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Recall work done by a force, F, moving from a point A to B is the line integral, w = di (1) If F happens to be conservative then work is done is simply, - (V(B) – V(A)) (2) W = where a force is conservative if and only if it is a gradient of a scalar potential (a function), F = -V (3) The minus sign in Eqs.2,3 arises only in physical science because it is necessary to equate the potential with potential energy. In pure math, Eqs.2,3 would be w = (V(B) – V(A)) and F = VV respectively. These in combination with Eq. 1, you should recognize as the vectorial form of the Fundamental Theorem of Calculus, f(x)dx = F(b) – F (a) = F. dř = w = (V(B) – V(A)) (a) Method 1: Let V(x,y,z) = } (2x² + 3y² + z²), B = Eq. 3 to calculate the work done moving from A → B. (2,3,1), and A = (0,0,0). Use Eq. 1 and (b) Method 2 : Let V(x, y, z) = } (2x² + 3y² + z²), B = (2,3,1), and A = calculate the work done moving from A → B. (0,0,0). Use Eq. 2 to

Recall work done by a force, F, moving from a point A to B is the line integral, w = di (1) If F happens to be conservative then work is done is simply, - (V(B) – V(A)) (2) W = where a force is conservative if and only if it is a gradient of a scalar potential (a function), F = -V (3) The minus sign in Eqs.2,3 arises only in physical science because it is necessary to equate the potential with potential energy. In pure math, Eqs.2,3 would be w = (V(B) – V(A)) and F = VV respectively. These in combination with Eq. 1, you should recognize as the vectorial form of the Fundamental Theorem of Calculus, f(x)dx = F(b) – F (a) = F. dř = w = (V(B) – V(A)) (a) Method 1: Let V(x,y,z) = } (2x² + 3y² + z²), B = Eq. 3 to calculate the work done moving from A → B. (2,3,1), and A = (0,0,0). Use Eq. 1 and (b) Method 2 : Let V(x, y, z) = } (2x² + 3y² + z²), B = (2,3,1), and A = calculate the work done moving from A → B. (0,0,0). Use Eq. 2 to

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Recall work done by a force, F, moving from a point A to B is the line integral, w = di (1) If F happens to be conservative then work is done is simply, - (V(B) – V(A)) (2) W = where a force is conservative if and only if it is a gradient of a scalar potential (a function), F = -V (3) The minus sign in Eqs.2,3 arises only in physical science because it is necessary to equate the potential with potential energy. In pure math, Eqs.2,3 would be w = (V(B) – V(A)) and F = VV respectively. These in combination with Eq. 1, you should recognize as the vectorial form of the Fundamental Theorem of Calculus, f(x)dx = F(b) – F (a) = F. dř = w = (V(B) – V(A)) (a) Method 1: Let V(x,y,z) = } (2x² + 3y² + z²), B = Eq. 3 to calculate the work done moving from A → B. (2,3,1), and A = (0,0,0). Use Eq. 1 and (b) Method 2 : Let V(x, y, z) = } (2x² + 3y² + z²), B = (2,3,1), and A = calculate the work done moving from A → B. (0,0,0). Use Eq. 2 to
Transcribed Image Text:Recall work done by a force, F, moving from a point A to B is the line integral, w = di (1) If F happens to be conservative then work is done is simply, - (V(B) – V(A)) (2) W = where a force is conservative if and only if it is a gradient of a scalar potential (a function), F = -V (3) The minus sign in Eqs.2,3 arises only in physical science because it is necessary to equate the potential with potential energy. In pure math, Eqs.2,3 would be w = (V(B) – V(A)) and F = VV respectively. These in combination with Eq. 1, you should recognize as the vectorial form of the Fundamental Theorem of Calculus, f(x)dx = F(b) – F (a) = F. dř = w = (V(B) – V(A)) (a) Method 1: Let V(x,y,z) = } (2x² + 3y² + z²), B = Eq. 3 to calculate the work done moving from A → B. (2,3,1), and A = (0,0,0). Use Eq. 1 and (b) Method 2 : Let V(x, y, z) = } (2x² + 3y² + z²), B = (2,3,1), and A = calculate the work done moving from A → B. (0,0,0). Use Eq. 2 to
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