The door of an automobile is open and perpendicular to the body. The automobile stats with an acceleration of 2ft//sec^(2), and the width of the door is 30 inches. Treat the door as a uniform rectangle, and neglect friction to find the speed of its outside edge a seen by the driver when the door closes.

The door of an automobile is open and perpendicular to the body. The a

1.	The door of an automobile is open and perpendicular to the body. The automobile stats with an acceleration of 2ft//sec^(2), and the width of the door is 30 inches. Treat the door as a uniform rectangle, and neglect friction to find the speed of its outside edge a seen by the driver when the door closes.
Answer» Solution : `ma cos theta xx (L)/(2) = I ALPHA` `ma cos theta xx (L)/(2) = ((1)/(3) mL^(2)) alpha` `alpha = (3a cos theta)/(2 L)` `(OMEGA d omega)/(d theta) = (3acos theta)/(2L) RARR int_(0) ^(omega) d omega = (3a)/(2L) [sin theta]_(0)^(pi//2)` `omega = sqrt((3a)/(L))` `V = L omega =rArr V = L sqrt((3a)/(L)) rArr V =sqrt(3aL)` `V = sqrt(3 xx 2 xx 2.5) = sqrt(15) ft//s^(2)`.