# Point body of mass hung from a ceiling on two ropes

• Simon Akbar
In summary, an object weighing 8.0 N is supported by two ropes at angles 30 degrees and 60 degrees to the horizontal, with tensions T1 = 4N and T2 = 6.93N. To find the maximum tension of the obtained forces, we can find the larger value between T1 and T2. To find the minimal required tensile strength of the rope, we can plot it as a function of the angle a, without plugging in a specific value. The sum of T1 and T2 is not necessarily equal to the minimal required tensile strength of the rope.
Simon Akbar

## Homework Statement

An object weighing 8.0 N is supported by two rope, which form the angles a and b to the horizontal, with tensions T1 and T2.
angle a = 30 degrees
angle b = 60 degrees
I have calculated these values:
T1 = 4N
T2 = 6.93N

How do I find the maximum tension of the obtained tension forces?
How do find the minimal required tensile strength of the rope?

## The Attempt at a Solution

Simon Akbar said:
How do I find the maximum tension of the obtained tension forces?
Simon Akbar said:
How do find the minimal required tensile strength of the rope?
Find the generic function for T1 and T2 in terms of angle they form with the horizontal and then find the maxima/minima of that function.

Simon Akbar said:
maximum tension of the obtained tension forces?
Maximum with respect to what, i.e. what is allowed to vary? Or maybe it is just the maximum of the two tensions?
Perhaps you should post the entire question, word for word.

q1) Find the larger value, Tmax , of the obtained tension forces.

q2) plot the minimal required tensile strength of the rope as a function of the angle a . Keep the mass and angle b the same.

Simon Akbar said:
q1) Find the larger value, Tmax , of the obtained tension forces.
Larger of T1 and T2 that you obtained in last post ?

Buffu said:
Larger of T1 and T2 that you obtained in last post ?
yes
If angle a is constant then angle b is also constant.

Then it is clear that T2 > T1 because I think 6.93 > 4.

If angle a is constant then angle b is also constant.

Sorry my mistake, if you change the position of rope T1 then a will change with b being constant.
Ignore this.

Simon Akbar said:
q2) plot the minimal required tensile strength of the rope as a function of the angle a . Keep the mass and angle b the same.
Then you need to redo your calculation for the two tensions, but this time without plugging in a number for angle a. Just keep it as a variable.

haruspex said:
Then you need to redo your calculation for the two tensions, but this time without plugging in a number for angle a. Just keep it as a variable.
Is the sum of T1 and T2 equal to the minimal required tensile strength of the rope?

Simon Akbar said:
Is the sum of T1 and T2 equal to the minimal required tensile strength of the rope?
The ropes do not know about each other. If you were to make one rope very strong, would that help the other rope avoid breaking?

## 1. What is a "point body of mass hung from a ceiling on two ropes"?

A point body of mass hung from a ceiling on two ropes is a physics concept that describes a body or object with a concentrated mass that is suspended from the ceiling by two ropes. This concept is commonly used in physics experiments and calculations.

## 2. How do you calculate the tension in the ropes?

The tension in the ropes can be calculated using the formula T = mgcosθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle between the ropes and the vertical direction. The tension in each rope will be equal to half of the total weight of the body.

## 3. What factors affect the stability of a point body hung from two ropes?

The stability of a point body hung from two ropes is affected by several factors, including the length and angle of the ropes, the mass of the body, and the strength and elasticity of the ropes. A shorter and steeper angle of the ropes will result in a more stable body, while a longer and shallower angle may cause the body to swing or become unstable.

## 4. Are there any real-life applications of a point body hung from two ropes?

Yes, this concept has real-life applications in fields such as engineering, construction, and architecture. For example, cranes and pulley systems use a similar principle of a point body being suspended from multiple ropes to lift heavy objects. Additionally, suspension bridges also use this concept to distribute the weight of the bridge evenly across multiple ropes or cables.

## 5. How does the position of the center of mass affect the motion of a point body hung from two ropes?

The position of the center of mass plays a crucial role in the motion of a point body hung from two ropes. If the center of mass is directly below the point of suspension, the body will remain stationary. However, if the center of mass is not directly below the point of suspension, the body will start to swing back and forth, and the ropes will experience greater tension as they try to stabilize the body's motion.

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