Force & Torque Homework: 10kg Plank on Wall/Floor

[veronicak5678]

Homework Statement

A 10 kg plank leans against a frictionless wall and floor at an angle of 60 degrees with the horizontal. A horizontal rope connects the center of mass of this uniform plank with the wall.
a- Use dynamics to find the normal force between the floor and the plank.
b- Find the normal force between the wall and the plank.
c- Determine the tension in the rope.
d- Show the net torque is zero when the pivot is located where the plank meets the wall.

Homework Equations

torque = Fsin(phi) radius

The Attempt at a Solution

a- normal floor = weight = 10kg (9.8) = 98 N
b- Using torque, I end up with -56.6.

-torque of normal floor + torque of normal wall = 0
98 N (sin 210) length/2 = normal wall (sin 120) length /2

normal wall = -56.6
What am I doing wrong?

 

[asleight]

Homework Statement

A 10 kg plank leans against a frictionless wall and floor at an angle of 60 degrees with the horizontal. A horizontal rope connects the center of mass of this uniform plank with the wall.
a- Use dynamics to find the normal force between the floor and the plank.
b- Find the normal force between the wall and the plank.
c- Determine the tension in the rope.
d- Show the net torque is zero when the pivot is located where the plank meets the wall.

Homework Equations

torque = Fsin(phi) radius

The Attempt at a Solution

a- normal floor = weight = 10kg (9.8) = 98 N
b- Using torque, I end up with -56.6.

-torque of normal floor + torque of normal wall = 0
98 N (sin 210) length/2 = normal wall (sin 120) length /2

normal wall = -56.6
What am I doing wrong?

Using the point where the plank rests on the ground as the point of rotation, a torque due to tension and one due to gravity act in the negative direction, both of which are negated by a normal force imposed upon the plank by the wall in the clockwise direction. Does this help?

 

[veronicak5678]

If I use that as the rotation spot, I don't think I will have enough info to solve. I don't know the tension force or the length of the plank. I was using the center as the pivot to avoid lookig at tension and weight.

 

[veronicak5678]

I tried using that spot and this is what i came up with:

torque tension + torque weight - torque normal floor = 0
56.6 N * sin 240 * length/2 + 98 N * sin 150 * length/2 - 98 N * sin 210 * length = 0

But this equation leaves me with 49N * length, not 0.