# Finding Tension is three cables attached to a particular mass?

• savva
In summary, the object of mass m suspended from three cables with tensions T1, T2, and T3. The horizontal component of T1 is 900N and the horizontal component of T2 is also 900N. T2 has a tension of 1175N. T3 can be found using Newton's 1st Law in both the horizontal and vertical directions and is equal to 2315N. The mass of the suspended object is 236kg.
savva

## Homework Statement

An object of mass m is suspended from a cable tied to two other cables, each fastened to a supporting beam, as shown below. The tensions in the three supporting cables are T1, T2, and T3. The diagram of the system is available via the link below:

http://i40.tinypic.com/15goxg3.jpg

The tension T1 = 1800 N.

I worked out the first three parts, but could not work out parts d) and e)
(a) Determine the horizontal component of T1.
(b) Determine the horizontal component of T2.
(c) Determine the tension T2.
(d) Determine the tension T3.
(e) Determine the mass of the suspended object.

## The Attempt at a Solution

(a) Determine the horizontal component of T1.
Th = 1800cos(60) = 900N
(b) Determine the horizontal component of T2.
Th = 1800cos(60) = 900N (The same component for T2) - The only thing is I do not understand why this is the same - I only knew to calculate it the same because I have the answers given.
(c) Determine the tension T2.
T2 = 900/cos(40) = 1175N

Any help would be appreciated greatly

T1/sin40=T2/sin60=T3/sin 80
you can work out the T3 tension from this equality.and it is easily seen from figure mass m equals T3.

savva said:
(a) Determine the horizontal component of T1.
Th = 1800cos(60) = 900N
(b) Determine the horizontal component of T2.
Th = 1800cos(60) = 900N (The same component for T2) - The only thing is I do not understand why this is the same - I only knew to calculate it the same because I have the answers given.
Try applying Newton's 1st Law in the horizontal direction to solve for the horizontal component of T2

utku said:
T1/sin40=T2/sin60=T3/sin 80
you can work out the T3 tension from this equality.and it is easily seen from figure mass m equals T3.

using that method, I can't seem to get the correct answer:

1800/sin40 = 1175/sin60 = T3/sin80

((1800/sin40) - (1175/sin60)) x sin80 = 1421.6N

The answer for part d) T3 = 2313N

What method do I apply to get this if it is not the one I currently used?

Try applying Newton's 1st Law in the horizontal direction to solve for the horizontal component of T2. Then apply his 1st law in the vertical direction to solve for T3.

Newton's 1st Law:

$\Sigma F_x = 0$
$\Sigma F_y = 0$

Ok, I've got it now, thanks for your help:

Information given as well as calculations done previously can help to solve part d and subsequently e.

Part d)

T3 = Tv1 + Tv2

Tv1 = 1800sin(60) = 1560N
Tv2 = 900tan(40) = 755N

Therefore, T3 = 1560 + 755 = 2315N

for part e)

m = T3/g = 2315/9.8 = 236kg

## 1. How do you calculate the tension in three cables attached to a particular mass?

To calculate the tension in three cables attached to a particular mass, you will need to use Newton's Second Law of Motion, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration will be zero since the mass is not moving. You will also need to use the equation for equilibrium, which states that the sum of all forces in the x-direction and the y-direction must equal zero.

## 2. Why is it important to find the tension in the cables?

Knowing the tension in the cables is important because it helps determine whether the cables are strong enough to support the mass. If the tension is too high, the cables could break and cause the mass to fall. If the tension is too low, the cables may not be able to hold the mass in place. It is also important for safety reasons to ensure that the cables are not under too much stress.

## 3. What factors affect the tension in the cables?

The tension in the cables can be affected by several factors, including the weight of the mass, the angle of the cables, and the strength and elasticity of the cables themselves. The tension will also change if the mass is moving or if there are any external forces acting on the cables, such as wind or vibration.

## 4. Can the tension in the cables be greater than the weight of the mass?

Yes, it is possible for the tension in the cables to be greater than the weight of the mass. This can happen if the angle of the cables is steep or if the cables are not strong enough to support the weight. In this case, the tension in the cables will need to be reduced by adjusting the angle or using stronger cables to prevent any potential accidents.

## 5. How can the tension in the cables be adjusted?

The tension in the cables can be adjusted by changing the angle of the cables or by using different cables with varying strengths and elasticity. The tension can also be adjusted by adding or removing weights from the mass. It is important to ensure that the tension is within a safe range to prevent any accidents or damage to the cables.

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