To determine Find the magnitude of the force F 2 and the angle α . Explanation Given information: Refer to the given Figure in the textbook. Calculation: The given diagram is redrawn as shown in Figure 1. Draw the free body diagram for the Figure 1 as shown in Figure 2. Equate the horizontal component of forces shown in Figure 2. F 1 cos α = F 2 cos 60 ° Simplify the above equation to find F 1 . F 2 = F 1 ( cos α cos 60 ° ) = F 1 ( cos α ( 1 2 ) ) F 2 = 2 F 1 cos α (1) Equate the vertical component of forces shown in Figure 2. F 1 sin α + F 2 sin 60 ° = 50 Substitute equation (1) in above equation to find F 1 . F 1 sin α + 2 F 1 cos α sin 60 ° = 50 F 1 sin α + 2 F 1 cos α ( 3 2 ) = 50 F 1 sin α + 3 F 1 cos α = 50 F 1 ( sin α + 3 cos α ) = 50 Substitute 35 N for F 1 in above equation. 35 ( sin α + 3 cos α ) = 50 sin α + 3 cos α = 50 35 3 cos α = 10 7 − sin α Take square on both sides for the above equation. ( 3 cos α ) 2 = ( 10 7 − sin α ) 2 3 cos 2 α = ( 10 7 ) 2 − 2 ( 10 7 ) sin α + sin 2 α 3 ( 1 − sin 2 α ) = 100 49 − 20 7 sin α + sin 2 α { ∵ cos 2 θ + sin 2 θ = 1 } 3 ( 1 − sin 2 α ) = 100 −

Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

14th Edition

ISBN: 9780134665573

Author: Joel R. Hass, Christopher D. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 12.2, Problem 48E

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Find the magnitude of the force F2 and the angle α.

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Chapter 12.2, Problem 47E

Chapter 12.2, Problem 49E

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Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

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