(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Work-Energy Theorum: Spring potential energy vs Kinetic Energy

1. The problem statement, all variables and given/known data

A 1350-kg car rolling on a horizontal surface has a speed v = 40 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.5 m. What is the spring constant of the spring? Ignore Friction and assume spring is mass-less.

2. Relevant equations

[tex] W = \Delta E[/tex]

[tex] E_{pspring} = \frac{1}{2}(kx^2) [/tex]

[tex] E_k = \frac{1}{2}(mv^2) [/tex]

3. The attempt at a solution

First right off the bat, i converted 40 km/h to its m/s equivalent of aprox. 11.11 m/s

i state the law of conservation of energy: Energy before = Energy after

Therefore:

[tex]

E_k = E_{pspring}

\frac{1}{2}(mv^2) = \frac{1}{2}(kx^2)

[/tex]

then i isolate k

[tex] k = \frac{-mv^2}{x^2} [/tex]

now heres the issue, is x negative? because the displacement is against the direction of motion?

and 2.5m = x, (-2.5)^2 gives me a answer of 4266 Nm

but -(2.5)^2 is entirely different.. This has been a long lasting math issue for me.

And what if x is positive?

i know k MUST be positive right?

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# Work-Energy Theorum: Spring potential energy vs Kinetic Energy

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