Statics Flashcards

Force F = 2i − 3j + 6k kN acts at position r = i + 2j − k m. What is the moment about the origin?

Answer: 9i − 8j − 7k kN·m

M = r × F: i(2·6 − (−1)(−3)) − j(1·6 − (−1)·2) + k(1·(−3) − 2·2) = 9i − 8j − 7k kN·m.

The centroid y-coordinate of a semicircle of radius R, measured from its flat diameter, is:

Answer: 4R/(3π)

Integration of the semicircular area yields ȳ = 4R/(3π) from the flat (diameter) edge.

A cable supports a 200 N weight at a junction, with left segment at 30° and right segment at 45° from horizontal. Which equation set is correct?

Answer: T1cos30° = T2cos45° and T1sin30° + T2sin45° = 200

ΣFx = 0 gives T1cos30° = T2cos45°; ΣFy = 0 gives T1sin30° + T2sin45° = 200 N.

The product of inertia Ixy equals zero for any cross-section that has:

Answer: At least one axis of symmetry

When at least one axis of symmetry exists, paired area elements on opposite sides cancel, making Ixy = 0.

A rigid body is subjected to a pure couple. Which statement is true about the couple moment?

Answer: It produces the same moment value about any reference point

A pure couple's moment is a free vector — it has the same magnitude and direction regardless of the reference point chosen.

A force of 100 N is directed at 210° from the positive x-axis. What is its y-component?

Answer: −50 N

Fy = 100 sin(210°) = 100 × (−sin30°) = 100 × (−0.5) = −50 N.

In 2D static analysis, how many reaction components does a pin support provide, and why?

Answer: 2 — it prevents translation in both x and y but allows rotation

A pin prevents translation in both x and y directions (2 reaction forces) but allows free rotation, providing exactly 2 unknowns.