Engineering Mechanics: Statics and Dynamics, 14th Edition
Authors: Russell C. Hibbeler
ISBN-13: 978-0133915426
See our solution for Question 6P from Chapter 4 from Hibbeler's Engineering Mechanics.
Problem 6P
Step-by-Step Solution
We are given the vertical force $P = 25\;{\rm{lb}}$ at the grip and the inclined force $F = 155\;{\rm{lb}}$ at the claw.
We are asked to determine the moment of each force about point A and also to determine that whether the vertical force P is sufficient to pull out the nail or not.
Step 2
The free-body diagram of the crowbar can be drawn as:
To calculate the moment caused by the force F about point A, we have:
\[\begin{array}{c} {M_A} = F\sin 60^\circ \times \left( {3\;{\rm{in}}} \right)\\ {M_A} = \left( {155\;{\rm{lb}}} \right)\sin 60^\circ \times \left( {3\;{\rm{in}}} \right)\\ {M_A} = 402.70\;{\rm{lb}} \cdot {\rm{in}} \end{array}\]Similarly, to calculate the moment caused by the force P about point A, we have:
\[\begin{array}{c} {M_A} = P \times \left[ {\left( {14\;{\rm{in}}} \right) + \left( {1.5\;{\rm{in}}} \right)\tan 20^\circ } \right]\cos 20^\circ \\ {M_A} = \left( {25\;{\rm{lb}}} \right) \times 13.66\;{\rm{in}}\\ {M_A} = 341.5\;{\rm{lb}} \cdot {\rm{in}} \end{array}\]Since, the moment caused by the force F is greater than the vertical force P. So, the force P is not sufficient to pull the nail.