STATICS MIDTERM MULTIPLE CHOICE

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.

-30

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

12 m^2

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

20 N•m

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

50 N

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

zero

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

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

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

0

What is the moment of the 12 N force about point A (MA)?

36 N·m

In 3-D, when a particle is in equilibrium, which of the following equations apply?

All of the above. ((Σ Fx) i + (Σ Fy) j + (Σ Fz) k = 0; Σ F = 0; Σ Fx = Σ Fy = Σ Fz = 0)

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 ?

All three angles are arbitrarily picked.

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

Coordinate direction angles

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

E) Any of these points.

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

F (U)

Why can you not determine the forces in these cables?

There are more unknowns than equations.

In 3-D, when you don't know the direction or the magnitude of a force, how many unknowns do you have corresponding to that force?

Three

Can you resolve a 2-D vector along three directions (say at 0, 60, and 120°)?

Yes, but not uniquely

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

angles (α-alpha, β-beta and γ-gamma)

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

any line in 3-D space or the y axis

If a particle has 3-D forces acting on it and is in static equilibrium, the components of the resultant force (Σ Fx, Σ Fy, and Σ Fz) ___.

have to equal zero, e.g., 0i + 0j + 0k

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

r x F

For vector addition you have to use ______ law.

the Parallelogram

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

(C)

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)

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?

3

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

30 i + 30 j + 30 k

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

50 i

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

80 sin (30°) i - 80 cos (30°) j

Four forces act at point A and point A is in equilibrium. Select the correct force vector P.

? None of the above. { -20i - 10j + 10k} N ?

A position vector, rPQ, is obtained by

Coordinates of Q minus coordinates of P

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

F(rPQ/rPQ)

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

F2 cos 50°- 20 = 0

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

Forces

What is not true about an unit vector, UA?

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

Which one of the following is a scalar quantity?

Mass

If F and r are force and position vectors, respectively, in SI units, what are the units of the expression (r * (F / F)) ?

Meter

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

Newtonian Mechanics

In 3-D, when you know the direction of a force but not its magnitude, how many unknowns corresponding to that force remain?

One

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

PQcos(theta)

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

Parallel (pointing in the opposite direction)

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

Perpendicular

The vector operation (P x Q) •R equals

R • (P x Q).

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

Right-handed

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

Scalar

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

T1 = T2

Can you resolve a 2-D vector along two directions, which are not at 90° to each other?

Yes, uniquely

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

a scalar quantity ( + or - ).

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

rAB

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 ______.

rDB

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

rPQ = - rQP

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

sum of two vectors