how to solve the tension force of a two ropes connected in a box of 100lb and is being hang. the angles of the ropes are 60? Meaninig the box is in the center.

November 9, 2017 - 6:18pm

#1
vector analysis

surface area of cone formula calculus integration review how to draw shear and bending moment diagrams surface area of frustum of cone formula shear flow in built up members tsa formula length of angle bisector differentiating inverse trig functions moment of inertia of a square tube who made the quadratic formula 6x 3y 12 engineering calculator casio what is an intercepted arc pentagonal pyramid vertices bending stress definition hoop stress formula define compressive stress maxwell diagram truss analysis deferred annuity meaning volume of a truncated square pyramid altitude of triangle formula for pythagorean theorem laplace sinh constant acceleration problems tangent to a circle formula integration with inverse trig functions numericals on projectile motion centroid of shapes pentagonal right prism inverse laplace transform calculator solve bernoulli equation truss bridge calculations tan double angle formula polar coordinate integration secant tangent angles derivation of volume of sphere surface area of hemisphere pyramid calculation formula finding radius of a sphere projectile motion formulas equation of the tangent to a circle csc 2 identity volume of a sphere formula calculator formula for finding radius of a circle casio fx 115 es plus hands on equations verbal problems radius of curvature of a beam semiannually in math three moment equation examples differential and integration formulas what does gyration mean similar figures in geometry inverse trig formulas frustum of cone volume pythagoras theorem derivation intercepted arc pyramid and cone truss questions and solutions what is the difference between arithmetic mean and geometric mean solid cylinder volume formula eccentric loading formulas for a triangle tangent line and normal line calculus trig half angle properties of a cuboid what is the longitude and latitude of manila frustum cone calculator basic parabola equation isosceles triangle formula tangent to a circle formula area of a regular pentagon formula different methods to prove pythagoras theorem how to find the volume of a regular tetrahedron plane wing lift parabola equation vertex

On what is described in your problem, it would look like this:

Upon closer understanding of the problem, it would look like this:

To get the tension of the strings AB and BC, we can consider the string AB as vector $U$, the string BC as a vector $V$ and the resultant force

would be the weight of the box (symbolized as vector $W$)

So...

$$U+V=W$$

Then we set the point B as the origin of the rectangular coordinate system, so the new equation would be:

$$[X_1, Y_1] + [X_2, Y_2] = [X_3, Y_3]$$ $$[r_1\cos 60^o, r_1 \sin 60^o]+[r_2\cos 60^o, r_2\sin 60^o]=[100\cos 270^o, 100\sin 270^o]$$ $$[r_1\cos 60^o, r_1 \sin 60^o]+[r_2\cos 60^o, r_2\sin 60^o]=[0, -100]$$

Notice that the box was hanged on the middle of the string AC, so the tension in the strings AB and BC would be the same, so $U = V $

$$U+V=W$$ $$V+V=W$$ $$2V=W$$ $$2[r_2\cos 60^o, r_2\sin 60^o]=[0, -100]$$ $$[2r_2\cos 60^o, 2r_2\sin 60^o]=[0, -100]$$

Then doing this now:

$$2r_2\cos 60^o = 0$$ $$2r_2\sin 60^o = -100$$

Now getting the $r_2$ in $2r_2\cos 60^o = 0$:

$$r_2 = 0$$

That's not right....

Now getting the $r_2$ in $2r_2\sin 60^o = -100$:

$$r_2 = 57.7$$

We now conclude that the tension in one of the strings would be $57.7$ pounds.

To elaborate...tension in string AB would be $57.7$ pounds and the tension in the string BC would be $57.7$ pounds too...

Alternate solutions are encouraged:-)