After the Rebel Alliance's victory in Return of the Jedi, the New Republic emerged. Imagine they decided to name a new star cruiser after Emperor Palpatine—an odd choice, considering he was their adversary. This thought experiment leads us to modern times, where the removal of Confederate statues sparks similar debates. For instance, the statue of Jefferson Davis was toppled in Richmond, VA. It's crucial to remember that Davis was the Confederacy's president, clearly not a hero in the eyes of the New Republic.

Now, let's pivot to physics. When considering the best method to take down a statue, we must first understand concepts like torque and equilibrium.

Torque

Torque can be complex, as it primarily relates to three-dimensional objects. You might already grasp some principles; for example, when opening a door, you push away from the hinge. Similarly, to loosen a tight bolt, you use a longer wrench.

Torque can be viewed as a rotational force, influencing an object's rotational motion, akin to how linear forces affect its straight-line movement. The formal definition of torque is the vector cross product of the torque arm (r) and the force (F). While cross products can be challenging, we can simplify it by focusing on the magnitude of torque.

Here are some key points regarding torque:

• You must select a reference point to define torque. In this scenario, I labeled it "o."
• The torque arm (r) is the vector from the reference point to where the force is applied.
• The angle (theta) is between the applied force and the torque arm.
• In this scalar version of torque, counterclockwise torque is typically considered positive, while clockwise is negative.
• You can combine the sin(theta) term with the force, resulting in torque as the product of the torque arm and the perpendicular component of force.

That's a brief overview of torque.

Equilibrium

Equilibrium is straightforward for point objects, which have no dimensions. In this case, equilibrium means zero acceleration (0 m/s²). According to Newton's Second Law, the total vector force must also be zero.

Consider a block at rest on an inclined plane with friction. This situation can be depicted with a diagram and equation.

While this equation might seem unusual, it reflects how to add vectors. We can treat the object as a point despite its actual dimensions.

Now, imagine a diving board supported by two posts at one end. In this case, the locations of the forces matter.

For an object to be in equilibrium, the net force and net torque around any point must be zero. Notably, gravitational force seems to act at a single point known as the center of mass.

Statue Physics

Now let's apply this to a statue. Imagine a simple statue on a base, akin to a monolith from 2001: A Space Odyssey—easy to illustrate and non-controversial.

Here, three forces interact: downward gravitational force and two upward contact forces from screws in the base. For stability, these forces must balance vertically.

The net torque must also be zero. Choosing the center of mass for torque calculations yields a straightforward scenario.

However, what if protestors decide to pull this monolith down? They might attach a rope at the top and pull sideways.

This situation complicates matters. The sideways force must also achieve equilibrium, resulting in adjustments to the contact forces. However, the torque is what will ultimately bring the statue down. Calculating torque at the right contact point shows that as tension in the rope increases, the left contact force may eventually pull down instead of pushing up.

As the rope is pulled, it generates torque, which must counterbalance the positive torques from the other forces. If one contact force breaks due to excessive tension, the statue will tip.

To maximize the chance of successfully toppling the statue, one should aim for the highest torque from the rope. Here are four methods for protestors to consider:

Assuming equal tension in the rope, rank these methods from lowest to highest torque.

The answers are as follows:

1. A: Very low torque due to minimal distance from the pivot.
2. B: Larger torque arm but small angle reduces the effective force.
3. D: Not the maximum torque, despite expectations.
4. C: Maximizes torque due to the angle being closer to 90 degrees.

Other considerations include the length of the rope, attachment points, and safety risks during the process.

Lastly, there's an alternative to physics-based removal: engaging local officials to address the statues legally—likely the most effective solution.