In the design of a control mechanism, the vertical slotted guide is moving with a constant velocity x'= 15in/s during the interval of motion from

Question

x= -8in to x= +8in. For the instant when x= 6in 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 p of the path at this position. I have the picture if you need to see it but it won't let me post the link on here.

I figured out that the equation for the parabola is y= 10 -(x^2)/10 and that the velocity in the y is -18in/s meaning the total velocity is 23.43in/s. How do I get the n- and t- components of the acceleration from this?

Answer 1

The n- and t- components of the acceleration can be calculated using the equation a = v' + v^2/r, where v' is the change in velocity and v is the velocity. In this case, the n-component of the acceleration is a = -18in/s + (23.43in/s)^2/r, and the t-component of the acceleration is a = 0 + (23.43in/s)^2/r. The radius of curvature p can then be calculated using the equation p = v^2/a, where a is the acceleration. Therefore, the radius of curvature p is equal to (23.43in/s)^2/a, where a is the acceleration.