physics spring constant q

Question

A 2000 kg mining cart rolls down a 50-meter, frictionless, inclined plane. The plane makes an angle of 10° with the horizontal. Just beyond the bottom end of the inclined plane, there is a horizontal spring that is used to slow the cart to rest. In order to completely stop the cart, the spring compresses a distance of 1 meter. Determine the spring constant k.

Answer 1

We know that

Final Kinetic Energy is comprenes the spring and

Stored as Elantic potential Energy.

1/2 m *v^2 = 1/2 k* x^2

mg * sin 10° * 50 = 1/2 k * x^2

2000×9.8×0.1736×50 = 1/2 k * x^2

170175.2141=1/2 k * x^2

(170175.2141×2)/x^2= k

Put x=1(distance)

K= (170175.2141×2)/(1)^2

K= 3403501.4282 Nm

k = 340KNm

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