How Long Does It Take for a Transverse Wave to Travel Through a Whirling Rope?

[kidsmoker]

Homework Statement

"A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity w. You can ignore the force of gravity on the rope. Find the time required for a transerve wave to travel from one end of the rope to the other."

Homework Equations

w = 2*pi*f
wave speed = frequency*wavelength = sqrt(tension/mass per unit length)

The Attempt at a Solution

I'm a bit confused here. If the force of gravity on the rope is being ignored, then what is the tension in the rope?

 

[alphysicist]

Hi kidsmoker,

Homework Statement

"A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity w. You can ignore the force of gravity on the rope. Find the time required for a transerve wave to travel from one end of the rope to the other."

Homework Equations

w = 2*pi*f
wave speed = frequency*wavelength = sqrt(tension/mass per unit length)

The Attempt at a Solution

I'm a bit confused here. If the force of gravity on the rope is being ignored, then what is the tension in the rope?

Think about what has to be true for the mass to travel in a circular path.

 

[kidsmoker]

There's a force mw^2A acting towards the centre? Do I take this as the tension in the string? I'm still not sure what to do sorry...

 

[LowlyPion]

There's a force mw^2A acting towards the centre? Do I take this as the tension in the string? I'm still not sure what to do sorry...

What is "A" in your equation?

 

[kidsmoker]

Sorry, the radius of the circular motion. I called it A cos it's like the amplitude.

 

[LowlyPion]

Sorry, the radius of the circular motion. I called it A cos it's like the amplitude.

In your problem that is actually "L" and yes that is the centripetal force on the string which is your Tension that you are looking for.

 

[kidsmoker]

Are you sure? Why would it be equal to the length of the string?

 

[LowlyPion]

Are you sure? Why would it be equal to the length of the string?

Perhaps this will help?
http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html#cf
Wait a minute is there a mass at the end of the rope or is the rope itself mass M total?

Maybe I am misreading the problem?

 

[kidsmoker]

I ws completely misreading the question too. I thought that the string was hanging vertically and you were whirling the top end in a circle, so that these circular waves travel down the string. I realize now that it means that the whole string is horizontal and it's being whirled in a circle like this, so as to keep it taut. In that case the problem is easy :P

Thanks anyway!