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28 November, 16:35

A 34,000-lb airplane lands on an aircraft carrier and is caught by an arresting cable. The cable is inextensible and is paid out at A and B from mechanisms located below deck and consisting of pistons moving in long oil-filled cylinders. The piston-cylinder system is designed to maintain a constant tension in the cable. Knowing that the landing is 110 mi/h and the airplane travels a distance d = 90 ft after being caught, determine the tension in the cable.

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  1. 28 November, 18:03
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    F = 153637 lb

    Explanation:

    Let's use the kinematic equations to find the airplane's braking speed

    v² = v₀² + 2 a d

    The final speed is zero

    a = - v₀² / 2d

    Let's reduce the magnitudes

    v₀ = 110 mi / h (5280 ft / 1 mile) (1 h / 360 s) = 161.33 ft / s

    a = - 161.33²/2 90

    a = - 144.60 ft / s²

    Now we can use Newton's second law to find the tension

    F = m a

    F = (34000/32) 144.60

    F = 153637 lb
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