Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 58Q

(a)

To determine

The gravitational force exerted by the Moon on a 1-kg rock at a point on the Earth’s surface closest to the Moon. Given that the average distance from the Moon to the center of Earth is 384,400km and the diameter of Earth is 12,756 km.

(a)

Expert Solution
Check Mark

Answer to Problem 58Q

Solution:

3.43×105N.

Explanation of Solution

Given data:

Average distance from the Moon to the center of Earth is 384,400km.

Diameter of Earth is 12,756 km.

Mass of the rock is 1-kg.

Formula used:

Write the expression for universal law of gravitation between two objects.

F=Gm1m2r2

Here G is the universal law of gravitation, m1 is the mass of first object, m2 is the mass of second object and r is the separation between the two objects.

Explanation:

The the average distance from the Moon to the center of Earth is 384,400km and the diameter of Earth is 12,756 km.

For a point on Earth closest to the Moon, separation between the Moon (d) and the rock is calculated as,

d=(Average distance between earth and moon)12( diameter of earth)=384,400 km  12(12,756 km)=3.78×105 km(1000 m1 km)=3.78×108 m

Refer to the expression for universal law of gravitation between two objects.

F=Gm1m2r2

Upon substituting 6.67×1011Nm2kg-2 for G, 7.348×1022kg for m1, 1 kg for m2 and d for r,

F = (6.67×1011 Nm2kg2)(7.348×1022 kg)(1 kg)(d)2

Substitute 3.78×108 m for d.

F = (6.67×1011 Nm2kg2)(7.348×1022 kg)(1 kg)(3.78×108 m)2=3.43×105 N

Conclusion:

Hence, the gravitational force of attraction that the Moon would exert on a 1-kg rock at a point on the Earth’s surface closest to the Moon is 3.43×105 N.

(b)

To determine

The gravitational force exerted by the Moon on a 1-kg rock at a point on the Earth’s surface farthest to the Moon. Given that the average distance from the Moon to the center of Earth is 384,400km and the diameter of Earth is 12,756 km.

(b)

Expert Solution
Check Mark

Answer to Problem 58Q

Solution:

3.21×105N.

Explanation of Solution

Given data:

Average distance from the Moon to the center of Earth is 384,400km

Diameter of Earth is 12,756 km.

Mass of the rock is 1-kg.

Formula used:

Write the expression for universal law of gravitation between two objects

F=Gm1m2r2

Here G is the universal law of gravitation, m1 is the mass of first object, m2 is the mass of second object and r is the distance of separation between the two objects.

Explanation:

The the average distance from the Moon to the center of Earth is 384,400km and the diameter of Earth is 12,756 km.

For a point on Earth farthest to the Moon, separation between the Moon (d) and the rock is calculated as,

d=(Average distance between earth and moon)+12( diameter of earth)=384,400 km + 12(12,756 km)=3.91×105 km(1000 m1 km)=3.91×108 m

Refer to the expression for universal law of gravitation between two objects.

F=Gm1m2r2

Upon substituting 6.67×1011Nm2kg-2 for G, 7.348×1022kg for m1, 1 kg for m2 and d for r,

F = (6.67×1011 Nm2kg2)(7.348×1022 kg)(1 kg)(d)2

Substitute 3.91×108 m for d.

F = (6.67×1011 Nm2kg2)(7.348×1022 kg)(1 kg)(3.91×108 m)2=3.21×105 N

Conclusion:

Hence, the gravitational force that the Moon would exert on a 1-kg rock at a point on the Earth’s surface farthest from the Moon is 3.21×105 N.

(c)

To determine

The difference between the gravitational force that the Moon would exert on a 1-kg rock at a point on the Earth’s surface closest to the Moon and and at a point on the Earth’s surface farthest to the moon.

(c)

Expert Solution
Check Mark

Answer to Problem 58Q

Solution:

0.22×105 N.

Explanation of Solution

Given data:

Average distance from the Moon to the center of Earth is 384,400km.

Diameter of Earth is 12,756 km.

Mass of the rock is 1-kg.

Explanation:

The gravitational force of attraction (F) between the Moon and a 1-kg rock, at a point on the Earth’s surface closest to the Moon, is 3.43×105 N. [From part(a)].

The gravitational force of attraction (F) between the Moon and a 1-kg rock, at a point on the Earth’s surface farthest to the Moon, is 3.21×105 N [From part(b)].

Calculate the difference (say D) between the gravitational force that the Moon would exert on a 1-kg rock at a point on the Earth’s surface closest to the Moon and at a point on the Earth’s surface farthest to the moon.

D=FF=(3.43×105 N)(3.21×105 N)=0.22×105 N

As the difference between the gravitational force exerted by Moon on a 1 kg stone closest to the Earth’s surface and on a 1 kg stone farthest to the Earth’s surface is 0.22×105 N. The tidal energy generated by this will be very small as compared to Earth’s gravity which tries to maintain the spherical surface.

Conclusion:

Hence, the difference between the gravitational force that the Moon would exert on a 1-kg rock at a point on the Earth’s surface closest to the Moon and at a point on the Earth’s surface farthest to the moon is 0.22×105 N.

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