Is the Slipping Ladder Problem a Torque or Static Equilibrium Problem?

[Hereformore]

I'm a little confused as to the conceptual premise behind torque-ladder problems? Like "at what height up the ladder is the man and ladder most likely to slip?"

I understand how to solve such problems, but i have trouble understanding how it is a torque problem.

Is it a torque problem or rather a static equilibrium problem? I know they're kind of the same thing, but as a torque problem, I can't imagine the object actually rotating. Rather i imagine it slipping but once it starts slipping the torque conditions constantly change as the angle theta of the ladder against the ground changes.

As an equilibrium problem, it makes sense because in static equilibrium using torue allows us to use more information to understand the force interactions.

Am I "right" in being confused about this as a traditional torque problem?

 

[Dale]

Is it a torque problem or rather a static equilibrium problem? I know they're kind of the same thing,

As you mention, they are essentially the same thing. Specifically, static equilibrium means that the sum of the forces are zero and also that the sum of the torques are 0. So any static equilibrium problem has a torque problem buried inside.

 

[Hereformore]

As you mention, they are essentially the same thing. Specifically, static equilibrium means that the sum of the forces are zero and also that the sum of the torques are 0. So any static equilibrium problem has a torque problem buried inside.

I see. So in considering such scenarios, it has to be in static equilibrium right? I guess it just seems odd that the question asks about a scenario outside of equilibrium, when you can really only accurately determine what's going on when it is in equilibrium.

It threw me off because i was trying to picture the ladder rotating and it didnt make sense to me. But it's more exploiting the torque at equilibrium right?

 

[Dale]

But it's more exploiting the torque at equilibrium right?

Right. The forces still exert torques at equilibrium, even though at equilibrium it is not rotating and all of the torques sum to 0.

 

[PJC01]

I can provide some clarification on this topic. The slipping ladder problem can be considered both a torque problem and a static equilibrium problem, as you mentioned. Both approaches can be used to solve the problem and provide a deeper understanding of the forces and interactions involved.

First, let's define torque. Torque is the measure of the force that causes an object to rotate around an axis or pivot point. In the case of a ladder leaning against a wall, the pivot point is where the ladder makes contact with the ground. When a person climbs the ladder and reaches a certain height, the weight of the person and the ladder creates a torque that could potentially cause the ladder to slip.

So, why is it also considered a static equilibrium problem? In static equilibrium, all forces acting on an object must be balanced in order for the object to remain stationary. In the case of the slipping ladder, the forces acting on the ladder include the weight of the person and the ladder itself, as well as the normal force from the ground pushing back on the ladder. In order for the ladder to remain in place and not slip, these forces must be balanced.

Using torque, we can calculate the force of the ladder slipping and the point at which it will occur. This is important for understanding the stability of the ladder and ensuring it does not slip while in use. However, as you mentioned, the torque conditions constantly change as the angle of the ladder changes, which is why it is also important to consider the problem from an equilibrium standpoint.

In conclusion, the slipping ladder problem can be approached from both a torque and a static equilibrium perspective, and both approaches provide valuable insights into the forces and interactions at play. It is important to understand both concepts in order to fully grasp the physics behind this type of problem. I hope this helps to clarify any confusion you may have had.