Question

Problem 5: 20 points A loaded cement mixer truck drives onto an old drawbridge (length = 40m and Mbridge = 18,000kg) where it stalls with the truck's center of gravity three quarters of the way across the span. The truck sets its brakes such that it won't move and the bridge is raised by means of a cable attached at the end of the bridge. The truck (and driver) have a mass of mtruck = 30,000kg. When the bridge has been raised by 30°, the cable forms an angle of 70° and all motion is stopped. a) Draw an extended free body diagram (not for a point mass) for the brid the forces acting on the bridge. Be sure to indicate the point of applicati and be sure to label all the forces. (5 points) b) Determine the tension T needed to maintain this position. (9 points) c) What are the horizontal and vertical components of the force the hing span of bridge? (6 points)

Answer 1

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-20 X Tom b = 18000kg me = 30000 kg L = 40m on mo T Tension Equilbrium cond" of Torque at o - Ti sin 70 = mig (30) cos 30 + mg (20) cosso T (40) Sin 70° = (30000) 9 (30) C0530 + (18000) g (20) 6385 => JT - 284499.45N - • F on span Horizontal component of force the hinge exerts F - T cos (70-90) - 28449945 cos (40%) 2 = 217939:22 N • Fy vertical component of force the hipe exertse F = mig + my g - Tsin (10-30) - (30000 +18000) 9 - 284499.45 sin (40") F = 287527.2INI Plz like Thanks