Concept explainers
A regular tetrahedron has six edges of length a. A force P is directed as shown along edge BC. Determine the moment of P about edge OA.
The moment of force on the point
Answer to Problem 3.61P
The moment of force on the point
Explanation of Solution
The tetrahedron has six sides of length as
Formula to calculate the moment along the edge
Here, moment of force along the edge
Sketch the tetrahedron as shown in Figure 1.
Refer From fig 1, the length of the
Here, the length of the edge is
From the triangle
Substitute
Since apply the Pythagoras theorem for the point
Substitute
Rewrite the above relation for
The position vector drawn from the point
Sketch the tetrahedron along the position vector drawn from the point
Refer From fig 2, the unit vector along
The force acting along the point
Here, the unit vector along
Replace
Refer From fig 2, the position vector drawn from the point
Conclusion:
From the equation (I) the moment along the edge
The moment along the edge
Therefore, the moment along the edge
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L