Coal discharged from a dump truck with an initial velocity (vc)0 = 5 ft/s ⦫ 50° falls onto conveyor belt B. Determine the required velocity vB of the belt if the relative velocity with which the coal hits the belt is to be (a) vertical, (b) as small as possible.
Fig. P11.127
(a)
The required velocity
Answer to Problem 11.127P
The required velocity
Explanation of Solution
Given Information:
The initial
The angle
Calculation:
Calculate the x component initial velocity
Substitute
Calculate the x component velocity
Calculate the y component initial velocity
Substitute
Calculate the y component kinematic velocity
Here, d is distance between the dump truck and belt.
Substitute
Substitute
Calculate the angle
Substitute
Calculate the velocity
Substitute
Write the expression for velocity vector
Write the expression for velocity vector
Substitute
Write the expression for relative velocity vector
When the belt positioned vertical, then x component of relative velocity
Write the y component relative velocity vector equation
Substitute
Write the y component relative velocity vector equation
Substitute
Write the x component relative velocity vector equation
Substitute 0 for
Solve the above equation for velocity
Therefore, the required velocity
(b)
The required velocity
Answer to Problem 11.127P
The required velocity
Explanation of Solution
Given Information:
The initial
The angle
Calculation:
Write vector for relative velocity
Substitute
Separate the i and j component.
Consider i component.
Consider j component.
Find the expression for
Substitute
Calculate the required velocity
Differentiate the equation 2 with respective to velocity
Solve the above equation for
Therefore, the required velocity
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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