(a) Explanation Given information: The potential function associated with force P is V ( x , y , z ) = − ( x 2 + y 2 + z 2 ) 1 / 2 . Calculation: Write the potential function associated with force P: V ( x , y , z ) = − ( x 2 + y 2 + z 2 ) 1 / 2 (1) Calculate the force P in ‘ x ’ component using the relation: Partial differentiate the equation (1) with respect to ‘ x ’. P x = ∂ V ∂ x Substitute − ( x 2 + y 2 + z 2 ) 1 / 2 for V . P x = ∂ ( − ( x 2 + y 2 + z 2 ) 1 / 2 ) ∂ x = 1 2 x 2 + y 2 + z 2 × ( 2 x ) = x ( x 2 + y 2 + z 2 ) − 1 / 2 Calculate the force P in ‘ y ’ component using the relation: Partial differentiate the equation (1) with respect to ‘ y ’. P y = ∂ V ∂ y Substitute − ( x 2 + y 2 + z 2 ) 1 / 2 for V (b) To determine Find the work done by P from O to D and show that the work done is equal to negative of the change in potential from O to D .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 13.2, Problem 13.82P

(a)

To determine

Find the x, y and z components of force P.

(b)

To determine

Find the work done by P from O to D and show that the work done is equal to negative of the change in potential from O to D.

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Chapter 13.2, Problem 13.81P

Chapter 13.2, Problem 13.83P

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VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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Find the x , y and z components of force P .

Solution Summary: The author calculates the force P in 'x' component using the relation: Partial differentiate the equation (1) with respect to ‘x’.