Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 1, Problem 44P
To determine
The combination of factors which will give correct dimension for period of planet.
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Schwarzschild radius RS of a black hole is the maximum
distance from the black hole’s center at which light cannot escape its
gravitational field. The quantity RS (with dimensions of length) is
dependent on the mass of the black hole M, the speed of light c, and
the gravitational constant G. Based on the dimensions of these four
parameters, predict an equation for the Schwarzschild radius. Hint:
G has dimensions of [L3/MT2]
When you are at a height x above the surface of the earth, your weight can be found by the following formula:
W(x) = mg (1 + x/R) −2 ,
where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth.
For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere).
In this question, we will approximate W(0) and W(R).
(a) Find L0(x), the linear approximation of W(x) at x = 0.
(b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
(c) Find LR(x), the linear approximation of W(x) at x = R.
(d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon's orbit increases by 3.84×106 m (1%)?
Chapter 1 Solutions
Physics for Scientists and Engineers
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