Static Equilibrium On a Beam Question

[hardygirl989]

Homework Statement

A uniform beam of length L and mass m shown in the figure below is inclined at an angle of θ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough horizontal surface. The coefficient of static friction between the beam and surface is μs. Assume the angle θ is such that the static friction force is at its maximum value.

(e) What happens if the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure above?

Picture: http://www.webassign.net/serpse8/12-p-016.gif

Homework Equations

N/A

The Attempt at a Solution

I figure out most of the question, but I am having trouble with part e. I guess I just need clarification on the vocabulary. Would the beeam slip since it does move to the left or does it stay stationary because the person moved it to the left? Can anyone help? Thanks.

 

[gneill]

Assume that the person places it carefully so that it is not in motion before he let's go. The question then is, will the beam start to slip in its new position or will it remain in place?

 

[hardygirl989]

If the person places it so carefully, then is it safe to assume that the beam will remain stationary?

 

[gneill]

If the person places it so carefully, then is it safe to assume that the beam will remain stationary?

Nope. That will depend upon the sum of the forces acting.

 

[asteriatic]

In response to this content, it is important to understand the concept of static equilibrium. Static equilibrium is a state in which all forces acting on an object are balanced, resulting in no net force and no change in motion. In this scenario, the beam is in static equilibrium when it is at rest and the forces acting on it are balanced.

In part e of the question, the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure. This means that the beam is no longer in its original position and the forces acting on it are no longer balanced. As a result, the beam will no longer be in a state of static equilibrium and will begin to move.

The direction of movement will depend on the placement of the beam. If the beam is placed back on the ground slightly to the left, the center of mass of the beam will shift to the left. This will cause the beam to tip over and fall towards the left. This is because the force of gravity acting on the beam will no longer be acting through its center of mass, resulting in a net torque that causes the beam to rotate.

It is important to note that the coefficient of static friction between the beam and the surface will also play a role in the beam's movement. If the coefficient of static friction is high enough, it may prevent the beam from slipping and cause it to remain in its new position. However, if the coefficient of static friction is not high enough, the beam will slip and fall towards the left.

In conclusion, when the beam is lifted upward and placed back on the ground slightly to the left, it will no longer be in a state of static equilibrium and will begin to move. The direction and type of movement will depend on the placement of the beam and the coefficient of static friction between the beam and the surface.