statics exam 1

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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


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