A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge −q on the outer spherical shell. Take V to be zero when r is infinite.

Calculate the potential V(r) for r<r a .

Calculate the potential V(r) for ra<r<rb

Calculate the potential V(r) for r>rb

Find the potential of the inner sphere with respect to the outer.

Use the equation Er=−∂V∂r and the result from part (b) to find the electric field at any point between the spheres (ra<r<rb).

Use the equation Er=−∂V∂r and the result from part (c) to find the electric field at a point outside the larger sphere at a distance r from the center, where r>

A bicycle wheel has a diameter of 63.0 cm and a mass of 1.74 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 8.99-cm-diameter sprocket in order to give the wheel an acceleration of 4.49 rad/s²?
N

(b) What force is required if you shift to a 5.70-cm-diameter sprocket?
kN

Captin Kirk has been forced to take the Enterprise to the center of the galaxy, which is approximately 26000 light-years from the Earth, but the warp drive is broken so that the ship will be limited to speeds loss than that of light.

1. what force would it take to accelerate such a mass at 1.0g(9.8m/s^2) to its final velocity , and how long would this take , starting from v=0?

2. what would the wavelength, frequency, and color of gamma-ray photons emitted by the ship headed back towards the Earth look like on Earth if emitted at a wavelength corresponding to the highest ever observed in real life for gamma rays in natural radiation?

3. If the Enterprise slows down to o.4c and fires torpedoes at 0.5c at a Klingon vessel approaching it at 0.3c then how fast are those torpedoes approaching the Klingons, from their perspective?

Body A in the figure weighs 92 N, and body B weighs 71 N. The coefficients of friction between A and the incline are μs = 0.51 and μk = 0.22. Angle θ is 39°. Let the positive direction of an x axis be up the incline. What is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline?

You find a long spring and decide to create some standing waves. You note that the spring has an unstretched length of 2.0 m and a weight of 20.0 N. You anchor one end of the spring to a pold and stretch it to a length of 10.0 m. You shake the spring up and down with a period of .250 s, creating a standing wave with 4 antinodes. What is the horizontal force with which you are pulling the spring?

Attempt 4 A uniform, solid sphere of radius 5.50 cm and mass 1.25 kg starts with a purely translational speed of 3.25 m/s at the top of an inclined plane. The surface of the incline is 2.50 m long, and is tilted at an angle of 34.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed ?2 at the bottom of the ramp.

A 1830-kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 34.5 m/s. Going up a hill, the car's engine needs to produce 74.7 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?

1.Which of the following is a consequence of Special Relativity?

QUESTION 2

2.What is a possible application of the principle of equivalency from General Relativity?

QUESTION 3

If you could turn any of the planets in our solar system into a black hole, which would produce the black hole with the largest radius

You might have seen sunglasses that change to a color when exposed to light, while revert to transpaparency when the light is blocked or dimmed. Thematerical used to make the glasses is called photochromic material that has light sensitive components inside. The technology is similar to that used to make a photographic film.

(a) Explain, using necessary chemical formula, the working principle of photochromic sunglasses.

(b) The color of the photochromic sunglasses is reversible, however, the image on a photographic film once exposed and developed, is fixed and becomes irreversible. Why?

The ground temperature a few meters below the surface is fairly constant throughout the year, and is near the average value of the air temperature. In areas in which the air temperature drops very low in the winter, the exterior unit of a heat pump designed for heating is sometimes buried underground in order to use the earth as a thermal reservoir. Why is it worthwhile to bury the heat exchanger, even if the underground unit costs more to purchase and install than one above ground?

A 0.18 kg puck is initially stationary on an ice surface with negligible friction. At time t = 0, a horizontal force begins to move the puck. The force is given by F→=(15.0-3.94t2)î, with F→ in newtons and t in seconds, and it acts until its magnitude is zero. (a) What is the magnitude of the impulse on the puck from the force between t = 0.560 s and t = 1.79 s? (b) What is the change in momentum of the puck between t = 0 and the instant at which F = 0?

A 0.00618-kg bullet is fired straight up at a falling wooden block that has a mass of 1.52 kg. The bullet has a speed of 616 m/s when it strikes the block. The block originally was dropped from rest from the top of a building and had been falling for a time t when the collision with the bullet occurs. As a result of the collision, the block (with the bullet in it) reverses direction, rises, and comes to a momentary halt at the top of the building. Find the time t.

TYPE WRITTIN PLEASE !!!

WHAT IS UNUSUAL ABOUT THE DISCOVERY OF URANUS ?

A truck accelerates uniformly from rest to 19.5 m/s in 5.3 s along a level stretch of road. Determine the average power required to accelerate the truck for the following values of the weight (ignore friction).

(a) 1.00x10^4 N

(b) 1.20 x10^4 N

A student stands several metres in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is 75.0 cm long, has a mass of 2.25 g, and is under a tension of 400 N. A second student, moving towards the wall, hears 8.30 beats per second. Determine:

a. frequency of sound produced by the wire;

b. the speed at which the second student approaches the wall.