- #1
Sujith Sizon
Gold Member
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I recently came across a lot of problems where components of Hinge Reaction were asked along different axis .
What is hinge reaction ? How do i calculate it ? How do i find its direction ? Does it change angular velocity / acceleration of the body ?Sample Question ) A square lamina of side ##a## is hinged at corner ##A## . An impulse ##P_0## is applied on the lamina as shown . Find the impulse on the hinge due to hinge on the lamina just after ##P_0## is applied ?
http://i.stack.imgur.com/nIAdD.jpg
My attempt-
Angular impulse = Change in angular momentum
##P_{0}a=\frac{2}{3}ma^2 \omega##
##\omega=\frac{3P_0}{2ma}##
Now i found out centripetal force:
##mr {\omega}^2=m\frac{a}{2}{(\frac{3P_0}{2ma})}^{2}##
But the actual answer to the question is ##\frac{P_0}{4} \sqrt{10}##. Why doesn't the centrepetal force yield an accurate value for hinge reaction ?
What is hinge reaction ? How do i calculate it ? How do i find its direction ? Does it change angular velocity / acceleration of the body ?Sample Question ) A square lamina of side ##a## is hinged at corner ##A## . An impulse ##P_0## is applied on the lamina as shown . Find the impulse on the hinge due to hinge on the lamina just after ##P_0## is applied ?
http://i.stack.imgur.com/nIAdD.jpg
My attempt-
Angular impulse = Change in angular momentum
##P_{0}a=\frac{2}{3}ma^2 \omega##
##\omega=\frac{3P_0}{2ma}##
Now i found out centripetal force:
##mr {\omega}^2=m\frac{a}{2}{(\frac{3P_0}{2ma})}^{2}##
But the actual answer to the question is ##\frac{P_0}{4} \sqrt{10}##. Why doesn't the centrepetal force yield an accurate value for hinge reaction ?
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