A 1400 kg steel beam is supported by two ropes.

What is Tension in Rope 1 and what is Tension in Rope 2

## Answer

Along the x - direction:

T1 sin20 = T2

sin30

0.342 T1 = 0.5T2

==> T1 / T2 = 0.5 / 0.342

T1

= 1.461T2 ........1

Along the vertical direction

T1cos20 + T2 cos30

=mg

==> 0.939T1 + 0.866T2 =

13720 .....2

Substituting 1 in 2 we get

1.3718T2

+0.866T2 = 13720

2.237

T2 = 13720

∴

T2 = 6133.2 N

and

T1 = 8960.2 N

T_{1}sin(20) = T_{2}sin(30)

T_{1}cos(20) + T_{1}cos(30) = mg

T_{1}cos(20) + T_{1}sin(20)cos(30)/sin(30) =

mg

T_{1}cos(20)sin(30) + T_{1}sin(20)cos(30)

=mgsin(30)

T_{1}sin(20 + 30) = mgsin(30)

∴T_{1} = mgsin(30)/sin(50) = 8955 N

T_{2} = mgsin(20)/sin(50) = 6126 N