A 2-kg mass is dropped 2.0 m above a spring with a spring constant 40.0 N/m. How much does the spring compress? Use g=10 m/s^2.

Question

mrnood · Answer

If the spring compresses a distance of x then the mass falls a TOTAL of (2+x) metres when it stops

Thus the PE it loses is mg(2+x)

All this energy is stored in the spring due to its compression, and that is given by 0.5kx^2   (k is the spring constant)

SO

$$\frac{ kx ^{2} }{ 2} = mg(x+2)$$

Thus solve for x

anonymous · Answer

x = 1.17 ish, but I don't think that is the right answer. Did I miscalculate something? I used the quadratic equation in order to find x.

mrnood · Answer

$$20 x ^{2}=10*2(x+2) =20(x+2)$$

$$x ^{2}-x-2=0$$