"A bead with mass m slides without friction on a wire which lies in a vertical plane near the earth. The wire lies in the x-z plane and is bent into a shape conforming to the parabola az = x2, where a is a positive known constant. (X is horizontal and z is vertical) The particle moves in the x-z plane but its motion is constrained by the requirement that it remains on the wire.
Find the kinetic energy in terms of m, a, x, x-dot. (Eliminate z and z-dot using the constraint)"
z = x2/a and z-dot = (x-dot)2/a
(I think these are the restraint equations, unless I did these wrong.)
The Attempt at a Solution
I know that K = (1/2)mv2, so in this case wouldn't that translate to K = (1/2)*m*((x-dot)2 + (z-dot)2)?
If so, then continuing on, K = (1/2)*m*(x-dot)2+((x-dot)2/a)2) or K = (1/2)*m*(x-dot)2+[(x-dot)4/a2]
Am I doing this right?