The Work Done Against Gravity in Propelling an Object with Mass

question 125

Essay

The work done against gravity in propelling an object with mass m kg to an altitude of h m above the surface of the earth is given by $W = \int _ { 637 \times 10 ^ { 6 } } ^ { 637 \times 10 ^ { 6 } + h } \frac { G M _ { E } m } { r ^ { 2 } } d r$ where 6.37 $\times$ 10⁶ m is the radius of the earth, $G \approx 6.667 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$ and $M _ { E } \approx 5.90 \times 10 ^ { 24 } \mathrm {~kg}$ is the mass of the earth.(a) Find the work required to launch a 1000-kilogram satellite vertically to an altitude of 1000 km.(b) The formula shows that the work is dependent on h. Show that $\int _ { 637 \times 10 ^ { 6 } } ^ { \infty } \frac { G M _ { Z } m } { r ^ { 2 } } d r$ is convergent. What is the physical significance of the fact that this improper integral is finite?

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Definitions:

Disclosure

The action of making new or important information known, especially relating to business operations, financial conditions, or regulatory compliance.

Specific Identification Method

An inventory valuation method that tracks the actual cost of each individual item of inventory.

Inventory Accounting

The process of valuing a company's inventory, including raw materials, work-in-progress, and finished goods.

LIFO

Last In, First Out, an inventory valuation method where the most recently produced or acquired items are sold or used first.