statics exam 1
If a force of magnitude F can be applied in four different 2-D configurations (P,Q,R, & S), select the cases resulting in the maximum and minimum torque values on the nut. (Max, Min).
(Q,S)
If r = {1 i + 2 j} m and F = {10 i + 20 j + 30 k} N, then the moment of F about the y-axis is ____ N·m.
-30
If M = r x F, then what will be the value of M • r ?
0
If F1 = 1 N, x1 = 1 m, F2 = 2 N and x2 = 2 m, what is the location of FR, i.e., the distance x.
1.67m
Find the dot product of the two vectors P and Q. P = {5 i + 2 j + 3 k} m Q = {-2 i + 5 j + 4 k} m
12m^2
If F = 10i+10j+10k & G = 20i+20j+20k, then F+G = ?
30i+30j+30k = F+G
If r = { 5 j } m and F = { 10 k } N, the moment r x F equals { _______ } N·m.
50i
What is the location of FR, i.e., the distance d?
5m
A couple is applied to the beam as shown. Its couple moment equals _____ N·m.
60
What is not true about an unit vector, UA?
Always points in the direction of the x-axis
The forces on the pole can be reduced to a single force and a single moment at point ____ .
Any of these points.
The resultant force (FR) due to a distributed load is equivalent to the _____ under the distributed loading curve, w = w(x)
Area
A force of magnitude F, directed along a unit vector, is given by F = ?
F(U)
Force vector F, directed along a line PQ is given by
F(^rPQ/rPQ)
For this force system, the equivalent system at P is ___________ .
FRP = 40 lb (along +x-dir.) and MRP = +30 ft •lb
The moment of a couple is called a _________ vector.
Free
The dot product of two vectors P and Q is defined as
PQ cos theta
If a dot product of two non-zero vectors equals -1, then the vectors must be ________ to each other.
Parallel (in the opposite direction)
The vector operation (P xQ) • R equals
R • (P x Q).
The dot product of two vectors results in a _________ quantity
Scalar
The Dot product can be used to find all of the following except ____ .
Sum of two vectors
For a frictionless pulley and cable, tensions in the cable (T1 and T2) are related as
T1=T2
The triple scalar product u • ( r x F ) results in
a scalar quantity ( + or - ).
When determining the moment of a force about a specified axis, the axis must be along _____________.
any line in 3-D space
The line of action of the distributed load's equivalent force passes through the ______ of the distributed load.
centroid
The original force and couple system and an equivalent force-couple system have the same _____ effect on a body.
external
Consider two couples acting on a body. The simplest possible equivalent system at any arbitrary point on the body will have
one couple moment.
If a dot product of two non zero vectors is 0, then the two vectors must be __________ to each other
perpendicular
Moment of force F about point O is defined as MO = ___________ .
r x F
F1 and F2 =-F1 form a couple. The moment of the couple is given by ____
r2 x F1
You can determine the couple moment as M = r x F If F = {20 k} lb, then r is:
rCB
P and Q are two points in a 3D space. How are the position vectors rPQ and rQP related?
rPQ=-rQP
Two points in 3D space have coordinates of P(1,2,3) and Q(4,5,6) meters. The position vector is given by
rQP = -3i-3j-3k
A general system of forces and couple moments acting on a rigid body can be reduced to a ___
single force and a single moment
If three couples act on a body, the overall result is that:
the net force equals 0 but the net couple moment is not necessarily equal to 0
When a particle is in equilibrium, the sum of forces acting on it equals ___ .
zero
