ilovepdf.com_split_5

ilovepdf.com_split_5 - 123 Question 325 A particle of mass...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 123 Question 325 A particle of mass m slides without friction along a track in the form of a parabola as shown in Fig. P3-25. The equation for the parabola is y = r 2 2 a where a is a constant, r is the distance from point O to point Q , point Q is the pro- jection of point P onto the horizontal direction, and y is the vertical distance. Further- more, the particle is attached to a linear spring with spring constant K and unstretched length x . The spring is always aligned horizontally such that its attachment point is free to slide along a vertical shaft through the center of the parabola. Knowing that the parabola rotates with constant angular velocity (where = bardbl bardbl ) about the vertical direction and that gravity acts vertically downward, determine the differential equation of motion for the particle in terms of the variable r . g m r y O P Q Figure P3-25 Solution to Question 325 Kinematics For this problem it is convenient to define a fixed inertial reference frame F and a non-inertial reference frame A . Corresponding to reference frame F , we choose the following coordinate system: Origin at Point O E x = Along OP When t = E y = Along Oy When t = E z = E x E y 124 Chapter 3. Kinetics of Particles Furthermore, corresponding to reference frame A , we choose the following coordinate system: Origin at Point O e x = Along OP e y = Along Oy e z = e x e y The position of the particle is then given in terms of the basis { e x , e y , e z } as r = x e x + y e y = x e x + (x 2 /a) e y (3.554) Furthermore, since the parabola spins about the ey-direction, the angular velocity of reference frame A in reference frame F is given as F A = = e y (3.555) The velocity in reference frame F is then found using the rate of change transport...
View Full Document

Page1 / 6

ilovepdf.com_split_5 - 123 Question 325 A particle of mass...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online