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You are tasked with calibrating the springs for a pinball machine. Your method of testing the springs is by attaching masses onto the end of the springs and measuring the stretch from initial position to final position. You hang a 14kg mass on a spring and notice that it stretches from 50 to 78cm. What is the spring constant for that spring

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boffeemadrid

Answer:

[tex]490.5\ \text{N/m}[/tex]

Explanation:

m = Mass attached to spring = 14 kg

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

x = Displacement of spring = [tex]78-50=28\ \text{cm}[/tex]

k = Spring constant

The force balance of the system is given by

[tex]kx=mg\\\Rightarrow k=\dfrac{mg}{x}\\\Rightarrow k=\dfrac{14\times 9.81}{0.28}\\\Rightarrow k=490.5\ \text{N/m}[/tex]

The spring constant for that spring is [tex]490.5\ \text{N/m}[/tex].

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