Download Engineering Mechanics Statics (Homework #1, Due on March.11)

Engineering Mechanics Statics
(Homework #1, Due on March.11)
1. Using the base units of the SI system, show that Eq. 1–2 is a dimensionally
homogeneous equation which gives F in newtons. Determine to three
significant figures the gravitational force acting between two spheres that
are touching each other. The mass of each sphere is 200 kg and the radius is
300 mm.
2. The plate is subjected to the two forces at A and B as shown. If θ=60°,
determine the magnitude of the resultant of these two forces and its
direction measured clock wise from the horizontal.
2.1 Determine the angle of u for connecting member A to the plate so that
the resultant force of FA and FB is directed horizontally to the right. Also,
what is the magnitude of the resultant force ?
Probs.2-2.1
Probs.3-3.1
3. Resolve F1 into components along the μ and υ axes and determine the
magnitudes of these components.
3.1 Resolve F1 into components along the μ and υ axes and determine the
magnitudes of these components.
4. If  = 45°, F1 = 5 kN, and the resultant force is 6 kN directed along the
positive y axis, determine the required F1 magnitude of F2 and its direction
u.
4.1 If  = 30°, and the resultant force is to be 6 kN directed along the
positive y axis, determine the magnitude of F1 and F2 and the angle θ if
the F2 is required to be minimum.
4.2 If  = 30°, F1 = 5 kN, and the resultant force is to be directed along the
positive y axis, determine the magnitude of resultant force if F2 is to be a
minimum .Also, what is F2 and the angle θ ?
Probs.4-4.2
Probs.5
5. The three concurrent forces acting on the screw eye produce a resultant force
2
FR=0. If F2 = F1 and F1 is to be 90° from F2 as shown, determine the
3
required magnitude of F3 expressed in terms of F1 and the angle θ.
6. The two forces F1 and F2 acting at A have a resultant force of FR={-100k}N.
Determine the magnitude and coordinate direction angles of F2.
6.1 Determine the coordinate direction angles of the force F1 and indicate them
on the figure.
Probs.6-6.1
7. The antenna tower is supported by three cables. If the forces of these
cables acting on the antenna are FB=520N, FC =680N, and FD=560N,
determine the magnitude and coordinate direction angles of the resultant
force acting at A.
Probs.7
8. Determine the x and y components of the 700-N force.
Probs.8