What is the maximum speed an object can spin without breaking the light string?

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In summary, the light string can support a stationary hanging load of 27.0 kg before breaking. An object of mass 2.81 kg attached to the string can rotate on a frictionless, horizontal table in a circle of radius 0.809 m. The range of speeds that the object can have before the string breaks can be calculated using the formula ƩF = (2.81)v2/(0.809), where ƩF is the force that the string can tolerate before breaking. This force can be determined by using the gravitational constant 'g' and solving for V. However, it should be noted that the natural frequency of the string can affect the breaking speed if the system approaches equilibrium. Otherwise,
  • #1
AryRezvani
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Homework Statement



A light string can support a stationary hanging load of 27.0 kg before breaking. An object of mass m = 2.81 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.809 m, and the other end of the string is held fixed as in the figure below. What range of speeds can the object have before the string breaks?

Homework Equations



ƩF=ma
ac=v2/r

The Attempt at a Solution



The light string can suppport a stationary hanging load of 27.0 kg before breaking.
Object's mass = 2.81 kg
r = 0.809 m

What range of speeds can the object have before the string breaks?

Substitute the formula for centripetal acceleration into Newton's second law and you get:

ƩF = m v2/r

Then you plug in the known values into the equation, and you get:

ƩF = (2.81)v2/(0.809). How would you calculate force in this case?
 
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  • #2
If the string can suppport a stationary hanging load of 27.0 kg before breaking, then what is the force the string can tolerate before breaking? Might involve the gravitational constant 'g'.
 
  • #3
Dick said:
If the string can suppport a stationary hanging load of 27.0 kg before breaking, then what is the force the string can tolerate before breaking? Might involve the gravitational constant 'g'.

ƩF=mg
ƩF=(27.0 kg)(9.8 m/s2)
ƩF=264.6 Newtons.

264.6 = (2.81)v^2/(0.809), then solve for V?
 
  • #4
AryRezvani said:
ƩF=mg
ƩF=(27.0 kg)(9.8 m/s2)
ƩF=264.6 Newtons.

264.6 = (2.81)v^2/(0.809), then solve for V?

Pretty much, yes!
 
  • #5
Dick said:
Pretty much, yes!

Thanks, brotha. :tongue:
 
  • #6
The light string still has some mass and stiffness, and it has a mass hanging from it. All this means that it has a natural frequency. If the mass spins at that frequency long enough to approach equilibrium, the the string will break at a much lower speed than you calculated here. But if the system quickly passes thru that frequency, and all modes of it, then there is no limit to how fast the mass could spin as far as the string is concerned.
 

1. How is the speed of rotation of an object measured?

The speed of rotation of an object is typically measured in rotations per minute (RPM) or radians per second (rad/s). RPM is the number of full rotations an object makes in one minute, while rad/s is the angle of rotation per second.

2. What factors affect the speed at which an object can spin?

The speed at which an object can spin is affected by its mass, shape, and distribution of mass. Objects with a larger mass or an uneven distribution of mass will spin slower due to a higher moment of inertia. Additionally, external factors such as friction and air resistance can also affect the speed of rotation.

3. Is there a limit to how fast an object can spin?

Yes, there is a limit to how fast an object can spin. This limit is known as the breaking point or critical speed, and it varies depending on the material, shape, and size of the object. Once an object reaches its critical speed, it will start to deform or break apart due to the centrifugal force acting on it.

4. Can an object spin faster in a vacuum?

Yes, an object can spin faster in a vacuum due to the absence of air resistance. Without air resistance, there is no force slowing down the object, allowing it to spin at higher speeds. However, the other factors affecting the speed of rotation, such as mass and shape, still apply.

5. What is the fastest recorded speed of an object spinning?

The fastest recorded speed of an object spinning is 1.25 million RPM, achieved by a centrifuge at the Oak Ridge National Laboratory in 2014. This was achieved by using a specialized motor and precise balancing techniques to reduce friction and vibrations. However, this speed is not sustainable, and the object will eventually break apart due to the immense centrifugal force acting on it.

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