At the instant shown in the diagram, what is the angular velocity of the crane\'
ID: 1857687 • Letter: A
Question
At the instant shown in the diagram, what is the angular velocity of the crane's boom AD?
The hydraulic actuator BC of the crane is extending (in- creasing in length) at a rate of 0.2 m/s. At the instant shown, w is the angular velocity of the crane's boom AD? Strategy: Use Eq. (17.8) to write the velocity of point C in terms of the velocity of point A, and use Eq. (17.11) to write the velocity of point C in terms of the velocity of point B. Then equate your two expressions for the velocity of point C. The hydraulic actuator BC of the crane is extending (increasing in length) at a constant rate of 0.2 m/s. At the instant shown, what is the angular acceleration of the crane's boom AD? 2 A m?Explanation / Answer
angle between BC and AD is alpha
tan(alpha) =2.4/1.2
alpha =63.43 degree
component of speed along AD is
Vp = V*cos(alpha) = 0.2*cos(63.43) =0.08944 m/s
now is V is speed Vp the tangential component (along AD) and Vn the normal component
V^2 = Vp^2+Vn^2
Vn = sqrt(V^2-Vp^2) = sqrt(0.2^2 -0.08944^2) =0.1789 m/s
Vn speed is speed of point C rotating around point A
R =AC =sqrt(3*3 +2.4*2.4) =3.84 m
angular velocity is the same for the entire segment AD
(angular velocity of point D is the same as that of point C because it is rotating about point A)
(only the liniar velocities are different because of different radius of giration)
omega = Vn/R = 0.1789/3.84 =0.0466 rad/sec
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