Conservation of Energy falling rod

  • #1
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 dont 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
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,148
7,273
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?
 

Related Threads on Conservation of Energy falling rod

  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
2
Views
9K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
18
Views
614
  • Last Post
Replies
3
Views
13K
Replies
0
Views
2K
  • Last Post
Replies
1
Views
9K
Replies
10
Views
7K
  • Last Post
Replies
3
Views
2K
Replies
1
Views
2K
Top