# Tension in a String: Solve for Unknown Lengths - 98.6N

• snormanlol
In summary, the conversation discusses finding the tension force (T) in a string loop with a perimeter of 5m and base of 2m. The equation 2T*sin(theta)=147.25 is used, but there is confusion over the perimeter of the triangle and the use of torque. It is determined that the triangle is isosceles and the equation for finding theta is arccos(1/1.5). The waveform in the diagram is misleading, and the loop length should be considered as the perimeter of the triangle.
snormanlol
Homework Statement
A mass M (15kg) is hanging on a string which is forming a closed loop (total length of the loop = 5m, with mass per unit length=2*10^(-3) kg/m). The string runs trough 2 mass and frictionless wheels, with a distance of 2 meters between them. Determine the tension T in the string.
Relevant Equations
F = m*a;
τ=I*α
I know that the answer has to be 98.6N. So I know that Fy=0 so that 2*T*sin(theta) = 147.25. Then I was think to take the torque of the left wheel but I can't find the lever arm of the tension force. I also know that u can solve the question by saying that the 2 sides of unknown length are 1.5 m but I'm not sure why u can do that.
Here is a picture of the problem:

#### Attachments

• 1566828920571.png
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well I think this equation ##2T\sin\theta=147.25## is correct. All you need is a geometric argument to determine ##\theta##. From the figure it seems that we can take the triangle to be isosceles. So how can you find ##\theta## if you know that the triangle is isosceles, has perimeter 5m and base 2m?

snormanlol
Well we can take Arctan(1/1.5) but I don't see why we can say that the perimeter is 5. Isn't the loop 5 m? And the length of the sides are unknown? That's why I tried using torque but I got the equation 2*T*sin(theta)=147.25 back.

What do you mean , since the total loop length is 5m, can't we say that the perimeter of the triangle is 5m?
Btw that should be ##\theta=\arccos(1/1.5)##..

SammyS
snormanlol said:
Isn't the loop 5 m?
Maybe the diagram, with its waveform in the horizontal section, is misleading you. Ignore the waveform at this stage (that is presumably for a later part of the question) and treat the horizontal part as straight. So the loop of string forms a triangle, and the length of the loop is the perimeter.

Ah yes it misleaded me thank you guys and yeah I meant arccos but I made a mistake. But thank you for the help guys.

Delta2

## 1. What is tension in a string?

Tension in a string refers to the force applied to a string when it is pulled or stretched. It is measured in Newtons (N) and can be calculated using the formula F = ma, where F is the tension force, m is the mass of the object, and a is the acceleration.

## 2. How do you calculate tension in a string?

Tension in a string can be calculated using the formula F = ma, where F is the tension force, m is the mass of the object, and a is the acceleration. In order to solve for unknown lengths, you may need to use additional equations such as the Pythagorean theorem or trigonometric functions.

## 3. What is the significance of the unknown lengths in this problem?

The unknown lengths in this problem represent the lengths of the string that are not given in the problem. These lengths are necessary to calculate the tension force using the formula F = ma.

## 4. What are some common units used to measure tension in a string?

Tension in a string is commonly measured in Newtons (N) or pounds (lbs). Other units such as dynes or kilogram-force may also be used in certain situations.

## 5. How does tension in a string affect the behavior of the string?

Tension in a string affects the behavior of the string by causing it to stretch or compress. The greater the tension force, the more the string will stretch. This can also affect the speed of a wave traveling through the string and the frequency of its vibrations.

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