The vertical force F acts downward at A on the two-membered frame a) Determine t
ID: 2269631 • Letter: T
Question
The vertical force F acts downward at A on the two-membered frame
a) Determine the magnitude of the component of F directed along the axe of AB. Set F = 550N .
The vertical force F acts downward at A on the two-membered frame Determine the magnitude of the component of F directed along the axe of AB. Set F = 550N. Express your answer to two significant figures and include the appropriate units. FAB= N Determine the magnitude of the component of F directed along the axe of AC. Express your answer to two significant figures and include the appropriate units. FAC= NExplanation / Answer
There are only three things to remember for any statics problem
Sum of forces in the x direction must equal zero
Sum of forces in the y direction must equal zero
Sum of moments about any convenient point must equal zero.
Let Fab be the force acting along AB
Let Fac be the force acting along AC
assume both are tensile
assume to "the right" and "up" are positive directions
assume clockwise moments are positive
summing forces in the x direction to zero
Fabsin45 + Faccos30 = 0
Fabsin45 = -Faccos30
Fab = -Faccos30/(sin45)
Summing forces in the y direction to zero
Fabcos45 - Facsin30 - 550 = 0
Fabcos45 - Facsin30 = 550
subbing from above
(-Faccos30/sin45)cos45 - Facsin30 = 550
as sin45 = cos45
-Fac(cos30 + sin30) = 550
Fac = -550 / (cos30 + sin30)
Fac = -402.6 N
as the result is negative, our actual force is compressive, not tensile as in our assumption.
from earlier
Fab = -Faccos30/sin45
Fab = -(-402.6)cos30/(sin45)
Fab = 493.1 N
as this result is positive, the force is actually tensile as in our assumption.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.