3. Refer to Ch 4, pg 132- 4 in BM. We are going to calculate the velocity of the Earth today (let’s say 7 Feb 2020) using the vis viva equation. Take a deep breath...

(a) Calculate the "mean anomaly" of the Earth M. This is the angle from perihelion to the position of Earth as if the Earth were in a circular orbit. You have to look up the perihelion of the Earth. See pg 34 in BM. This is just calculating a fraction of a circle. 1

A thin-walled metal spherical shell of radius a = 1.80 cm has a charge qa = 8.00×10-6C. Concentric with it is a thin-walled metal spherical shell of radius b = 5.20 cm and charge qb = 2.50×10-6 C.

Find the electric field at distance r = 0 cm from the common center. Tries 0/10

Find the electric field at distance r = 3.70 cm from the common center. Tries 0/10

Find the electric field at distance r = 8.90 cm from the common center. Tries 0/10

Discuss the criterion one would use to determine how the charges are distributed on the inner and outer surface of the shells. What is the charge on the outer surface of the outer shell?

An artillery shell is fired with an initial velocity of 300 m/s at 52.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 47.5 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

I intend to start making visual observations, and I want to know more about the difference between using barlow lenses and one or two eyepieces and using a complete kit of eyepieces, both for planetary and deep space objects.

. What ethical consequences did the scientists involved have to consider while working
     on the atomic bomb?

A flat cushion of mass m is released from rest at the corner of the roof of a building, at height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in the figure below. The air exerts no vertical force.

(A) Show that the path of the cushion is a straight line. (Submit a file with a maximum size of 1 MB.)

(B) Does the cushion fall with constant velocity?

(c) If m = 1.19 kg, h = 8.20 m, and F = 2.12 N, how far from the building (in m) will the cushion hit the level ground?

(D) If the cushion is thrown downward with a nonzero speed at the top of the building, what will be the shape of its trajectory?

What are the wavelength ranges for the following?

(a) the AM radio band (540–1600 kHz)

(b) the the FM radio band (88–108 MHz)

A 50 kg crate slides down a ramp that is inclined by 30 degrees from the horizontal. The acceleration of the crate parallel to the surface of the ramp is 2.0m/s^2, and the length of the ramp is 10m.

Determine the kinetic energy accumulated by the crate when it reaches the bottom of the ramp if it started from rest at the top of the incline.

Calculate the amount of energy lost by the crate due to friction in its journey down the ramp.

Compute the magnitude of the frictional force that acts on the crate as it slides down the ramp and calculate the coefficient of kinetic friction between the ramp and the crate.

About 30,000 Joules of energy is stored in a typical 1.5 volt D-cell battery. If two such batteries are joined to produce a total of 3 volts in a circuit and cause 1.2 amps of current, how long will the batteries be able to deliver power to the circuit at this level? The resistance of an electric heater is 8 ohms when connected to 120 volts, how much energy does it use during 40 minutes of operation?

A bumper car with mass m₁ = 116 kg is moving to the right with a velocity of v₁ = 4 m/s. A second bumper car with mass m₂ = 97 kg is moving to the left with a velocity of v₂ = -3 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

1)What is the velocity of the center of mass of the system?

2)What is the initial velocity of car 1 in the center-of-mass reference frame?

3)What is the final velocity of car 1 in the center-of-mass reference frame?

4)What is the final velocity of car 1 in the ground (original) reference frame?

5)What is the final velocity of car 2 in the ground (original) reference frame?

6)In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision?

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rh = 0.209 m and mass 4.51 kg, and two thin crossed rods of mass 7.80 kg each. You would like to replace the wheels with uniform disks that are 0.0588 m thick, made out of a material with a density of 5990 kilograms per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?

A boy stands on a diving board and tosses a stone into a swimming pool. The stone is thrown from a height of 2.50 m above the water surface with a velocity of 4.00 m/s at an angle of 60.0

II. Dimensions Involving Derivatives When we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding.

Part A) Consider the diffusion constant that appears in Fick’s first law: J = −D dn dx. In this expression, J represents a flow of particles (the number of particles per unit area per second), n represents a concentration of particles (the number of particles per unit volume), and x represents a distance. We can assume that they have the following dimensionalities: [J] = 1 L 2T , [n] = 1 L 3 , [x] = L.

1. What is the dimensionality of dx? Explain. (Hint: Remember from calculus that dx is just an infinitessimally small portion of x.)

2. Based on part (A), what is the general rule for the dimensionality of any differential? That is, given any physical quantity, Z, how does the dimensionality of dZ compare to that of Z?

3. Given any two physical quantities, Y and Z, what is the dimensionality of the derivative dY dZ in terms of [Y ] and [Z]?

Part B) Einstein discovered a relation that expresses how D depends on the parameters of the system: the size of the particle diffusing (R), the viscosity of the fluid it is diffusing in (η), and the thermal energy parameter (kBT). Assume that we can express D as a product of these three quantities to some power, like this: D = (kBT) a (η) b (R) c .

1. Rewrite the equation above in terms of M, L, and T, by substituting in your answer for the dimensionality of D from question 4 above, and the dimensionalities of the other constants, which are: [kBT] = ML2 T

2 , [η] = M LT , [R] = L 2. By “balancing” M, L, and T on each side of the expression above, determine three equations in terms of a, b, and c that will guarantee that D will have the correct dimensionality.

3. Solve these equations and write an expression for how D depends on the three parameters. (The correct equation has a factor of 1/6π that cannot be found from dimensional analysis.)

A positive point charge Q1=2.8×10−5C is fixed at the origin of coordinates, and a negative point charge Q2=−4.1×10−6C is fixed to the x axis at x=+2.0m. Find the location of the place(s) along the xx axis where the electric field due to these two charges is zero.

. How does the appearance of the diode change when the maximum voltage is above or below the threshold