# Thread: Vector as forces problem

1. ## Vector as forces problem

I really need some help with this:
A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

2. Originally Posted by Soul to soul
I really need some help with this:
A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

Start by recognising that you have a 3-4-5 triangle in there and hence a 90 degree angle at the point where the 15 kg mass is attached ....

Note that Lami's Theorem makes the problem simple.

3. Originally Posted by Soul to soul
I really need some help with this:
A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

let A be the point where the 15 cm string is attached to the ceiling.
C be the point where the 20 cm string is attached to the ceiling.
B be the point directly above the hanging mass between A and C.
M is the mass position.

ABM and CBM are right triangles.

AC = 25 cm , AB = x cm , BC = (25-x) cm

using Pythagoras ...

$\displaystyle 15^2 - x^2 = 20^2 - (25 - x)^2$

$\displaystyle x = 9$ ... BM = 12 cm

let $\displaystyle T_1$ = tension in the 15 cm string
$\displaystyle T_2$ = tension in the 20 cm string
$\displaystyle g$ = acceleration due to gravity

system is in equilibrium ...

$\displaystyle \sum{F_x} = 0$

$\displaystyle T_1 \cdot \frac{3}{5} = T_2 \cdot \frac{4}{5}$

$\displaystyle \sum{F_y} = 0$

$\displaystyle T_1 \cdot \frac{4}{5} + T_2 \cdot \frac{3}{5} = 15g$

solve the system for $\displaystyle T_1$ and $\displaystyle T_2$

4. Thanks a lot, now I know how to solve it!