a Block and Spring

[nasi112]

I took this question previously. My colleagues got [math]4 \ kg[/math], but I got [math]3 \ kg[/math].

Here How I did it.

let [math]g = 10 \ m/s^2[/math]
initial total energy = final total energy

[math]mgh = mgx +\frac{1}{2}kx^2[/math]
[math]mgh - mgx = \frac{1}{2}kx^2[/math]
[math]m = \frac{0.5kx^2}{g(h - x)} = \frac{0.5(3000)(-0.1)^2}{10[0.4 - (-0.1)]} = 3 \ kg[/math]
Did I do anything wrong in my calculations?

 

[skeeter]

it’s correct

I would have let the zero for [math]U_g[/math] be at the compressed position ...

[math]mgh = \dfrac{1}{2}kx^2[/math]
[math]m = \dfrac{kx^2}{2gh} = \dfrac{3000(0.01)}{20(0.5)} = 3 \, kg[/math]

 

[nasi112]

That is a fantastic idea. Thanks a lot skeeter.