Geometría interactiva y funciones · Common Core Grade 7-8 Geometry (Cylinder Volume), Cambridge IGCSE Physics (Density & Displacement Method), High School Physics (Fluid Statics).
Visualizador de desplazamiento de agua por inmersión
Visualizador del método de inmersión y volumen por desplazamiento de líquidos
- Cálculo en cliente
- Sin registro
- Derivación en vivo
- Modo proyector
- Hoja de trabajo A4
Ventana de demostración geométrica● 60 FPS
Variables de control del experimento
cm
cm
cm
cm
cm
Derivaciones y métricas en tiempo real
Nivel de agua actual h
--
Real-time water depth in bucket
Subida del nivel del agua Δh
--
Height rise above initial h0
Longitud sumergida de la varilla
--
Wetted length of the rod
Volumen desalojado
--
Displaced water volume
Derivación de fórmulas en tiempo real
Fórmula básica:
--Sustitución de valores:
--Conclusión: --
Versión para primaria:🎮 Desarrollo, área y volumen del ortoedro ↗
Ejemplos clásicos y análisis de errores en exámenes
Annular Area Contraction: 100 cm² Bucket & 20 cm² Vertical Rod
Problema: A cylindrical bucket with base area 100 cm² contains water to a depth of 16 cm. A sufficiently long iron rod with cross-sectional area 20 cm² is vertically inserted until touching the bottom. What is the new water height?
Estrategia analítica: Water volume is invariant: V = 100 × 16 = 1600 cm³. With the rod touching bottom and protruding, water is confined to the annular region with effective base area S_annular = 100 - 20 = 80 cm². New water height h = 1600 / 80 = 20 cm.
Derivación paso a paso:
- Step 1: Compute invariant water volume V = 100 × 16 = 1600 cm³.
- Step 2: Effective annular surface area S_eff = 100 - 20 = 80 cm².
- Step 3: New liquid height h = 1600 / 80 = 20 cm.
- Step 4: Water level increase Δh = 20 - 16 = 4 cm.
- Step 5: Verify submerged rod length equals 20 cm (consistent with protruding rod condition).
⚠️ Error conceptual frecuente: Naive non-feedback error: calculating displacement as S_rod × h0 and dividing by S_bucket. The rising water wets additional rod length, which must be solved via effective annular area.
Hoja de indagación en clase y tareas
Q1. A submerged iron block in a cylinder of radius 10 cm causes water level to rise 3 cm. Find iron volume (π=3.14).
Answer Key: 942 cm³ (3.14 × 10² × 3)
Q2. A rod is pushed down further by 2 cm into a bucket. How does the water level change?
Answer Key: Rises by exactly (2 × S_rod) / (S_bucket - S_rod)
Preguntas frecuentes y errores conceptuales
If the rod is pushed so deep that it becomes fully submerged, does water level keep rising at the accelerated rate?
No! Once the rod tip is fully submerged, displaced volume caps out at the rod's total volume. Pushing it deeper causes no further water level rise.