Question

How do you do this???

Answer 1

Step-by-step Answer:

This is a problem of "three concurrent forces meeting at a point" and can be solved by

1. Triangle of forces

2. parallelogram of forces

3. resolving the forces into the x-y components.

Since you appear to be working on vectors at the moment, I will solve using the third method.

For three concurrent forces to be in static equilibrium (our case here), the sum of x-components must equal zero, same for the sum of y-components.

We will let the force on the left wire to be R, and that on the right be T.

Resolving forces in the x-direction,

Sum-X = -Rcos(20)+100cos(90)+Tcos(30)=0

Simplify to get T=Rcos(20)/cos(30).............(1)

Next,

Sum-Y = Rsin(20)+Tsin(30)-100cos(0) = 0

or

Rsin(20)+Tsin(30)=100 .................(2)

Substitute (1) in (2)

Rsin(20)+Rcos(20)sin(30)/cos(30)=100

Simplify to get

R=100/(sin(20)+cos(20)sin(30)/cos(30))=113.05 ........(3)

Substitute (3) in (2) to get T=122.67