NCEES Statics 5

Question 1

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

Accepted Answer

9i − 8j − 7k kN·m

Answer

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

Question 2

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

Accepted Answer

4R/(3π)

Answer

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

Question 3

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?

Accepted Answer

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

Answer

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

Question 4

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

Accepted Answer

At least one axis of symmetry

Answer

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

Question 5

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

Accepted Answer

It produces the same moment value about any reference point

Answer

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

NCEES Practice Test