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Tower Stability Lab

Stack blocks of different widths, observe how the center of mass shifts, and find the tipping point. Add an earthquake force to test how horizontal loads challenge even a well-balanced structure.

Guided Experiment: Stability Investigation

If you shift the upper blocks further from center, at what point do you predict the tower will tip?

Write your hypothesis in the Lab Report panel, then click Next.

Tower View

4u3u2uCoM

Stability

Stable

Tower is balanced. Center of mass is within the base footprint.

Stability Margin97.8%
TippedCriticalStable
CoM Offset
+0.04
units from center
Base Half-Width
2.0
units (edge limit)

Controls

Blocks (3/10)
Block 3
2 units
-0.3 u
Left (-1)CenterRight (+1.0)
Block 2
3 units
+0.2 u
Left (-1.5)CenterRight (+1.5)
Base Block
4 units

Earthquake Simulator

None

Applies horizontal force. Click Run to oscillate sinusoidally.

Run the simulation to oscillate the earthquake force sinusoidally. A tall, unbalanced tower will tip sooner.

Data Table

(0 rows)
#TrialBlock CountTower Height(units)Base Width(units)CoM Offset(units)Earthquake ForceResult
0 / 500
0 / 500
0 / 500

Reference Guide

Center of Mass

The center of mass (CoM) is the average position of all mass in the tower, weighted by how much mass is at each location.

xcom=miximix_{\text{com}} = \frac{\sum m_i \, x_i}{\sum m_i}

Each block has mass proportional to its width (uniform density, equal height). A wider block near the edge pulls the CoM further from center.

Stability Condition

A tower is stable as long as the center of mass lies directly above the base footprint. It tips when the CoM moves past the base edge.

xcomwbase2|x_{\text{com}}| \leq \frac{w_{\text{base}}}{2}

The stability margin shows how close the CoM is to the edge as a percentage. 100% is perfectly centered; 0% means the tower is at the tipping point.

Earthquake Engineering

Earthquakes apply horizontal forces to structures. In this lab, the earthquake adds an effective displacement to the CoM proportional to the force and tower height.

xeff=xcom+Feq0.3hx_{\text{eff}} = x_{\text{com}} + F_{\text{eq}} \cdot 0.3 \cdot h

Taller towers amplify the earthquake effect. Real engineers use wide bases, base isolators, and mass dampers to counteract this.

Real-World Applications

The same physics governs skyscrapers, bridges, and cranes. Engineers keep the CoM low and centered to maximize stability.

  • Wide bases resist overturning moments
  • Counterweights shift the CoM back toward center
  • Base isolation decouples a building from ground motion
  • Tuned mass dampers absorb oscillation energy

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