Calculate the Work Done by the Force Field When a Particle Moves Under Its Influence Around the Edge

question 132

Short Answer

Calculate the work done by the force field $\mathbf { F } ( x , y , z ) = \left( x ^ { 2 } + 10 z ^ { 2 } \right) \mathbf { i } + \left( y ^ { 2 } + 14 x ^ { 2 } \right) \mathbf { j } + \left( z ^ { 2 } + 12 y ^ { 2 } \right) \mathbf { k }$ when a particle moves under its influence around the edge of the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ that lies in the first octant, in a counterclockwise direction as viewed from above.

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Definitions:

Depletion Expense

The allocation of the cost of natural resources over the period they are consumed or sold.

Coal Mine

A site for the extraction of coal from the earth, typically involving underground or open-pit operations.

Accumulated Depreciation

The total depreciation for a fixed asset that has been charged to expense since the asset was acquired and made available for use.

Trade-in Allowance

The amount credited to a buyer by a seller for the property or goods being part-exchanged.