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27.01.2020 •
Physics
To find the volume of a few marbles a student will need which of the following scientific tools?
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Ответ:
Ответ:
A) 49,050 N
B) 16 m
Explanation:
Question:
El dibujo de la pregunta se obtiene de un documento titulado "TRABAJO DIVERSO Y ENERGÍA" que se encuentra en línea y se presenta aquí.
La masa dada del vagón, m = 1,000 kg
La altura del punto en el que descansa el vagón, punto 1, h₁ = 12 m
A) El radio en el punto 2, el punto más bajo, R = 6 m
La fuerza, 'N', que la vía ejerce sobre el vagón en el punto 1 viene dada por la siguiente relación;
N = El peso del vagón + La fuerza de movimiento del vagón
∴ N = m × g + m × a
Dónde;
g = La aceleración debida a la gravedad ≈ 9,81 m / s²
a = La aceleración del vagón
Observamos que para el movimiento circular, la fuerza de movimiento del vagón, m × a = La fuerza centrípeta que actúa sobre el vagón = m × v² / R
∴ m × a = m × v² / R
Dónde;
v² = La velocidad del vagón en el punto 2 = 2 · g · h₁
Por lo tanto;
N = m × g + m × a = m × g + m × v² / R = m × g + m × 2 · g · h₁ / R
∴ N = 1000 × 9,81 + 1000 × 2 × 9,81 × 12/6 = 49,050
La fuerza que ejerce el vagón en el punto 2, N = 49,050 N
B) En el punto 3, tenemos;
N = m · g - m · a₃
La fuerza centrípeta en el punto 3, m · a₃ = m · v₃² / R₃
∴ La altura en el punto 3, h₃ = 4 m
El cuadrado de la velocidad en el punto 3, v₃² = 2 · g · (h₁ - h₃)
Para que el vagón esté seguro en el punto 3, la fuerza de la vía sobre el vagón, N = 0 para que el vagón permanezca en la vía actuando
Por lo tanto;
N = m · g - m · a₃ = 0
m · g = m · a₃ = m · v₃² / R₃ = m · (2 · g · (h₁ - h₃)) / R₃
∴ R₃ = (2 · g · (h₁ - h₃)) / g = (2 · (h₁ - h₃)) = 2 × (12 - 4) = 16
El radio de curvatura en el punto 3 para que el punto sea seguro es R₃ = 16 m.