(a)
To compare: the force of gravity on a person due to the Sun at 1000 times farther away from its center and when the person was standing at its surface.
(a)
Explanation of Solution
Introduction:
Gravity is a force that forces a body with mass into the earth's core, or into some other physical object. Gravity plays an important part in the survival of earthly life.
Newton’s law of gravitation states that the force of gravity on a body of mass m from the Sun of mass Mcan be expressed as,
Here,
The force of gravity on the person from the sun at his initial position can be written as,
Here,
Substitute
This is the force of gravity on the person from the sun at his new position,
Conclusion:
Hence, the force of gravity from the sun decreases by
(b)
To compare: the illuminance on his hand from the sun at the new position to what it was when he was standing on its surface.
(b)
Explanation of Solution
Introduction:
The illuminance on his hand by the sunlight is equal to the luminous flux of the sun divided by the area of the sphere whose radius is equal to his distance from the sun’s centre.
The expression for illuminance is given by the formula
Here,
Use this relation to write the illuminance of his hand at his initial position,
Here,
Substitute
Conclusion:
Hence, the illuminance of his hand is decreased by
(c)
To compare: the effect of distance upon the gravitational force and illuminance.
(c)
Explanation of Solution
Introduction:
The illuminance on his hand by the sunlight is equal to the luminous flux of the sun divided by the area of the sphere whose radius is equal to his distance from the sun’s centre. Gravity is the force by which earth or other body draws particles into its centre. The tidal force forces the planets in orbit around the earth.
From the above result of part (a) and (b), one can see that both the force of gravity and the illuminance decrease by the same amount with the increase in the distance from the Sun. in fact, both of them decreases as the square of the distance to Sun from the person. So, both forces of gravity and the illuminance follow the inverse square law.
Conclusion:
Hence, both the force of gravity and the illuminance follow the inverse square law.
Chapter 18 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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