(a) Explanation Given information: The load carried by the front bucket is 3 , 200 lb . Consider the mechanism supports half of the load on the bucket. Assumption: Apply the sign convention for calculating the equations of equilibrium as below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Calculation: Show the free body diagram of the bucket as shown in Figure 1. Refer to Figure 1. Consider the force in the member AB is denoted by F A B . Consider the horizontal force at D is denoted by D x . Consider the sum of the moment at D is zero. Then, ∑ M D = 0 ( 1600 lb × 15 in . ) − ( F A B × 16 in . ) = 0 ( F A B × 16 in . ) = ( 1600 lb × 15 in . ) F A B = ( 1600 lb × 15 in . ) 16 in . F A B = 1500 lb Consider there are two identical support mechanisms. Show the free body diagram of the arm BCE . Calculate the value of the angle β using the relation: tan β = 8 in . 20 in . β = tan − 1 ( 8 in . 20 in . ) β = 21.8 ° Consider the force in the cylinder CD is denoted by F C D (b) To determine Find the force exerted by the cylinder FH .

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 6.4, Problem 6.154P

(a)

To determine

Find the force exerted by the cylinder CD.

(b)

To determine

Find the force exerted by the cylinder FH.

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Chapter 6.4, Problem 6.153P

Chapter 6.4, Problem 6.155P

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Vector Mechanics for Engineers: Statics, 11th Edition

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Find the force exerted by the cylinder CD .