(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A car with mass m rolls d down a frictionless [tex]\theta^0[/tex] degree incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the car in a distance of x?

3. The attempt at a solution

[PLAIN]http://img4.imageshack.us/img4/8837/unledxrq.jpg [Broken]

I am honestly very embarrassed that I can't do these basica problems properly and I am a rising sophomore.

I tried

[tex]\sum W = \Delta K[/tex]

[tex]mg(d\sin\theta) - \int_{x = 0}^{x = x} kx dx = -\frac{1}{2}mv_0^2[/tex]

I thought that at the top before it collides that

[tex]-\frac{1}{2}mv_0^2 = -mg(dsin\theta)[/tex]

[tex]mg(d\sin\theta) - \int_{x = 0}^{x = x} kx dx = -mg(d\sin\theta)[/tex]

[tex] \int_{x = 0}^{x = x} kx dx = 2mg(d\sin\theta)[/tex]

[tex] k = \frac{4mgd\sin\theta}{x^2}[/tex]

Apparently this is wrong and the answer is just mgh = 0.5kx^2.

I decided to not use LaTeX for the correct answer because I am upset.

If assume initial velocity is 0 I get it right

[tex] k = \frac{2mgd\sin\theta}{x^2}[/tex]

Why? How do I know it started with 0 velocity?

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# Find the spring constant

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