a knight is trying to scale the castle wall using a ladder the mass of the knight is 73.1 kg the ladder is 2.50m long and has a mass of 8.50 kg the wall is frictionless but the coefficient of static friction between ladder and the ground is 0.250 the ladder makes an angle of 53.1 degrees with the horizontal when placed against the castle wall how far up the ladder can the knight wall before the ladder slips what is the magnitude of the force of the wall on the ladder what is the magnitude of the force of the ground on the ladder

consider Three-Dimensional harmonic oscillator with the same frequencies along all three directions. a) determine the wave function and the energy of the ground state. b) how many quantum numbers are needed to describe the state of oscillation? c) the degeneracy of the first excited state. express the wave function involved in the schrodinger equation as a product given by x, y, z and separate the variables.

write down the semi classical distribution function for phonons based on boltzmann distribution

TABLE 2. ROTATION DATA FOR THE ANDROMEDA GALAXY

Fill in blanks please

einstein model take that in solid state, there are 3N normal mode vibration that all have the same mode frequency of ω0. the density of states σ(ω) for this model is

σ(ω) = δ(ω − ω0) .

a. with the given information, and by neglecting the zero point energy, calculate the total energy and the heat capacity Cv in this solid state model.

b. when the temperture is high, show that Cv → 3N kB. this value is often called Dulong-Petit value.

At starbase Faraway Point, you observe two spacecraft approaching from the same direction. The Picard approaches starbase Faraway Point with a speed of 0.806 c, and the La Forge approaches the starbase with a speed of 0.918 c. Suppose the Picard now launches a probe toward the starbase.

What velocity must the probe have relative to the Picard if it is to be at rest relative to the La Forge?

What velocity must the probe have relative to the Picard if its velocity relative to the La Forge is to be 0.100c?

For the situation described in part B, what is the velocity of the probe relative to the Faraway Point starbase?

Faraway Point starbase launches a probe toward the approaching starships. The probe has a velocity relative to the Picard of -0.918 c. The Picard approaches starbase Faraway Point with a speed of 0.806 c, and the La Forge approaches the starbase with a speed of 0.918 c. What is the velocity of the probe relative to the La Forge?

What is the velocity of the probe relative to Faraway Point starbase?

A 500 lines per mm diffraction grating is illuminated by light of wavelength 620 nm .

Part B

What is the angle of each diffraction order?

Enter your answers using two significant figures in ascending order separated by commas.

In this example we will see that time dilation is a rather small effect for reference frames in which u≪c. An airplane flies from San Francisco to New York (about 4800 km, or 4.80×106m) at a steady speed of 300 m/s (about 670 mi/h) (Figure 1). How much time does the trip take, as measured (a) by observers on the ground and (b) by an observer inside the plane?The π+ meson (or positive pion) is an unstable particle that has a lifetime (measured in its rest frame) of about 2.60×10−8s. If the particle is moving with a speed of 0.992 c with respect to your laboratory, what is its lifetime as measured in the laboratory?

A person takes 15 minute showers in 100°F water using a 2.0 gallon per minute shower head. Ignoring losses, how many cubic feet of natural gas did the shower need if the house has a 40,000 BTU/hour water heater? The incoming water temperature is 50°F. Is it possible for this person to complete this shower without the water temperature dropping?

Consider a system of four nonidentical spin 1/2 particles. Find the possible values of the total spin of this system and state explicitly the number of angular momentum eigenstates for each of the total spin values.

An ideal flow can be described by a velocity potential . What does express? Illustrate (choose your own flow example) how you with help of the velocity potential and equipotential lines can find the flow direction and if the flow velocity increase, is constant or decrease

Two point charges lie on the x axis. A charge of + 2.50 pC is at the origin, and a charge of − 4.70 pC is at x=−12.0cm. What third charge should be placed at x=+24cm so that the total electric field at x=+12.0cm is zero?

Two people start at rest from the same point on a circular track of radius R = 20 m. Person #1 runs counterclockwise around the track with a con- stant angular acceleration of α1 = 0.0010 rad/s2. At the same time, Person #2 runs clockwise around the track with a constant angular acceleration of α2 = 0.0025 rad/s2. Determine the speed of each person when they meet for the first time after they start running.

I know from the class to start by finding time when they meet using |θ1| + |θ2| = 2π   yielding 1/2 α1(T)^2= 1/2 α2 (T)^2

can you please solve this problem

Also explain why |θ1| + |θ2| = 2π and

Where this equation come from 1α1T2 + 1α2T2 = 2π