CE Exam 1

if M=rxF, what will be the value of Mdot r?

0

find the dot product of the two vectors P and Q, where P={5i+2j+3k}m and Q={-2i+5j+4k}m.

12m^2

in 3D, when a particle is in equilibrium, which of the equations apply? sumFx=sumFy=sumFz=0 sumF=0 sumFxi+sumFyj+sumFzk=0 none of them all of them

all of them

for a force vector, the following parameters were randomly generated. magnitude=0.9N and directional angles are: alpha=30, beta=70, and gamma=100. What is wrong with this 3D vector?

all three angles are arbitrarily picked

vector A has d=3m, F=12N pointing straight up from end of A, forming 90 degree angle. What is the moment Ma of the 12N force about point A?

36 Nm

couple applied to beam as shown (1m line with 50N arrow pointing down at the end of it, followed by 2m line with arrow pointing up at end of it, making triangle with sides 3,4,5). Both forces are 50N. Its moment equals

50(2)(3/5)=60Nm

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

50N

resolve the force F into x and y components and express it as a Cartesian coordinate vector (xy plane with arrow in fourth quadrant, angle=30 degrees with y-axis, F=80N

80cos(30)i-80sin(30)j

the position vector rPQ is obtained by

Coordinates of Q minus coordinates of P

a force of magnitude F, directed along a unit vector u, is given by F=

F(u)

F2 in first quadrant with angle=50 with the x-axis, F1 pointing straight down, force to the left=20 lb, point C in the middle. the sum of the forces in the x direction is

F2sin(40)-20lb=0

resolve the force vector, F, into components along the u and v directions (force vector in first quadrant with F=200N, u is 30 degrees to the right of vector and 45 degrees with x-axis, v is 70 degrees to left of vector

Fu= 173.2N, Fv=153.2N

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). (wrench with P,Q,R,S pointing inward at hole on handle)

Max configuration: Q Min configuration: S

frictionless pulley and cable, tensions are related as (T2 pointing straight down, T1 pointing down and to left with angle theta with the x-axis)

T1=T2

the triple scalar product udot(rxF) results in

a scalar quantity (+ or -)

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

centroid

If you know only Ua, you can determine the _____ of A uniquely.

coordinate angles (alpha, beta, gamma)

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

coordinate direction angles

which of the following is a scalar quantity? position force mass velocity

mass

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

perpendicular

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

scalar

in statics, a couple is defined as ----- separated by a perpendicular distance.

two forces of equal magnitude acting in opposite directions

When a particle is in equilibrium, the sum of forces acting on it equals

zero

If r={5j}m and F={10k}N, the moment rxF equals

{50i}Nm