Force Constant k of Spring - Potential Energy Homework

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Homework Help Overview

The problem involves a spring that is compressed and then used to launch a rock vertically. The objective is to determine the force constant k of the spring based on the potential energy equations for gravitational and elastic potential energy.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of potential energy using the formula P.E. = mgh and the relationship to elastic potential energy. There is an emphasis on the importance of using correct units and the implications of those units on the calculations.

Discussion Status

Some participants have offered corrections regarding the use of SI units and the proper interpretation of energy units. There is a progression in the discussion as participants refine their calculations based on these corrections, although explicit consensus on the final value of k has not been reached.

Contextual Notes

Participants are addressing issues related to unit conversions and the definitions of energy and spring constant. The original poster's calculations are being scrutinized for accuracy in terms of both numerical values and units used.

themadhatter1
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Homework Statement


A spring is compressed a distance of 1m and a 2 kg rock is shot straight up with the spring. The rock attains a maximum height of 500m. What is the force constant k of the spring?

Use g=10m/s^2

Homework Equations


P.E.= mgh
P.E. elastic= (1/2)(k)(x^2)

The Attempt at a Solution



P.E.= mgh
P.E.=(2000g)(10m/s^2)(500m)
P.E.= 10000000 Newtons

P.E. elastic= (1/2)(k)(x^2)
k= P.E elastic/ (1/2)(x^2)
k= 10000000/ (1/2)(1)
k=2000000 Newtons ?
 
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themadhatter1 said:
P.E.= mgh
P.E.=(2000g)(10m/s^2)(500m)
P.E.= 10000000 Newtons
Use SI units ie kilogram, not gram. Furthermore, energy is in joules, not Newtons! Also, the spring constant k is in Newtons per meter, not Newtons. Please read up on units, okay?
 
Fightfish said:
Use SI units ie kilogram, not gram. Furthermore, energy is in joules, not Newtons! Also, the spring constant k is in Newtons per meter, not Newtons. Please read up on units, okay?

Thanks,

So, if I correct my units I would have:

P.E.= mgh
P.E.=(2kg)(10m/s^2)(500m)
P.E.= 10000 joules

P.E. elastic= (1/2)(k)(x^2)
k= P.E elastic/ (1/2)(x^2)
k= 10000/ (1/2)(1)
k=20000 N/m ?

Is this correct?
 
Looks good; that is one very strong spring indeed.
 

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