How Do Masses Move With a String Instead of a Spring?

AI Thread Summary
The discussion centers on the dynamics of two masses connected by a string, highlighting that they will accelerate towards each other with varying speeds until they reach the string's natural length. Once this length is reached, the masses will continue to approach each other while compressing the string, which will slow their speeds due to the variable tension in the string. The participants clarify that the behavior differs from that of a spring, emphasizing the importance of understanding the string's properties in calculating the time taken for the slowing-down process. The conversation also notes that each mass experiences acceleration from rest over a distance equal to the natural length of the string, followed by a constant velocity during the final approach. Overall, the key focus is on the unique characteristics of the string affecting the motion of the masses.
aiyiaiyiai
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Homework Statement
Two particles of equal mass (m) on a smooth horizontal table are connected by the a thin elastic string of natural length (a) in which a tension mg would produce an extension (a). The particles are held at rest at a distance (3a) apart.
i. Describe their motions between the time they are released and when they collide.
ii. If the particles are released simultaneously, calculate the time elapsed before they
collide, given a = 0.20 m.
Relevant Equations
F=kx
T=2*pi*sqrt(m/k)
I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how long they take for the slowing-down process?
 
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What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.
 
aiyiaiyiai said:
I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring elastic string. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely at constant velocity once the distance between them has reached the value of a (natural length of the elastic string).
For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.
 
Lnewqban said:
For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.
OMG, I didn't realize it is a string! thx!
 
yes my bad. I didn't realize it is a string. 😂
vela said:
What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.
 

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