# Metal plate leaning against a wall

1. Apr 27, 2010

### darkspy123

1. The problem statement, all variables and given/known data

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.

2. Relevant equations
Torque(net) = 0
F(x)=0
F(y)=0

3. 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 =(

2. Apr 27, 2010

### darkspy123

any one?

3. Apr 27, 2010

### ehild

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

ehild

4. Apr 29, 2010

### darkspy123

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