Integral Relation Between Force and potential energy - Edubirdie

University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

265

Pages:

5
Author:

Jabin F.

Integral Relation Between Force and Potential Energy: dU = -F.dr U = -∫F.dr + c Example: If F = A(yî + xj), then find potential energy. Solution: ∇ x F = 0 U = -∫F.dr + c = -∫A(yî + xj) · (dxi + dyj + dzk) + c U = -A∫(ydx + xdy) + c = -A∫d(xy) + c U = -Axy + c Ans Example: A conservative force is given to be F = k[(x² + y²)î + 2x²yj]. Calculate U. Solution: ∇ x F = 0 U = -∫F.dr + c = -∫k[(x² + y²)dx + 2x²ydy] + c = -k [[x³dx] + [(3x²y²dx + 3x³ydy)] + C = -k [x⁴/4 + ∫d(x³y³)] + C = -k [x⁴/4 + x³y³] + C Ans

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