Answer to Question #115027 in Classical Mechanics for Monica

Question

A 2.0 kg mass is dropped from a height of 6m. Once it has fallen 6m it lands on a platform that is supported by a spring with a spring constant of 500 N/m.
Include a diagram

a) How fast is the mass going right before it makes contact with the platform? /5
b) How far will the spring compress? /5

Answer 1

A)

as the mass is under free-fall condition so we can apply equation $v^2=u^2+2gh$

$v^2=0+2\times10\times6=120$

$v=2\sqrt{30}m/s$

B)

applying mechanical energy conservation

$K_i+U_i=K_f+U_f\\\frac12\times2\times120+0=0+\frac12\times k\times x^2$

$240=500\times x^2$

$x=0.69m$