Engineering Mechanics: Statics and Dynamics, 14th Edition
Authors: Russell C. Hibbeler
ISBN-13: 978-0133915426
See our solution for Question 28FP from Chapter 2 from Hibbeler's Engineering Mechanics.
Problem 28FP
Chapter:
Problem:
Determine the projected component of the force along the line OA...
Step-by-Step Solution
Step 1
Step 2
Step 3
We are given the force $F = 650\;{\rm{N}}$.
We are asked to determine the projected component of the force along the line OA.
Step 2
The following is the diagram to calculate the projected component of the force.
To find the unit vector we will use the formula,
\[\begin{array}{l} \vec u = \left( {\frac{{12}}{{13}}\hat i + \frac{5}{{13}}\hat j} \right)\\ \vec u = \left( {0.923\hat i + 0.385\hat j} \right) \end{array}\]Step 3
To find the projected component of force we will use,
\[\vec F = F \cdot \vec u\]On plugging the known values in the above relation, we get,
\[\begin{array}{l} \vec F = \left( {0\hat i + 650\;{\rm{N}}\hat j} \right) \cdot \left( {0.923\hat i + 0.385\hat j} \right)\\ \vec F = 250.25\;{\rm{N}} \end{array}\]To find the projection of the force we will use the following relation,
\[{F_{OA}} = \vec F\vec u\]On plugging the known values in the above relation, we get,
\[\begin{array}{l} {F_{OA}} = \left( {250.25\;{\rm{N}}} \right) \cdot \left( {0.923\hat i + 0.385\hat j} \right)\\ {F_{OA}} = \left( {230.9\hat i + 96.3\hat j} \right)\;{\rm{N}} \end{array}\]