Determine the magnitude of the vertical force F acting on the handle of the wrench so that this force produces a component of moment along the AB axis (x axis) of the pipe assembly of (M_A)_x=\left\{-5i\right\} N•m. Both the pipe assembly ABC and the wrench lie in the x-y plane. Suggestion: Use a scalar analysis.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
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As with the previous question, we will use scalar analysis. Let us calculate the perpendicular distance from the x-axis to force F as follows:
Diagram not to scale
The distance d can be calculated using geometry.
d=0.2475 m
Let us now write an equation for the moment along the x-axis.
M_x=(F)(d)
Substitute the values we know:
-5=(-F)(0.2475)(Force F is negative because it is applied downwards (negative z-axis))
F=20.2 N
Final Answer: