Question

In: Math

a. Suppose the earth were wrapped tightly in a 25,000 mile belt. Now suppose someone adds...

a. Suppose the earth were wrapped tightly in a 25,000 mile belt. Now suppose someone adds 1 mile to the belt. If the belt is raised uniformly above the earth’s surface, how high above the surface will it be? Give your answer in feet. (Guess first, before you calculate this.)

b. This time, suppose someone adds 1 foot to the belt. Again, raise the belt uniformly above the earth’s surface—how high will the belt be? Give you answer in inches.

c. Finally, suppose a regulation NBA basketball is wrapped tightly in a 29.5 inch belt. Now suppose someone adds 1 foot to the belt. If the belt is raised uniformly above the ball’s surface, how high will it be? Give your answer in inches. Are you surprised by this result?

Expert Solution

Ans:

a) Length of the belt = 25000 mile

which is also equal to the circumference of the earth

Therefore we can find out the radius of the circle as shown below

Now when 1 mile is added to the belt the new circumference of the belt will be = 25001 mile

Therefore the new radius of the belt will be given by

Therefore the difference between the two radii is the height by which the belt will rise above the surface

b) In this case 1 foot is added to the belt

Now 1 foot = 0.000189394 miles

There the new radius will be

Therefore the height of the belt above surface is

c) Now here total length of the belt = 29.5 inch

Therefore the radius of the ball is

Now 1 foot is added to the belt

1 foot = 12 inch

Therefore new length of the belt = 29.5+12=41.5

Therefore new radius of the ball is

Therefore the height of the belt from surface is

As the diameter of the ball is very small compared to the diameter of the earth the little increase in the length of the belt results in more increase in height of the belt above the surface as compared to the case of earth.

milcah answered 1 year ago

Suppose that an asteroid traveling straight toward the center of the earth were to collide with...

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. What would have to be the mass of this asteroid, in terms of the earth's mass M , for the day to become 26.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform...

Suppose the Earth were a 0.10 Mʘ companion star to the Sun, but still orbiting with...

Suppose the Earth were a 0.10 Mʘ companion star to the Sun, but still orbiting with a semi-major axis of 1 AU about the real Sun. What would some alien astronomer measure the spectral line splitting width to be of the blue-green (λ=490 nm) line in the Hydrogen spectrum of the Sun? Express your answer in units of nm

1. Now suppose that a new technology were created that lowers the costs of production, graphically...

1. Now suppose that a new technology were created that lowers the costs of production, graphically illustrate and explain the changes that arise in the short-run and long-run within a perfectly competitive industry. Please show all the work with the steps, please.

Suppose you think if you were to retire right now you would have needed $50,000 each...

Suppose you think if you were to retire right now you would have needed $50,000 each year to supplement your social security and maintain your desired lifestyle. But because there is on average 3% annual inflation, when you retire in 30 years from now you need more than $50,000 per year to maintain the lifestyle you like. How much will be equivalent to $50,000 at the retirement time when adjusted for inflation? How much will be the face value of...