Deriving the Equation for Spring Deflection of a Dropped Mass

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Homework Help Overview

The discussion revolves around deriving the equation for the deflection of a spring when a mass is dropped onto it. The subject area includes concepts of mechanics, specifically energy conservation and spring dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the conservation of mechanical energy, questioning how potential and kinetic energy relate to the spring's deflection. There are attempts to set up an energy balance equation involving the mass, height, gravitational acceleration, and spring stiffness.

Discussion Status

Some participants have suggested using energy conservation principles to establish a relationship between the variables. There is an emphasis on finding a derivative rather than solving the equation outright, indicating a focus on understanding the functional relationship between the variables involved.

Contextual Notes

Participants note the need to express the deflection distance as a function of mass, gravitational acceleration, and spring stiffness without reaching a final solution or conclusion.

rotin089
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i have the following question and i have no idea how to answer it can any please help out...

consider a Mass M which is dropped a height z onto a spring of stiffness k N/m. when the mass hits the spring, the spring will deflect a distance x before the mass stops moving down. show that the distance x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.

please help
 
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Hint: Is anything conserved?
 
energy both pe and ke
 
rotin089 said:
energy both pe and ke
The total mechanical energy is conserved. Use that to set up an energy equation to solve for X.
 
i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.
 
rotin089 said:
i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.
Set up the energy balance equation--which will involve x, z, M, g, and k--then you can rearrange to get x as a function of the other parameters. (That's what I mean by 'solving for x'.)
 

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