of rising directly to the top of the glass as foam.

How can this be explained? Why is it that I observe this behavior drinking Guinness and not other carbonated drinks? What system properties (ie, temperature, nature of the solute and solvent) would affect this behavior?