How Do Support Posts Affect Equilibrium in a Planked System?

[Barkingwalrus]

Homework Statement

A uniform plank 10m long and of mass 40kg is supported by two posts...?
A uniform plank 10m long and of mass 40kg is
supported by two posts, the first 1m from the left
end and the other 6m from the left end. A mass of
10kg is placed 8m from the left end. Find the force
each of the support posts exerts on the plank if it is
in equilibrium.

I'm not looking for just an answer. I would appreciate it you could tell me what needs to be done.

Here is the illustration that goes along with the question. http://i55.tinypic.com/2s61zj8.png

Homework Equations

T= F x ℓ

The Attempt at a Solution

Torque on the left: T = F2 x 1m (CCW)
Torque on the plank: T = -400N x 5m (CW)
Torque by the weight T= -100N x 7m (CW)

I really don't know where to go on from there. This is my first year in physics and I'm having trouble.

 

[ideasrule]

Torque on the left: T = F2 x 1m (CCW)
Torque on the plank: T = -400N x 5m (CW)
Torque by the weight T= -100N x 7m (CW)

Before calculating torque, you have to decide which point you're using to calculate torque. You seem to have chosen the leftmost point of the plank, which is perfectly fine, as long as you're aware of it.

Your torque calculations are all correct, provided that you define the counterclockwise direction to be positive. You also need to calculate the force exerted by the second support.

I really don't know where to go on from there. This is my first year in physics and I'm having trouble.

In order for the system to be in equilibrium, torques and forces both have to sum to 0. For forces, write out Newton's second law, taking into consideration the directions of all the forces.

 

[Barkingwalrus]

Thanks you were really helpful

 

[gneill]

Your terminology is a bit confusing. "Torque on the left", "Torque on the plank", Torque by the weight" are not precise, and it would be difficult to produce equations from them!

A torque is taken about a particular center of rotation. The first thing to do is identify the centers of rotation of interest. In this case it's the support points where the posts meet the planks. Next, identify the weights that will be causing the torques, and their positions.

In this case there are two weights specified: the weight of the 40kg plank and that of the 10kg mass. Assuming that the plank is uniform, the location of its weight can be assigned to its center of mass at location 5m from the left end of the plank. The 10kg mass is located at position 8m from the same left end.

Pick one of the centers of rotation and calculate the net torque. Suppose you choose the right hand support. The center of mass of the 40kg plank is a meter to left of this support, while the "object" of 10kg mass is located 2m to its right. Can you write the equation for the net torque about this rotation center?

 

[rwisz]

Hello,

To solve this problem, you need to use the principle of torque equilibrium. This means that the net torque acting on the plank must be equal to zero for it to be in equilibrium.

First, you need to find the total torque acting on the plank. This will include the torque from the two support posts and the torque from the weight placed on the plank.

The torque from the first support post can be calculated as T1 = F1 x d1, where F1 is the force exerted by the first post and d1 is the distance between the first post and the pivot point (which in this case is the left end of the plank).

Similarly, the torque from the second support post can be calculated as T2 = F2 x d2, where F2 is the force exerted by the second post and d2 is the distance between the second post and the pivot point.

The torque from the weight can be calculated as T3 = mg x d3, where m is the mass of the weight, g is the acceleration due to gravity, and d3 is the distance between the weight and the pivot point.

Now, since the plank is in equilibrium, the net torque must be equal to zero. This means that T1 + T2 + T3 = 0.

Substituting the values we have calculated, we get:

F1 x 1m + F2 x 4m + 10kg x 9.8m/s^2 x 7m = 0

Solving for F1 and F2, we get:

F1 = -392N and F2 = 294N

This means that the first support post exerts a force of 392N on the plank towards the right, and the second support post exerts a force of 294N on the plank towards the left.

I hope this helps. Let me know if you have any further questions. Good luck with your physics studies!