5. Consider the earth to be a sphere of radius 6370 km. (a) Express the coordinates...

5. Consider the earth to be a sphere of radius 6370 km. (a) Express the coordinates of Jacksonville and Los Angeles in spherical coordinates if the z-axis points from the center of the earth towards the north pole and the x-axis crosses the 0-deg longitude. (b) Find the straight line distance between these two cities and (c) the distance between the two cities along the surface of the earth 'as the crow flies'.

Expert Solution

Colby Messinger answered 1 day ago

A circular rock 5 km in radius hits the earth head-on, at speed 36 km/s. The...

A circular rock 5 km in radius hits the earth head-on, at speed 36 km/s. The rock's density is 3 g/cm3. The earth's mass is 6*1024 kg. Treating the earth as initially stationary, calculate its final in speed due to the impact. Because of the system's trouble with small numbers, calculate the speed in μm/s -- the distance unit is the micron or micrometer, 10-6 meter. I am so confused on where to start, like is the rocks density m2...

A solid is bounded by the sphere centered at the origin of radius 5 and the...

A solid is bounded by the sphere centered at the origin of radius 5 and the infinite cylinder along the z-axis of radius 3. (a) Write inequalities that describe the solid in Cartesian coordinates. (b) Write inequalities that describe the solid in cylindrical coordinates. (c) Why is this solid difficult to describe in spherical coordinates? Which of the variables ρ, θ, φ are difficult to describe? Explain.

A tank has the shape of a sphere with a radius of 5 m. It is...

A tank has the shape of a sphere with a radius of 5 m. It is filled with water up to 9 m. (i) Let x be the height in meters measured from the bottom of the tank. The weight in Newtons of a thin layer of water between x and x + Δx is approximately P (x) Δx. What is P (x)? P (x) = Express the answer by a formula. Recall that the density of water is ρ...

(5) Describe the consequences of a 10-km asteroid striking Earth?

Consider a particle which is constrained to move along the surface of the sphere of radius...

Consider a particle which is constrained to move along the surface of the sphere of radius 5, centered at the origin. (a) If we write r(t) for the motion, write down the condition ‘constrained to move along the surface of the sphere of radius 5 centered at the origin’ in terms of r(t). (Hint. For later use, try to get rid of square roots.) (b) Explain why, for such a motion, we must have r 0 (t) ⊥ r(t). (Hint....

A sphere with radius a = 8 cm is in a conductive sphere shell with an...

A sphere with radius a = 8 cm is in a conductive sphere shell with an internal radius of b = 12 cm and an outer radius of c = 18 cm with a load of -200 mC. a) Determine the load distribution in the sphere and sphere shell. b) Calculate the value of the electric field in r = 0 cm, r = 4 cm, r = 8 cm, r = 10 cm, r = 14 cm, r =...

Consider a conducting hollow sphere with radius R that is placed in a homogeneous electric field...

Consider a conducting hollow sphere with radius R that is placed in a homogeneous electric field E_0 = E_0 e_z a) Calculate the electrostatic potential φ_0(r) for the homogeneous electric field E_0= E_0 e_z only and write the result in spherical coordinates. b) Assume that the sphere is grounded i.e. put the potential φ(R)=0 and calculate the electrostatic potential φ(r)=0 inside and outside the sphere. Hint: Consider that the electrostatic potential far away from the sphere should just give rise...

Consider a hollow, infinite sphere of radius R. the hollow space is free of charge, but...

Consider a hollow, infinite sphere of radius R. the hollow space is free of charge, but a surface charge sigma = sigma not cos theta exists on the inside surface of the conductor at s =R. Can this sphere be a conductor? ( I.e, can you induce this charge on a conducting surface somehow)

1.Consider a satellite of the earth in a circular orbit of radius R. Let M and...

1.Consider a satellite of the earth in a circular orbit of radius R. Let M and m be the mass of the earth and that of the satellite, respectively. Show that the centripetal acceleration of the satellite is aR = -(v^2/R)*(r/r) where v = |v| is the magnitude of the velocity V and r/r is a unit vector in the radial direction. 2.Using Newton's second low of motion and the law of universal gravitation, determine the speed v=|V| and the...

Consider a cylinder of radius R = 1000 km and, for our purposes here, infinite length....

Consider a cylinder of radius R = 1000 km and, for our purposes here, infinite length. Let it rotate about its axis with an angular velocity of Ω = 0.18◦/s. It completes one revolution every 2000 s. This rotation rate leads to an apparent centrifugal acceleration for objects on the interior surface of Ω2 R equal to 1 g. Imagine several competing teams living on the interior of the cylinder, throwing water balloons at each other. (a) Show that when...

Question