STATICS #1 EXAM

Select the correct FBD of particle A.

(D)

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

C) 12 m^2

For this force system, the equivalent system at P is ___________ .

D) FRP = 40 lb (along +x-dir.) and MRP = +30 ft •lb

Assuming you know the geometry of the ropes, you cannot determine the forces in the cables in which system above?

(C)

x = __________.

B) 4 m

If M = r x F, then what will be the value of M • r?

A) 0

If r = { 5 j} m and F = { 10 k } N, the moment r x F equals { _______ } N·m.

A) 50 i

A position vector, rPQ, is obtained by

A) Coordinates of Q minus coordinates of P

A force of magnitude F, directed along a unit vector U, is given by F= ______ .

A) F (U)

The moment of a couple is called a _________ vector.

A) Free

________________ still remains the basis of most of today's engineering sciences.

A) Newtonian Mechanics

The dot product of two vectors P and Q is defined as

A) PQcos(theta)

The triple scalar product u • ( r x F ) results in

A) a scalar quantity ( + or - ).

The line of action of the distributed load's equivalent force passes through the ______ of the distributed load.

A) centroid

The dot product of two vectors results in a _________ quantity.

A) scalar

The Dot product can be used to find all of the following except ____ .

A) sum of two vectors

Moment of force F about point O is defined as MO= ___________ .

A) ~r~ x ~F~

If r= {1 i + 2 j} m and F= {10 i+ 20j+ 30 k} N, then the moment of F about the y-axis is ____ N·m.

B) -30

Using the CCW direction as positive, the net moment of the two forces about point P is

B) 20 N •m

Particle P is in equilibrium with five (5) forces acting on it in 3-D space. How many scalar equations of equilibrium can be written for point P?

B) 3

What is the moment of the 10 N force about point A (MA)?

B) 30 N·m

A couple is applied to the beam as shown. Its couple moment equals _____ N·m.

B) 60

Using this FBD of Point C, the sum of forces in the x-direction ((sum of)FX) is ___ .Use a sign convention of + --->

B) F2cos 50°- 20 = 0

The vector operation (P x Q) •R equals

B) R • (P x Q).

For a frictionless pulley and cable, tensions in the cable (T1 and T2) are related as _____ .

B) T1= T2

If you know just UA, you can determine the ________ of A uniquely.

B) angles (alpha, beta and gamma)

The symbols (alpha), (beta), and (gamma) designate the __________ of a 3-D Cartesian vector.

B) coordinate direction angles

The original force and couple system and an equivalent force-couple system have the same _____ effect on a body.

B) external

If a dot product of two non-zero vectors equals -1, then the vectors must be ________ to each other.

B) parallel (pointing in the opposite direction)

F1 and F2=-F1 form a couple. The moment of the couple is given by ____

B) r2 x F1

P and Q are two points in a 3-D space. How are the position vectors rPQ and rQP related?

B) rPQ= - rQP

Consider three couples acting on a body. Equivalent systems will be _______ at different points on the body.

B) the same even when located

Two points in 3 - D space have coordinates of P (1, 2, 3) and Q (4, 5, 6) meters. The position vector rQP is given by

B) {- 3 i-3 j-3 k}m

Determine the magnitude of the resultant (F1+ F2) force in N when F1= { 10i+ 20j} N and F2= { 20i+ 20j} N .

C) 50 N

FR= ____________

C) 600 N

Resolve F long x and y axes and write it in vector form. F= { ___________ } N

C) 80 sin (30°) i- 80 cos (30°) j

For an arbitrary force vector, the following parameters are randomly generated. Magnitude is 0.9 N, alpha= 30º, beta= 70º, gamma= 100º. What is wrong with this 3-D vector ?

C) All three angles are arbitrarily picked.

Force vector, F, directed along a line PQ is given by

C) F(~rPQ~/rPQ)

The subject of mechanics deals with what happens to a body when ______ is / are applied to it.

C) Forces

What is not true about an unit vector, UA?

C) It always points in the direction of positive X- axis.

Which one of the following is a scalar quantity?

C) Mass

Why?

C) There are more unknowns than equations.

The resultant force (FR) due to a distributed load is equivalent to the _____ under the distributed loading curve, w = w(x).

C) area

Consider two couples acting on a body. The simplest possible equivalent system at any arbitrary point on the body will have

C) one couple moment.

If a dot product of two non-zero vectors is 0, then the two vectors must be _____________ to each other.

C) perpendicular

For finding the moment of the force F about the x-axis, the position vector in the triple scalar product should be ___ .

C) rAB

You can determine the couple moment as M = r x F

C) rCB

When a particle is in equilibrium, the sum of forces acting on it equals ___ . (Choose the most appropriate answer)

C) zero

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).

D) (Q, S)

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.

D) 1.67 m

If F= {10 i+ 10 j+ 10 k} N and G= {20i+ 20j+ 20 k} N, then F+G= { ____ } N

D) 30i+ 30 j+ 30 k

What is the location of FR, i.e., the distance d?

D) 5 m

In statics, a couple is defined as __________ separated by a perpendicular distance.

D) None of the above

Vector algebra, as we are going to use it, is based on a ___________ coordinate system.

D) Right-handed

When determining the moment of a force about a specified axis, the axis must be along _____________.

D) any line in 3-D space

The force F is acting along DC. Using the triple product to determine the moment of F about the bar BA, you could use any of the following position vectors except ______.

D) rDB

A general system of forces and couple moments acting on a rigid body can be reduced to a ___ .

D) single force and a single moment.

For vector addition you have to use ______ law.

D) the Parallelogram

If three couples act on a body, the overall result is that

D) the net force equals 0 but the net couple moment is not necessarily equal to 0

The forces on the pole can be reduced to a single force and a single moment at point ____ .

E) Any of these points.