Metal plate leaning against a wall

[darkspy123]

Homework Statement

A metal plate (with mass = 7kg and Length = 1.6m) is leaning against a frictionless wall and made an angle (Phi). The foot of the plate is made of circular edge that is situated at a V-grooved gap with angle (Theta). There are three normal force: F(wall) for the normal force at the top of the plate and F(L) & F(R) for the normal force at the bottom of the ladder.

a) Find F(wall) if Theta is 120 degree and Phi is 10
b) Find F(L) and F(R) if Theta is 120 degree and Phi is 10
c) Find the minimum angle Phi for the plate to stand without sliding up if Theta is 150 degree.

Homework Equations

Torque(net) = 0
F(x)=0
F(y)=0

The Attempt at a Solution

a) I got F(wall) = 6.05N by doing torque about the bottom leg
b) I have
F net(x) = F(LX) - F(RX) - F(wall) so F(LX) = F(RX) + F(wall)

F net(y) = mg - F(LY) - F(RY) so mg = F(LY) + F(RY)

Torque (net about the tip of the plate) = [ (1.6m)*F(LX)*sin(80) + (.8)*mg*sin(10) ] - [ (1.6m)*F(LY)sin(10) + (1.6m)*F(RY)sin(10) + (1.6m)*F(RX)sin(80) ]

Now I'm stuck because i have 4 unknowns and three equations =(

 

[darkspy123]

any one?

 

[ehild]

Use the given angle to calculate the components of FL and FR.ehild

 

[darkspy123]

I'm so stupid lol. Thanks i got it now