It is a law of physics that the gravitational force exerted by the Earth on an o

Question

It is a law of physics that the gravitational force exerted by the Earth on an object above the Earth's surface varies inversely as the square of its distance from the Earth's center. Thus, an object's weight w(x) is related to its distance x from the Earth's center by a formula of the form w(x) = k/(x^2) where k is a constant of proportionality that depends on the mass of the object.

a) Use this fact and the assumption that the Earth is a sphere of radius 4000 miles to obtain the formula for w(x) in Example 4.

b) Find a formula for the weight w(x) of a satellite that is x mi from the Earth's surface if its weight on Earth is 6000 lb.

c) How much work is required to lift the satellite from the surface of the Earth to an orbital position that is 1000 mi. high?

Explanation / Answer

you might find this helpful too!

1) w(x)= k/((x+4000)^2)

2) if weight at 4000 miles is 6000 lb then weight at x miles is:

w(x) = 6000*(4000^2)/((x+4000)^2) lb

3) work done = integrating from 4000*5280feet to 5000*5280 feet (k/x^2 dx)

= -1*k* x^-1 = k (3.7878787878787878787878787878788e-8 - 4.7348484848484848484848484848485e-8

=> work done = k* 9.469696969696969696969696969697e-9 foot pound

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.