Speed of a transverse wave in srting

[Nemo's]

Homework Statement

A 2 kg block hangs from a rubber cord, being supported so that the cord is not stretched. The unstretched length of the cord is 0.5m, and its mass is 5 g. The "spring constant" for the cord is 100N/m. The block is released and stops momentarily at the lowest point.

a- Determine the tension in the cord when the block is at this lowest point.
b- What is the length of the cord in this "stretched" position ?
c- If the block is held in the lowest position, find the speed of a transverse wave in the cord.

Homework Equations

F=kx, v=√(T/μ)

The Attempt at a Solution

a- T=2g =19.6 ms^-2 correct answer: 39.2 N
b- x=19.6/100 correct answer: .892 m
c- v=√(19.6/.01)=44.3 m/s correct answer: 83.6 m/s

 

[TSny]

a- T=2g

If T = mg at the lowest point, what would the acceleration of the mass be at the lowest point?

 

[Nemo's]

The acceleration of the mass would be g ?? I just don't know what is so special about this "lowest point" ??

 

[TSny]

As the block moves downward after being released, it picks up speed for a while but then it decelerates until it momentarily comes to rest at the lowest point. In order to decelerate the tension force T acting upward must be greater than the gravitational force mg acting downward. So, at the lowest point, it is not true that T = mg.

But you know that the block will have zero velocity at the lowest point. Can you use energy concepts to figure out how far the block moves downward from the point of release to the lowest point?

 

[HalfLostAndSearching]

I would like to point out that the speed of a transverse wave in a string is dependent on the tension in the string and the linear density of the string, not the mass of the block attached to it. Therefore, the values used to calculate the speed of the wave may not be accurate. Additionally, the wave speed can also be affected by other factors such as the material and thickness of the string. It would be helpful to provide more information about the string and its properties in order to accurately calculate the speed of the wave.