Randall D. Knight — Dynamics II: Motion in a Plane: Problem 32

A 100 g bead slides along a frictionless wire with the parabolic shape \(y = (2\text{ m}^{-1})x^2\). a. Find an expression for \(a_y\), the vertical component of acceleration, in terms of \(x\), \(v_x\), and \(a_x\). Hint: Use the basic definitions of velocity and acceleration. b. Suppose the bead is released at some negative value of \(x\) and has a speed of \(2.3\text{ m/s}\) as it passes through the lowest point of the parabola. What is the net force on the bead at this instant? Write your answer in component form.