TENSION CALCULATOR OF TWO STRINGS WITH DIFFERENT ANGLES

Tension calculator 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.


Tension Calculator of Two Strings

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 :

Tension in Two Ropes Calculator
 INPUT PARAMETERS
Mass [m]
Gravity [g]
Angle [α]
Angle [θ]

Note: Use dot "." as decimal separator.

 


RESULTS
Tension-1 [T1]
Tension-2 [T2]

Note: Default rounding is 7 decimal places.


Tension in Two Ropes Example:

Tension in Two Ropes Example

Calculate the tension in the two ropes shown below.

Solution:

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

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

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

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

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

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

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

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

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

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

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

Reference: