Concept explainers
The motion of the backhoe bucket shown is controlled by the hydraulic cylinders AD, CG, and EF. As a result of an attempt to dislodge a portion of a slab, a 2-kip force P is exerted on the bucket teeth at J. Knowing that θ = 45°, determine the force exerted by each cylinder.
Fig. P6.157
The force exerted by each cylinder shown in figure
Answer to Problem 6.157P
The force exerted by the cylinder
Explanation of Solution
Take all vectors along the
Let P is the force exerted on the bucket at J.
The magnitude of force
The free body diagram of the bucket is sketched below as figure 1.
Here,
Write the expression for the moment at
Here,
Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.
The moment at
Thus, the complete expression of net anticlockwise moment
Here,
At equilibrium, the sum of the moment acting at
Write the expression for the total moment acting at
From figure 1 , write the expression for the
From figure 1 , write the expression for the
The free body diagram of the bucket and arm
Here,
Write the expression for the moment at
Here,
Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.
The moment at
Thus, the complete expression of net anticlockwise moment
Here,
At equilibrium, the sum of the moment acting at
Write the expression for the total moment acting at
From figure 2 , write the expression for the
Geometry of cylinder
The free body diagram of the bucket and both arms is sketched below as figure 4.
Here,
Write the expression for the moment at
Here,
Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.
The moment at
Thus, the complete expression of net anticlockwise moment
Here,
At equilibrium, the sum of the moment acting at
Write the expression for the total moment acting at
From figure 3 , write the expression for the
Calculation:
Substitute
The negative sign indicate that the cylinder undergoes compression.
Substitute
The negative sign indicate that the cylinder undergoes compression.
Rearrange the equation (X) to get
Substitute
The positive sign indicate that the cylinder
Therefore, the force exerted by the cylinder
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Chapter 6 Solutions
Vector Mechanics for Engineers: Statics
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