- #1
Born
- 31
- 1
Homework Statement
A pole of negligible mass leans against a wall, at angle θ with the horizontal. Gravity is directed down.
(a) Find the constraint relating the vertical acceleration of one end to the horizontal acceleration of the other.
(b) Now suppose that each end carries a pivoted mass M. Find the initial vertical and horizontal components of acceleration as the pole just begins to slide on the frictionless wall and floor. Assume that at the beginning of the motion the forces exerted by the rod are along the line of the rod. (As the motion progresses, the system rotates and the rod exerts sidewise forces.)
Homework Equations
$$(b-y)^2+x^2=L^2$$
The Attempt at a Solution
I feel that the constraint is given be taking the second derivative of the previous equation and getting back $$ \ddot{x}x + \dot{x}^2 = \ddot{y}y + \dot{y}^2$$
The problem comes when analyzing the forces. I get
$$\hat{j}: Mg-F_{ry}=M\ddot{y}$$
$$\hat{i}: F_w-F_{rx}=0$$
For the mass falling vertically and
$$\hat{j}: Mg+F_{ry}-N=0$$
$$\hat{i}: F_{rx}=M\ddot{x}$$
for the mass on sliding on the floor (where F_r is the force of the rod; N, the normal force; and F_w, the force of the wall).
All help is welcome. Thanks in advanced!
Attachments
Last edited: