# TENSION CALCULATOR OF TWO STRINGS WITH DIFFERENT ANGLES

Tension calculator in physics to find tension in two ropes hanging with different (or same) angles and supporting an object with mass m. One rope makes an angle α with the vertical and the other makes an angle θ. It's assumed that the strings have negligible mass.

The object is not being accelerated and the net force on the object in X and Y direction must be 0.  The decomposition of forces results following equations.

$$\sum { { F }_{ x } } =0\quad , { T }_{ 1 }\sin { \alpha } -{ T }_{ 2 }\sin { \theta } =0$$
$$\quad \sum { { F }_{ y } } =0\quad , {T }_{ 1 }\cos { \alpha } +{ T }_{ 2 }\cos { \theta } - mg =0$$

### Tension Calculator of Two Ropes :

 INPUT PARAMETERS Mass [m] g kg oz lb Gravity [g] m/s^2 g m/h^2 cm/s^2 in/s^2 km/h^2 miles/h^2 ft/s^2 Angle [α] deg rad Angle [θ]

Note: Use dot "." as decimal separator.

 RESULTS Tension-1 [T1] N kN lbf Tension-2 [T2]

Note: Default rounding is 7 decimal places.

### Tension in Two Ropes Example:

Calculate the tension in the two ropes shown below.

Solution:

$$\sum { { F }_{ y } } ={ T }_{ 2y }-mg$$

$$0 ={ T }_{ 2y }-mg$$

$$mg={ T }_{ 2y }$$

$$mg={ T }_{ 2 }\sin { { 60 }^{ \circ } }$$

$$100\times 9.81/\sin { { 60 }^{ \circ } } ={ T }_{ 2 }$$

$$100\times 9.81/\sin { { 60 }^{ \circ } } =1132.76N={ T }_{ 2 }$$

$$\sum { { F }_{ x } } ={ T }_{ 1 }-{ T }_{ 2x }$$

$$0 ={ T }_{ 1 }-{ T }_{ 2x }$$

$${ T }_{ 2x }={ T }_{ 1 }$$

$${ T }_{ 2 }\cos { { 60 }^{ \circ } } ={ T }_{ 1 }$$

$${ T }_{ 2 }\cos { { 60 }^{ \circ } } =1132.76N\times 0.5={ 566.38N=T }_{ 1 }$$