An Ant standing peacefully on a String

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

I can find the wave speed,

$$v = \sqrt{\frac{\tau}{\mu}}$$

We are also told that,

$$\lamda = 0.5m$$

I'm just confused as to when the ant is ever weightless?

I can see a sinusoidal wave traveling along a string in my mind but and the point that I'd imagine the ant being weightless is when he is as the peak of the sinusoidal wave.

But why is this related to the amplitude?

Can someone clear things up for me? What should I be thinking about?

Thanks again!

 

[ehild]

How does the ant move as it sits on the string? What forces act on it? How is weight and weightlessness defined?

ehild

 

[jegues]

How does the ant move as it sits on the string? What forces act on it? How is weight and weightlessness defined?

ehild

The feeling of being weightless would be when the forces of gravity are canceled out, correct?

But aren't we told to neglect the mass of the ant?

How do I relate this to the amplitude?

 

[ehild]

How many forces of gravity act on the ant?
The mass of the ant is too small to influence the motion of the string, but it can not ignore is own weight.
How is the acceleration of SHM related to the amplitude?

ehild

 

[jegues]

How many forces of gravity act on the ant?
The mass of the ant is too small to influence the motion of the string, but it can not ignore is own weight.
How is the acceleration of SHM related to the amplitude?

ehild

It's going to be the 2nd derivative of the wave function wrt to time,

$$-\omega^{2}y_{m}sin(kx -wt) = g$$

But we want minimum amplitude so sin(kx-wt) goes to 1 and we can solve omega as well as the amplitude ym.

 

[ehild]

You know ω from the relation between wavelength and the speed of the wave.

ehild