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Ejercicios de examen solucionados física
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SOLUCIÓN BOLETÍN 1 FUNDAMENTOS FÍSICOS1.- Tomando como magnitudes fundamentales M, L y T, escribir las ecuaciones de dimensiones
de las siguientes magnitudes: a) Fuerza; b) Masa; c) Densidad; d) Trabajo; e) Potencia.
Sol: a) MLT-2, b) M, c) ML-3, d) ML2 T-2, e) ML2 T-3
Solución
𝑒𝑒
[𝐹𝐹] = [𝑚𝑚 𝑎𝑎] = �𝑚𝑚 � = 𝑀𝑀 𝐿𝐿 𝑇𝑇 −2
𝑡𝑡 2
[𝑚𝑚 ] = 𝑀𝑀
𝑚𝑚 𝑚𝑚
[𝑑𝑑 ] = � � = � 3 � = 𝑀𝑀 𝐿𝐿−3
𝑉𝑉 𝐿𝐿
𝑒𝑒
[𝑇𝑇] = [𝐹𝐹 𝑒𝑒] = �𝑚𝑚 2 𝑒𝑒� = 𝑀𝑀 𝐿𝐿2 𝑇𝑇 −2
𝑡𝑡
𝑇𝑇 𝐹𝐹 𝑒𝑒 𝑒𝑒 𝑒𝑒
[𝑊𝑊] = � � = � � = �𝑚𝑚 2 � = 𝑀𝑀 𝐿𝐿2 𝑇𝑇 −3
𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡
2.- Escribir las ecuaciones de dimensiones de las magnitudes del problema anterior tomando como
magnitudes fundamentales F, L y T.
Sol: a) F, b) FL-1T2, c) FL-4T2, d) FL, e) FLT-1
3.- Comprobar que los términos que aparecen en la ecuación de Bernouilli tienen la misma
ecuación de dimensiones
ρ v2
p+ + h g ρ = Cte
2
donde p = presión ; ρ = densidad ; v = velocidad ; h = altura ; g = aceleración de la gravedad
Solución
Veamos la ecuación dimensional de cada uno de los términos
𝐹𝐹 𝐹𝐹 𝑀𝑀 𝐿𝐿 𝑇𝑇 −2
[𝑝𝑝] = � � = � 2 � = = 𝑀𝑀 𝐿𝐿−1 𝑇𝑇 −2
𝑆𝑆 𝐿𝐿 𝐿𝐿2
𝜌𝜌 𝑣𝑣 2 𝑚𝑚𝑣𝑣 2 𝑀𝑀 𝐿𝐿2 𝑇𝑇 −2
� �=� �= = 𝑀𝑀 𝐿𝐿−1 𝑇𝑇 −2
2 𝑉𝑉 𝐿𝐿3
𝑚𝑚 𝑒𝑒 𝐿𝐿 𝑀𝑀 𝐿𝐿 𝑇𝑇 −2
[ℎ 𝜌𝜌𝜌𝜌] = �ℎ �= = 𝑀𝑀 𝐿𝐿−1 𝑇𝑇 −2
𝑉𝑉 𝑡𝑡 2 𝐿𝐿3
Efectivamente tienen las mismas dimensiones
4.- Determinar las dimensiones de la constante que aparece en la ley de Hooke: F = -K x . ¿Es
una constante universal?.
Sol: [k] = MT-2 , No
Solución
𝐹𝐹
Despejando la constante K de la fórmula, 𝐾𝐾 = −
𝑥𝑥
𝐹𝐹 𝑚𝑚𝑚𝑚 𝑀𝑀 𝐿𝐿 𝑇𝑇 −2
[𝐾𝐾 ] = �− �=� �= = 𝑀𝑀 𝑇𝑇 −2
𝑥𝑥 𝑥𝑥 𝐿𝐿
Notemos que el signo menos en realidad es la constante (-1) y no tiene dimensiones.
5.- Determinar las dimensiones de la constante de gravitación universal G que aparece en la ley
de Newton de la gravitación.
F = G M1 M
2
2
r
1
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