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

[AryRezvani]

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
a_c=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?

 

[Dick]

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'.

 

[AryRezvani]

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?

 

[Dick]

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!

 

[AryRezvani]

Pretty much, yes!

Thanks, brotha.

 

[Pkruse]

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.