# Find the time for the string to break

• TheSwedeAtLarge
In summary, the conversation discusses a dynamics assignment where the goal is to create a "real world" problem. The problem chosen involves finding the time and number of revolutions it takes for a lanyard to break when swung in a circle with a set torque, mass, and length. The results of the calculation show a high number of revolutions in a short amount of time, indicating a large torque. Feedback on the problem's realism is also mentioned.
TheSwedeAtLarge
Hi all!

I am currently working on an assignment for my dynamics course in which we need to create our own "real world" problems. I chose to do a problem which would solve the time at which the string of a lanyard would break when it is swung in a circle. My problem is with my end numbers. They seem very unreasonable but I am not sure if it is due to a calculation error, a dynamics error, or if it is simply the nature of the problem. I estimated the mass of the keys. The maximum load is from this website: http://www.engineeringtoolbox.com/polyester-rope-strength-d_1514.html
The torque of the motor is an arbitrary number that I chose.

Any feedback would be greatly appreciated.

1. Homework Statement

A motor is set up to spin a lanyard from rest with keys attached with a torque of 5 Nm. The polyester lanyard is 50 centimeters long with a diameter of 6 mm, assume it is massless. The keys have a mass m = 100 grams. The maximum load of polyester rope is Tmax = 3400 N. At what time will the rod break and after how many revolutions? Gravity acts in the -j direction. Neglect bending stresses and air resistance.

Schematic: http://imgur.com/V6mSuuD
FBD/KD: http://imgur.com/AQShsEv

F=ma
w = w0 + at

## The Attempt at a Solution

Find Angular Velocity[/B]
Sum forces in the y-direction and solve for w

Tmax – mg = mrw2

Find Angular Acceleration

M = (mra) * (r)
a=M/mr^2

Use kinematics to find the time to break

w = w0 + at

t = 1.3 s

Welcome to PF!

I think your calculation is OK. It just shows that 5 Nm is a "large" torque in this situation.

If you thought of the torque as due to a force F applied tangentially to the circular motion of the keys, then F would be 10 N. That might not sound like much, but that force would give the keys an acceleration of F/m = 100 m/s2. Thus, starting from rest, this acceleration would cause the keys to travel 200 meters in 2 seconds.

Did you calculate the number of revolutions of the lanyard in 1.3 s?

Thanks for the feedback! I was confused on what to set the torque at for it to be more realistic but I don't know what would work.

I think it gives 53.96 revolutions. Which is a ton in 1.3 seconds!

TheSwedeAtLarge said:
Thanks for the feedback! I was confused on what to set the torque at for it to be more realistic but I don't know what would work.

I think it gives 53.96 revolutions. Which is a ton in 1.3 seconds!
I think it's about half that number of revolutions. Still a lot.

## 1. How does the strength of the string affect the time it takes to break?

The strength of the string is directly related to the time it takes to break. The stronger the string, the longer it will take to break. This is because stronger strings have a higher tensile strength, meaning they can withstand more force before breaking.

## 2. What factors besides strength can affect the time for the string to break?

Aside from strength, the thickness and material of the string can also impact the time it takes to break. Thicker strings typically have a higher tensile strength and therefore take longer to break. The material of the string can also play a role, as some materials are more durable and can withstand more force before breaking.

## 3. How can I determine the exact time for the string to break?

The exact time for the string to break can be difficult to determine as it depends on various factors such as the strength, thickness, and material of the string, as well as the amount of force being applied. However, you can conduct experiments with different types of strings and gradually increase the force until the string breaks to get an estimate of the time it takes.

## 4. Can external factors, such as temperature, affect the time for the string to break?

Yes, external factors such as temperature can impact the time for the string to break. Extreme temperatures, both hot and cold, can weaken the material of the string and make it more prone to breaking. This is especially important to consider if the string is being used in an environment with extreme temperatures.

## 5. Is there a mathematical formula to calculate the time for the string to break?

There is no one specific formula to calculate the time for a string to break as it depends on various factors. However, there are equations that can be used to calculate the tensile strength of a material, which can give an estimate of the time it will take for the string to break. It is important to note that these equations may not be accurate for all types of strings and should be used as a general guideline.

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