Explanation Given information: The equation of elliptical path is r = r 0 2 − cos θ . Calculation: Write the equation of initial velocity ( u )of particle using the equation: u = 1 r (1) Here, r is the radius of elliptical path. Substitute r 0 2 − cos θ for r . u = 1 r 0 2 − cos θ = 2 − cos θ r 0 Differentiate Equation (1) with respect to θ . d u d θ = sin θ r 0 (2) Differentiate Equation (2) with respect to θ . d 2 u d θ 2 = cos θ r 0 Find the Equation of force ( F ). d 2 u d θ 2 + u = F m h 2 u 2 Substitute cos θ r 0 for d 2 u d θ 2 , 2 − cos θ r 0 for u

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Author: BEER

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Chapter 12.3, Problem 12.94P

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Show that force F is inversely proportional to the square of the distance r from the particle to the center of force O.

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Chapter 12.3, Problem 12.7CQ

Chapter 12.3, Problem 12.95P

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Show that force F is inversely proportional to the square of the distance r from the particle to the center of force O .

Solution Summary: The author shows that force F is inversely proportional to the square of the distance r from the particle to a center of force O.

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