Hi PF(adsbygoogle = window.adsbygoogle || []).push({});

I have a statics problem that i solve. BUT I’m insecure rather or not it is solved correctly.

The mechanical system is shown in the link below

http://peecee.dk/upload/view/340798

A weight less wire is supsended from the wall in point C and attached to a heavy bar at point A. The other end of the bar is attached to the wall but can move in the vertical direction.

The weight of the bar is F_g. All other dimensions known are given in the figure.

The aim is to find the force P required to push the bar down, so that the bar is in a horizontal position.

My solution:

First, the outer forces are noted

http://peecee.dk/upload/view/340799

A force balance in the x direction gives

R_bx=R_cx

In the y diection

-P-F_g+R_cy=0

Moment balance around point C, anti clockwise being positive gives,

-R_bx*(h-sin(alpha)*l)+F_g*(h-sin(alpha)*l*1/2)=0

⇔

R_bx=F_g*(h-sin(alpha)*l*1/2)/ (h-sin(alpha)*l) .. (eq1)

The main system is cut into two subsystems as shown in the link

http://peecee.dk/upload/view/340800

A force balance on the wire gives

R_cx=R_ax

R_ay=R_cy

And then a force balance on the bar.

in the x direction:

R_bx=R_ax

In the y direction:

R_ay-F_g-P=0

And moment around point A gives:

-F_g*1/2*l*cos(alpha)+R_bx*l*sin(alpha)-P*l*cos(alpha)=0

⇔

P= (-F_g*1/2*l*cos(alpha)+R_bx*l*sin(alpha))/(l*cos(alpha)) .. (eq2)

Using (eq1) in (eq2) gives an expression for P as:

P= -(1/2)*F_g*(-cos(alpha)*h+cos(alpha)*sin(alpha)*l+2*sin(alpha)*h-sin(alpha)^2*l)/(cos(alpha)*(-h+sin(alpha)*l))

Inserting reasonable values for h, l and alpha and F_g in the expression for P also gives reasonable results. However, I'm very much in doubt rather or not the moment in the main system is possible to do due to the boundary conditions (eq1). I on the other hand don’t see any solution

Any help is appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple statics problem?

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**