A plumb bob ( a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). ( a ) Find an approximate formula for 6 in terms of the mass of the mountain, m M , the distance to its center, D M , and the radius and mass of the Earth, ( b ) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m 3 . ( c ) Estimate the angle θ of the plumb bob if it is 5 km from the center of Mt. Everest. FIGURE 6-30
A plumb bob ( a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). ( a ) Find an approximate formula for 6 in terms of the mass of the mountain, m M , the distance to its center, D M , and the radius and mass of the Earth, ( b ) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m 3 . ( c ) Estimate the angle θ of the plumb bob if it is 5 km from the center of Mt. Everest. FIGURE 6-30
A plumb bob (
a
mass
m
hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). (a) Find an approximate formula for 6 in terms of the mass of the mountain, mM, the distance to its center, DM, and the radius and mass of the Earth, (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m3. (c) Estimate the angle
θ
of the plumb bob if it is 5 km from the center of Mt. Everest.
(a)
(i)
Define gravitational field strength and state whether it
is a scalar or vector quantity.
A mass m is at a height h above the surface of a planet
(ii)
of mass M and radius R.
The gravitational field strength at height h is g. By
considering the gravitational force acting on massm,
derive an equation from Newton's law of gravitation to
express g in terms of M, R, h and the gravitational
conșțant G.
The Sun rotates about the center of the Milky Way
Galaxy (Fig. 6-29) at a distance of about 30,000 light-
years from the center (1 ly = 9.5 × 105 m). If it takes
about 200 million years to make one rotation, estimate
the mass of our Galaxy. Assume that the mass distribu-
tion of our Galaxy is concentrated mostly in a central
uniform sphere. If all the stars had about the mass of our
Sun (2 x 1030 kg), how many stars would there be in our
Galaxy?
%3D
(II)
Sun
AW (I) 1E
bins viool
30,000 ly ov
(c) As an aerospace engineer, your spaceship orbits the Moon at a height of 20 km.
Assuming it is subject only to the gravitational pull of the Moon, find its speed and the
time it takes for one orbit. For the Moon, its mass is 7.34 x 1022 kg and its radius is
1.738 x 10 m.
Chapter 6 Solutions
Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.