Static equilibrium mass and plank problem

[Drisc0]

Homework Statement

A plank having length L and mass M rests in equilibrium on two supports (1 and 2) that are separated by a distance D. The supports are located at equal distances from the enter of the plank. A mass m hangs from the right end of the plank. If L=6m and D=2m, which of the following expressions correctly describes the normal force N1 that support 1 exerts on the plank:
N1=Mg+mg
N1=Mg-mg
N1=Mg/2+mg
N1=Mg/2-mg
N1=Mg-mg/2

Homework Equations

ƩT = Iα = rF where T is torque, I is moment of inertia, α is angular acceleration, r is a distance, F is a force.

The Attempt at a Solution

I know the answer is the second to last one but I can't figure out why. I don't understand what happened to N2 and I'm not sure how Mg/2 is derived and I keep messing up the signs. This is probably an easy problem I'm just having a lot of trouble figuring it out. Any help is much appreciated!

 

[azizlwl]

Make a simple example.
A uniform beam of length L holds 2 identical mass m at both end and balance by a fulcrum at the centre.
What equations do you apply here?

 

[Drisc0]

I'm really not sure, If I had to take a guess I would try summing all the torques to zero.
2mg(L/2) - N = 0

I'm working on another similar problem but am lost on it as well. In the other problem its a 25kg mass on one end and a 85kg mass on the other end of a 2m long board of mass 20kg with a fulcrum that can be placed anywhere for the best balance. I'm supposed to find where to place the fulcrum.

I tried setting 25gD=85g(2-D) and solving for D but that still got me the wrong answer. I think I need to somehow incorporate the mass of the beam as well but I can't figure it out.

 

[Drisc0]

I managed to solve the second problem by merely finding the center of mass, is this the same thing I would do for this problem?

 

[PhanthomJay]

I'm really not sure, If I had to take a guess I would try summing all the torques to zero.

Yes, the sum of all torques about any point is 0, since it is given that the plank is in equilibrium.

2mg(L/2) - N = 0

You are not summing torques about any point = 0 correctly. Since you are looking for the Normal reaction force N1 (at the first support), it is convenient to sum torques (moments) about the support 2 point. Watch clockwise and counterclockwise directions. Clockwise moments = counterclockwise moments. The resultant weight force of the plank, Mg, is located at its center of gravity (its center).. Solve for N1.

I'm working on another similar problem but am lost on it as well. In the other problem its a 25kg mass on one end and a 85kg mass on the other end of a 2m long board of mass 20kg with a fulcrum that can be placed anywhere for the best balance. I'm supposed to find where to place the fulcrum.

I tried setting 25gD=85g(2-D) and solving for D but that still got me the wrong answer. I think I need to somehow incorporate the mass of the beam as well but I can't figure it out.

The weight of the beam can be represented by a single force acting at its center.