At launch a rocket accelerates upward at a=2g. After 12 seconds the rocket runs out of fuel and enters freefall.

a.) Determine the rocket's maximum height.

b.) How long after take off does the rocket crash to the ground?

Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values for the coupling constants characterizing the unperturbed model, which presumably, is relatively easy to solve. We also assume the family of models transform smoothly under the coupling constants. Then, we perform a Taylor series analysis.

But what if the landscape of valid quantum gravity models is discrete? Even though superstring theory admits a dilaton modulus over 10 uncompactified dimensions, what about the landscape of models we get after compactifying 6 spatial dimensions with nonzero fluxes and some branes, and maybe some orbifolding? We still have moduli when supersymmetry remains unbroken, but what about the metastable states where SUSY is broken? What is the Taylor series of a Dirac delta function?

What about perturbation theory from the perspective of path integrals? With path integrals, the Wheeler-DeWitt constraint shows up in a different guise as a projection operator. We start off with some wavefunctionals, and then take the functional integral over some finite time interval T. In the limit as T goes to infinity, we are left with a projection operator singling out WDW solutions. But what happens when we interchange the order in which we take the limit of the coupling constant going to zero, and T going to infinity? If the spectrum of the Hamiltonian constraint is discrete, and varies with the coupling constant, such an interchange won't be valid! This is a fancy way of saying for most choices of coupling constants, the projection operator is zero.

There has been some heated debate as to whether the laws of physics allow for traversable wormholes. Some physicists claim we require exotic matter to construct wormholes, but then others counter the Casimir effect with ordinary matter is sufficient. But these same physicists seldom come up with an explicit solution or state of ordinary matter keeping the throat of a wormhole open via the Casimir effect. Yet others claim with extra dimensions, a Gauss-Bonnet interaction is sufficient to keep the wormhole throat open, but opposing physicists claim such a term can't arise from string theory.

So, my question is, do traversable wormholes exist as solutions to string theory?

Am I correct it remembering that unless a pulsars beams plane faces earth we can not detect them. And that similarly inbetween the pulses we can't see them either?

If so how does this differ from dark matter? Isn't it possible that there are a lot more pulsars that we just can't see them because they are pointing the wrong way.

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate the component of the weight parallel to the plane. I also want to find out the weight component perpendicular to the plane.

I don't want an outright answer, more of an explanation to help me understand. Thanks!

Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. The charges of each marble are q₁ = 5.95

A dipole lies on the y axis and consists of an electron at y1 = 0.50nm and a proton at y2 = -0.50nm .

Part A

Find the electric field midway between the two charges.

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

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Part B

Find the electric field at the point x = -1.5nm , y = 0.

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

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Part C

Find the electric field at the point x = -26nm , y = 0.

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

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(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