Weight suspended on three strings

[gnehus]

I'm having trouble on this problem: A weight of 21 kg is suspended by means of three strings T1,T2,T3. T1 and two are connected to a ceiling and meet at their end. T3 connects at the joint section of T2 and T3. All that you are given is the angles of T1 & T2 and the weight of the object. How would one find the tensions in each string. I understand how to find tension in a one string question...but not with three strings.

http://mysite.verizon.net/nehus/phys.bmp

 

[big man]

You have three unknowns so you will need three equations to solve the problem.

You need to break up the tensions T1 and T2 into their different components (that is, horizontal and vertical).

T3 will be equal to the force due to gravity on the mass (Mg). You now need to find two other equations. They have to do with the vertical components of T1 and T2 and the horizontal components.

 

[kyle8921]

First of all, it is important to understand that the weight of an object is equal to the sum of the forces acting on it. In this case, the weight of 21 kg is being supported by the three strings, so the sum of the tensions in the three strings must equal 21 kg.

To find the tensions in each string, we can use trigonometry and the concept of vector components. Let's label the angles given in the problem as θ1 and θ2. We can then break down the weight of 21 kg into its horizontal and vertical components, using the given angles.

The horizontal component of the weight can be found using the formula Wsinθ, where W is the weight and θ is the angle. In this case, the horizontal component would be 21 kg x sinθ1. Similarly, the vertical component can be found using the formula Wcosθ, which would be 21 kg x cosθ1.

Now, let's consider the forces acting on each string. T1 and T2 are pulling upwards and T3 is pulling downwards. This means that the vertical component of the weight must be balanced by the sum of the tensions in T1 and T2. So we can set up the following equation: T1 + T2 = 21 kg x cosθ1.

Next, we can look at the horizontal forces. T1 is pulling to the right and T2 is pulling to the left, so they must be equal in magnitude. This means that the horizontal component of the weight must be balanced by the tensions in T1 and T2. So we can set up another equation: T1 = T2 = 21 kg x sinθ1.

Finally, we can consider the forces acting on T3. It is pulling downwards with a tension of T3 and pulling to the left with a tension of T2. These two forces must be balanced by the horizontal component of the weight. So we can set up one more equation: T2 = 21 kg x cosθ2.

We now have three equations with three unknowns (T1, T2, and T3) and can solve for the tensions in each string. Once we have the values for T1, T2, and T3, we can use them to find the magnitude and direction of each string's tension using trigonometry.

In summary, to find the tensions in each string, we need to use the concepts of