A bob attached to a string of length L = 1.25 m, initially found at the equilibrium position, is given an initial velocity v = 0.8 m/s. The maximum displacement angle, Omax, is: (Take g=10 m/s)

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Answer 1

The maximum displacement angle is given as  13°

L = length = 1.25 meters

Initial velocity = 0.8m/s

displacement = ∅max

Work done is given as change in kinetic energy

[tex]\frac{1}{2} mvi^2+0=0+mgh\\\\h = \frac{vi^2}{2g} \\\\h = \frac{0.8^2}{2*10} =\frac{0.64}{20} =0.032 meteres[/tex]

L-h

= 1.25-0.032

= 1.218 meters

Cos∅max = x/L

[tex]=\frac{1.218}{1.25} \\\\= 0.9744\\\\[/tex]

∅max = Cos⁻¹(0.9744)

= 12.99°

≈ 13°

Therefore the maximum displacement angle is given as  13°

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what’s the context here?

2)Prueba de presión Cuando a una persona se le somete a una prueba de presión, por lo general se le indica que, al llegar el ritmo cardíaco a cierto punto, la prueba deberá detenerse. El máximo ritmo cardíaco permitido, m, en latidos por minuto, puede ser aproximado por la ecuación: m= - 0.875 x + 190 donde x representa la edad del paciente de 1 a 99. Usando este modelo matemático determinar: a) El ritmo cardiaco máximo para una persona de 50 años. b) La edad de una persona cuyo máximo ritmo cardiaco sea de 160 latidos por minuto.

Answers

Usando la ecuación de regresión que modela la frecuencia cardíaca máxima, podemos obtener el valor predicho de los problemas dados así:

La ecuación lineal que modela la frecuencia cardíaca máxima permitida en función de la edad del paciente está relacionada con la fórmula:

m = - 0,875x + 190

x = edad del paciente; m = máx. frecuencia cardíaca permitida

1.) Frecuencia cardíaca máxima permitida para una persona de 50 años:

Sustituye x = 50 en la ecuación:

m = -0,875 (50) + 190

m = 146,25

Por lo tanto, la frecuencia cardíaca máxima permitida es de aproximadamente 146 latidos / min.

2.) Edad para una persona con frecuencia cardíaca máxima de 160 latidos / min:

Sustituye m = 160 en la ecuación:

160 = -0,875x + 190

0,875x = 190 - 160

0,875x = 30

x = 30 / 0,875

x = 34,28

Por tanto, la edad de la persona sería de unos 34 años.

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