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A person on horseback is on a drawbridge which is at an angle e = 20.0° above the horizontal, as shown in the figure. The center of mass of the person-horse system is d = 1.30 m from the end of the bridge. The bridge is e = 9.50 m long and has a mass of 2,350 kg. A cable is attached to the bridge 5.00 m from the frictionless hinge and to a point on the wall h = 12.0 m above the bridge. The mass of person plus horse is 1,100 kg. Assume the bridge is uniform. Suddenly (and most unfortunately for the horse and rider), the ledge where the bridge usually rests breaks off, and at the same moment the cable snaps and the bridge swings down until it hits the wall.

A person on horseback is on a drawbridge which is at an angle e = 20.0° above the horizontal, as shown in the figure. The center of mass of the person-horse system is d = 1.30 m from the end of the bridge. The bridge is e = 9.50 m long and has a mass of 2,350 kg. A cable is attached to the bridge 5.00 m from the frictionless hinge and to a point on the wall h = 12.0 m above the bridge. The mass of person plus horse is 1,100 kg. Assume the bridge is uniform. Suddenly (and most unfortunately for the horse and rider), the ledge where the bridge usually rests breaks off, and at the same moment the cable snaps and the bridge swings down until it hits the wall.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A person on horseback is on a drawbridge which is at an angle 0 = 20.0° above the horizontal, as shown in the figure. The center of mass of the person-horse system is d = 1.30 m from the end of the bridge. The bridge is e = 9.50 m long and has a mass of 2,350 kg. A cable is attached to the bridge 5.00 m from the frictionless hinge and to a point on the wall h = 12.0 m above the bridge. The mass of person plus horse is 1,100 kg. Assume the bridge is uniform. Suddenly (and most unfortunately for the horse and rider), the ledge where the bridge usually rests breaks off, and at the same moment the cable snaps and the bridge swings down until it hits the wall. HTHI ATLA TAHI A AUTA A TH
Transcribed Image Text:A person on horseback is on a drawbridge which is at an angle 0 = 20.0° above the horizontal, as shown in the figure. The center of mass of the person-horse system is d = 1.30 m from the end of the bridge. The bridge is e = 9.50 m long and has a mass of 2,350 kg. A cable is attached to the bridge 5.00 m from the frictionless hinge and to a point on the wall h = 12.0 m above the bridge. The mass of person plus horse is 1,100 kg. Assume the bridge is uniform. Suddenly (and most unfortunately for the horse and rider), the ledge where the bridge usually rests breaks off, and at the same moment the cable snaps and the bridge swings down until it hits the wall. HTHI ATLA TAHI A AUTA A TH
(a) Find the angular acceleration (magnitude, in rad/s2) of the bridge once it starts to move. 1.46 rad/s? (b) How long (in s) does the horse and rider stay in contact with the bridge while it swings downward? (c) Find the angular speed (in rad/s) of the bridge when it strikes the vertical wall below the hinge. 2.04 rad/s (d) Find the force (in kN) exerted by the hinge on the bridge immediately after the cable breaks. horizontal component: magnitude 4.61 Calculate the tangential acceleration of the center of mass of the bridge, and use your result in Newton's second law for the x- and y-directions. kN direction to the right vertical component: magnitude 6.44 Calculate the tangential acceleration of the center of mass of the bridge, and use your result in Newton's second law for the x- and y-directions. kN direction upward (e) Find the force (in kN) exerted by the hinge on the bridge immediately before it strikes the wall. horizontal component: magnitude kN direction There is no horizontal component. v vertical component: 57.5 magnitude Write Newton's second law for the configuration. Note that the acceleration is centripetal, so a, = w?r. Solve for Hy. kN direction upward
Transcribed Image Text:(a) Find the angular acceleration (magnitude, in rad/s2) of the bridge once it starts to move. 1.46 rad/s? (b) How long (in s) does the horse and rider stay in contact with the bridge while it swings downward? (c) Find the angular speed (in rad/s) of the bridge when it strikes the vertical wall below the hinge. 2.04 rad/s (d) Find the force (in kN) exerted by the hinge on the bridge immediately after the cable breaks. horizontal component: magnitude 4.61 Calculate the tangential acceleration of the center of mass of the bridge, and use your result in Newton's second law for the x- and y-directions. kN direction to the right vertical component: magnitude 6.44 Calculate the tangential acceleration of the center of mass of the bridge, and use your result in Newton's second law for the x- and y-directions. kN direction upward (e) Find the force (in kN) exerted by the hinge on the bridge immediately before it strikes the wall. horizontal component: magnitude kN direction There is no horizontal component. v vertical component: 57.5 magnitude Write Newton's second law for the configuration. Note that the acceleration is centripetal, so a, = w?r. Solve for Hy. kN direction upward
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