Maximum acceleration of a spring

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Homework Help Overview

The problem involves a spring with a known spring constant and a mass attached to it, focusing on the dynamics of the system when the mass is displaced from its rest position. The original poster is attempting to calculate the maximum acceleration of the mass after it has been pulled down further from its equilibrium position.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the forces acting on the mass and the spring, questioning the correct application of Newton's second law in the context of the spring's displacement. There are inquiries about the total displacement of the spring and the forces involved, including whether the equation used for acceleration is correct.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on drawing free body diagrams (FBD) and clarifying the total displacement of the spring. There is a focus on understanding the forces at play rather than reaching a consensus on the solution.

Contextual Notes

There is an emphasis on the initial conditions of the system, particularly the displacement when the mass is at rest, which may not have been fully established in the original statement. This could affect the calculations being discussed.

rrosa522
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Homework Statement


A spring with a spring constant of 5.0 N/m has a 0.25 kg box attached to one end such that the box is hanging down from the string at rest. The box is then pulled down another 14 cm from its rest position. Calculate the maximum height, the maximum speed, and the maximum acceleration of the box.

Homework Equations

The Attempt at a Solution


I found maximum speed and height but I can't find the maximum acceleration
ma= kx+mg
(o.25)a= (5)(0.14m)+(0.25)(9.81)
a=12.61 m's^2
the answer is 2.8m/s^2
what am I doing wrong?
 
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Draw the FBD.

When the spring is stretched "another 14 cm", what is the total displacement of the spring? So what force does it apply? What direction?
 
gneill said:
Draw the FBD.

When the spring is stretched "another 14 cm", what is the total displacement of the spring? So what force does it apply? What direction?
is it ma=kx-mg instead of ma=kx+mg, even then I don't understand how acceleration can equal to 2.8m/s^2
 
You didn't answer my question: When the spring is stretched "another 14 cm", what is the total displacement of the spring? What was the initial displacement when the mass was just hanging at rest on the end of the spring?
 

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