- #1
Soaring Crane
- 469
- 0
Show that the conservation of energy holds also for the vertical spring where x is measured from the vertical equilibrium position (x_0 = mg/k) for a mass m.
This is what I did so far. Where do I go from here?
f = mg - kx_0 = 0
kx_0 = mg
E = KE + PE_grav + PE_spring
= ([mv^2]/2) - mg(x + x_0) + [(x + x_0)^2]/2
= ([mv^2]/2) - mgx - mgx_0 + (k/2)[x^2 + 2xx_0 + x_0^2]
= ([mv^2]/2) - mgx - mgx_0 + [(kx^2)/2] + xx_0k + [(kx_0^2)/(2)]
E_x0 = ([mv^2]/2) - mgx_0 + [(kx_0^2)/2]
Thanks for helping.
This is what I did so far. Where do I go from here?
f = mg - kx_0 = 0
kx_0 = mg
E = KE + PE_grav + PE_spring
= ([mv^2]/2) - mg(x + x_0) + [(x + x_0)^2]/2
= ([mv^2]/2) - mgx - mgx_0 + (k/2)[x^2 + 2xx_0 + x_0^2]
= ([mv^2]/2) - mgx - mgx_0 + [(kx^2)/2] + xx_0k + [(kx_0^2)/(2)]
E_x0 = ([mv^2]/2) - mgx_0 + [(kx_0^2)/2]
Thanks for helping.