Conservation of Energy falling rod

  • #1
dmoney123
32
1

Homework Statement



A uniform ladder having mass 14kg and length 3m is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle Theta at which the bottom end A starts to lift off the ground. For calculation assume the ladder is a slender rod and neglect friction at A.

yKHTn7j.jpg





Homework Equations



T_1+V_1=T_2+V_2[/B]


The Attempt at a Solution



T_1=0

V_1=mgh
=mgL/2

T_2=1/2I(omega)^2
where I for end of rod = 1/3mL^2

so 1/2(1/3mL^2)(omega)^2

V_2=mgh
=mgL/2cos(Theta)

Solve T_1+V_1=T_2+V_2

g(1-cos(Theta))=(omega)^2

I think we now need solve for the forces at point A, but I don't know how...

I also don't really understand at what point A would "lift"

Any help is appreciated!

Thanks[/B]
 

Answers and Replies

  • #2
haruspex
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g(1-cos(Theta))=(omega)^2
That's dimensionally wrong. You have an acceleration on the left and 1/time2 on the right.
I think we now need solve for the forces at point A
Yes. What are the forces acting on the rod? What components of acceleration can you identify at angle theta?
 

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