Find a couple of M.
Answer to Problem 16.142P
The couple of M=-7.19N.m.
Explanation of Solution
Given information:
The attached rod A mass is=0.8kg
And length is=160mm
Rod BP mass is=1kg
Length is=200mm
Explanation:
First consider the unit
So, we have to find the vertical distance from point P and point A(y)
Here, we take the coordinate points as (0,0.1m)
Then the position of the vector
Coordinate points of the point P with the point B is
Then the position vector is
Then the coordinate points with the point P and point E as (0,-0.16m)
Position vector is
Here, the unit vector k as angular direction in clockwise is negative and it is positive when counter clockwise.
Angular velocity of the rod BP in vector form is
Velocity of the rod BP is
Formulate the velocity equation of point P
Compare the i terms from equation (1) And (2)
Compare the equation (1) and (2) for j terms. We get,
So, the angular acceleration is zero.
Formulate the acceleration of the rod BP
Find the acceleration of the point P to the point E
Formulate the acceleration at the point P
Substitute the above values
Based on equations (3) and (4), we get,
Find the weight of the rod AE is get by
Then the moment of inertial of the rod AE is
Similarly, find the weight of the rod BP is
Then the moment of inertial of the rod BP
Here, the mass of the centers of rod AE and BP are to be considered as G and H.
Then the reference for point G with point A as (0,-0.08m).
Here the position vector is −(0.08m)j.
Similarly, the point H with point B as the reference as (-0.0866m,-0.05m). Position vector is −(0.0866m)i-(0.05m)j
Acceleration of the point G is
Find the acceleration at point H
Based on above figure, consider the moment about point B.
The magnitude of the couple applied on the rod is BP. It is considered as -7.19N.m and acts in a clockwise direction.
Find the force exerted on rod AE.
Answer to Problem 16.142P
The force exerted by rod AE is F=52.757N.
Explanation of Solution
Considering the above diagram of free body of the rod AE
The force exerted by rod AE by block P is 52.75N. It is acted upon the left direction.
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Chapter 16 Solutions
Vector Mechanics For Engineers
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