PreQuiz 9.1 .:. Go Up
Statics
Show your work, and circle your answers and use sig figs to receive full credit. Use g = 9.81 N/kg
1. Find the Equilibrant – express it as an angle magnitude vector. Draw it with its tail on the origin. Write your answer with 3 sig figs, but carry at least 5 so you don’t make rounding errors. (32.4 N, 89.2^{o} CW from x axis)

x 
y 
A 


B 


E 


Solution:
First  find the components of the vectors. This is easy here because I give you the Trig angle:
Ax = (17.0 N)cos(48^{o}) = 11.375 N
Ay = (17.0 N)sin(48^{o}) = 12.633 N
Bx = (17.0 N)cos(48^{o}) = 11.846 N
By = (17.0 N)sin(48^{o}) = 19.715 N
(Remember  if you have the trig angle, cos gives you the x component always, and sin the y  notice that these components make sense  B would have a negative x component because is to the left of the y axis)
Next  put these in the table and add them together  x to x and y to y:
x y A 11.375 N 12.633 N B 11.846 N 19.715 N Sum 0.471 N +32.348 N Equil +0.471 N 32.348 N The equilibrant is just negative the sum (i.e. it adds to the others to make zero...)
Now you have to draw the equilibrant:
The Equilibrant is the hypotenuse  the angle indicated is the tan^{1}(32.348 /0.471) = 89.2^{o }and the hypotenuse = sqrt(32.348^{2} + 0.471^{2}) = 32.351 N = 32.4 N
Question 1 is to see if you can find an equilibrant
2. Find the tensions in the cables C and D. Set up your x and y equations where indicated, and if you set up a matrix, write down what you are entering into it in matrix notation. (C = 192 N, D = 285 N)
Question 2 is a force equilibrium solvable with a matrix
X:
Y: