Calculate Spring Constant: Massless Spring & 0.140kg Mass

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A massless spring, initially 0.270 m long, is compressed to 71% of its length with a 0.140 kg mass placed on top, which takes 1.20 seconds to reach the peak after being released. Participants discuss using conservation of energy to determine the spring constant but encounter difficulties in calculating the height and velocity at which the mass leaves the spring. The acceleration of the mass is a key factor, with suggestions to apply Newton's second law (Fnet = ma) to find the acceleration at various displacements. The mass will detach from the spring when its acceleration is less than gravitational acceleration. Understanding these dynamics is crucial for accurately calculating the spring constant.
CAPA
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Homework Statement



A massless spring of length 0.270 m is in its relaxed position (left diagram). It is compressed to 71.0 percent of its relaxed length, and a mass M = 0.140 kg is placed on top and released from rest (shown on the right). The mass then travels vertically, taking 1.20 s to reach the top of its trajectory. Calculate the spring constant
Diagram http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype13/prob24_CompSpring.gif

Homework Equations





The Attempt at a Solution



I tried using conservation of energy, but kept getting stuck not being able to find how high it goes or the velocity when it leaves the spring
 
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Welcome to PF!

Hi CAPA! Welcome to PF! :smile:
CAPA said:
I tried using conservation of energy, but kept getting stuck not being able to find how high it goes or the velocity when it leaves the spring

It will leave the spring when the deceleration of the end of the spring is … ? :wink:
 


tiny-tim said:
Hi CAPA! Welcome to PF! :smile:


It will leave the spring when the deceleration of the end of the spring is … ? :wink:

we haven't really done any decelerating questions with springs. How would I go about finding that? would it be equal to gravity?
 
Hi CAPA! :smile:

(just got up :zzz:)

Use Fnet = ma to find the acceleration at a general displacement x.

The mass will leave the spring when that acceleration becomes less than -g. :wink:
 
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