Concept explainers
(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earth’s surface is
This rate of change with position is called a gradient.
(b) Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is
(c) Evaluate this difference for h = 6.00 m, a typical height for a two-story building.
(a)
To show: The rate of change of free fall acceleration with vertical position near the Earth’s surface is
Explanation of Solution
Explanation:
The rate of change free fall acceleration with position of any quantity is called gradient. And the free fall acceleration is the acceleration of a body falling freely in a vacuum near the surface of the Earth. it is also called as acceleration due to gravity.
Formula to calculate the acceleration due to gravity at distance
The differentiate for the above equation with respect to
The distance
Conclusion:
Therefore, the rate of change of free fall acceleration with vertical position near the Earth’s surface is
(b)
To show: The difference in free fall acceleration with between two points separated by vertical distance
Explanation of Solution
Explanation:
The force that attracts a body towards the center of the Earth, or towards any other physical body having mass called as gravity.
Formula to calculate the difference in free fall acceleration between two points is,
Formula to calculate the acceleration due to gravity at the Earth surface is,
Formula to calculate the acceleration due to gravity at a vertical distance
Substitute
The distance
Conclusion:
Therefore, the difference in free fall acceleration with between two points separated by vertical distance
(c)
To determine: The difference in free fall acceleration between two points separated by vertical distance
Answer to Problem 62AP
Answer: The difference in free fall acceleration between two points separated by vertical distance
Explanation of Solution
Explanation:
From equation (II),
Substitute
Conclusion:
Therefore, the difference in free fall acceleration with between two points separated by vertical distance
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Chapter 13 Solutions
Physics for Scientists and Engineers With Modern Physics
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