16.6: Appendix 1 Homework Problems
Exercise \(\PageIndex{1}\)
Determine the \(x\) and \(y\) components of the force vector shown below.
- Solution:
-
\(F_x = 692.8 \ N\)
\(F_y = 400 N\)
Exercise \(\PageIndex{2}\)
Determine the \(x\), \(y\), and \(z\) components of the vector shown below.
- Solution:
-
\(F_x = 4.17 \ kN\)
\(F_y = 2.54 \ kN\)
\(F_z = -3.50 \ kN\)
Exercise \(\PageIndex{3}\)
An 80-lb tension acts along a cable stretching from point O to point A. Based on the dimensions given, break the tension force shown into \(x\), \(y\), and \(z\) components.
- Solution:
-
\(F_x = 56.47 \ lbs\)
\(F_y = -37.64 \ lbs\)
\(F_z = 42.35 \ lbs\)
Exercise \(\PageIndex{4}\)
Determine the \(x\) and \(y\) components of the sum of the two vectors shown below.
- Solution:
-
\(F_{total} = [58.2, 41.7] \ lbs\)
Exercise \(\PageIndex{5}\)
There are two forces acting on a barge as shown below (\(\vec{F}_1\) and \(\vec{F}_2\)). The magnitude and direction of \(\vec{F}_1\) is known, but the magnitude and direction of \(\vec{F}_2\) is not. If the sum of the two forces is 600 N along the \(x\)-axis, what must the magnitude and direction of \(\vec{F}_2\) be?
- Solution:
-
\(\vec{F}_2 = 390.3 \ N\), at 41.2° below the x-axis