Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_101

2/101 In the design of a control mechanism, the vertical slotted guide is moving with a constant velocity \(\dot{x} = 15 \text{ in./sec}\) during the interval of motion from \(x = -8 \text{ in.}\) to \(x = +8 \text{ in.}\) For the instant when \(x = 6 \text{ in.}\), calculate the \(n\)- and \(t\)-components of acceleration of the pin \(P\), which is confined to move in the parabolic slot. From these results, determine the radius of curvature \(\rho\) of the path at this position. Verify your result by computing \(\rho\) from the expression cited in Appendix C/10.