Question

Could you please provide a clear and accurate worked solution for the following problem. I will leave feedback that matches the accuracy and effort of your solution. Please make any formulas used clear. Thank you.

There is an object with some forces acting on it. Through its centre of gravity at (0, 0, 0) there is a force of size and direction (1, 1, 1) Through (1, 1, 1) there is a force (-1,-1, 0) Through (0, 0, 1) there is a force (2,2,0) Through (0, 1, 0) there is a force (-2,-1, 0) 1. What is the total force on the object? 2. What is its direction? 3. Calculate the total couple applied to the object? 4. Can you combine the couple and the force into a single force acting on some specific point of the object?

Answer 1

Given Fi - Cliel) i+j+T Fz = (-1,-1,0) =-1-j (212,0) zitzi = (-2,-1,0) =-21-3 F3 F4 Flotal = Ft Ez + Ez + FG TAJTE _f 7 +27 +2] -2 ] Bjte Total jt E Magnitude of F Total Jastu? = Fz | Frotal 1=52 2 1 Direction Cosines ane ot -Frotal 1 (I Z Along X-aas = COS 5 (2/2) y-axis Oy = cos' 450 [te] cos' [%] Z-anis 今 45° CS Scanned with CamScanner

Couple 31 TX M, i i k 0 - M, i j k - i] 1 1 0 i j کیا - 21tz O O 2 2 o My ZE O 0 -2 -lo Mjetal = M, + M₂ + Mg + My -- + + 21 Motel _9+j tak 14 Let position Vector be 7=(att Lit CT ) M Tot = JXFTotal k (-i +j+2E) a с -i tj 12E = (b-c)] - aj tak b-c=-1 -a=1 solving as-1 CS Scanned with CamScanner Y = -lilil