Explanation Determine if the given statement is true by multiplying the force and the path over an integral. Given : Work is done by a constant force field F over any path C from P to Q Formula used : Work = F . P Q → Proof : Let the constant force field be represented as F = ( a , b , c ) and the path C from P to Q be represented in the parametrized form as c ( t ) = ( x ( t ) , y ( t ) , z ( t ) ) , t 0 ≤ t ≤ t 1 . Hence the work performed is given by ∮ C F ( c ( t ) ) . c ( t ) = ∫ t 0 t 1 ( a , b , c ) ( x ( t ) , y ( t ) , z ( t ) ) d t = ∫ t 0 t 1 ( a x

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17.2, Problem 57E

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To prove:

That work performed by a constant force field $F$ over any path $C$ from $P$ to $Q$ is equal to $F . \vec{P Q}$

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Chapter 17.2, Problem 56E

Chapter 17.2, Problem 58E

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Chapter 17 Solutions

Calculus - Standalone book

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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To prove : That work performed by a constant force field F over any path C from P to Q is equal to F . P Q →

Solution Summary: The author proves that work performed by a constant force field F over any path C from P to Q is equal to F.

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To prove:

That work performed by a constant force field $F$ over any path $C$ from $P$ to $Q$ is equal to $F . \vec{P Q}$

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Chapter 17 Solutions

To prove : That work performed by a constant force field F over any path C from P to Q is equal to F . P Q →

Solution Summary: The author proves that work performed by a constant force field F over any path C from P to Q is equal to F.

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To prove: That work performed by a constant force field F over any path C from P to Q is equal to F.PQ→

Want to see the full answer?

Chapter 17 Solutions

To prove:

That work performed by a constant force field $F$ over any path $C$ from $P$ to $Q$ is equal to $F . \vec{P Q}$