Concept explainers
The components of the reactions at C and D of the conveyor belt system.
Answer to Problem 14.68P
The reaction at D is
The reaction component at C along x direction is
The reaction component at C along y direction is
Explanation of Solution
Given information:
The discharge of coal from first conveyor belt at the rate
The magnitude of velocity
The total mass is
Calculation:
Consider the acceleration due to gravity as
Sketch the Free Body Diagram of coal discharge from first conveyor belt as shown in Figure 1.
Refer to Figure 1.
Calculate the mass of coal
Substitute
Calculate the velocity of the coal hits the second belt
Velocity along x direction.
Velocity along y direction.
Substitute
Sketch the Free Body Diagram of the second conveyor belt assembly as shown in Figure 2.
Refer to Figure 2.
Calculate the velocity
Velocity along x direction.
Velocity along y direction.
Apply angular momentum about C as shown below.
Substitute
Calculate the weight of the coal
Substitute
Calculate the component of the reaction at D as shown below.
Substitute
Hence, the reaction at D is
Apply the Equations of Equilibrium along x direction as shown below.
Substitute
Substitute
Hence, the reaction component at C along x direction is
Apply the Equations of Equilibrium along y direction as shown below.
Substitute
Substitute
Therefore, the reaction component at C along y direction is
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Chapter 14 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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