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
