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## Homework Statement

"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 = x

^{2}, 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)"

## Homework Equations

z = x

^{2}/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)mv

^{2}, 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}/a

^{2}]

Am I doing this right?