A uniform plank of mass M and length 2l is leaning angainst a smooth wall and makes an angle alpha with the smooth floor. The lower end of the plank is connected to the base of the wall with an inextensible massless string. using the principle of virtual work , find the tension in the string.

Question

A uniform plank of mass M and length 2l is leaning angainst a smooth wall and makes an angle alpha with the smooth floor. The lower end of the plank is connected to  the base of the wall with an inextensible massless string. using the principle of virtual work , find the tension in the string.

anonymous · Answer

|dw:1351326874591:dw|

anonymous · Answer

@Vincent-Lyon.Fr

anonymous · Answer

|dw:1351327709354:dw|
For horizontal equilibrium T=N1------------(A)
& for vertical N2=W----------------(B)(w=wieght of ladder acts at center of gravity G)
Taking moments along B, we get for equilibrium,
N1(2l sin (alpha))-W(l Cos(alpha)=0-------------(C)
here W=Mg
from (A), (B),(C) FIND T simple:)

anonymous · Answer

where did you use principle of virtual work?

vincent-lyon.fr · Answer

I am not so familiar with virtual work, but I think you must imagine you are pulling on the string, moving the lower end of the rope by an elementary displacement $dx$.
The power $F\,dx$ you exert must be equal to the increase in potential energy $m\,g\,dz$.

If you find the geometrical relationship between $dx$ and $dz$, you can then solve for F.