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11 days ago

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A firecracker breaks up into several pieces, one of which has a mass of 200 g and flies off along the x-axis with a speed of 82.

0 m/s. A second piece has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What are the magnitude and direction of the total momentum of these two pieces?A firecracker breaks up into several pieces, one of which has a mass of 200 g and flies off along the -axis with a speed of 82.0 m/s. A second piece has a mass of 300 g and flies off along the -axis with a speed of 45.0 m/s. What are the magnitude and direction of the total momentum of these two pieces?361 kg·m/s at 0.983° from the x-axis361 kg·m/s at 56.3° from the x-axis93.5 kg·m/s at 28.8° from the x-axis21.2 kg·m/s at 39.5° from the x-axis21.2 kg·m/s at 56.3° from the x-axis

1 answer:

Maru [1K]11 days ago

6 0

Answer:

La magnitud del momento total es de 21.2 kg m/s y su dirección es de 39.5° respecto al eje x.

Explanation:

¡Hola!

El momento total se calcula como la suma de los momentos de las piezas.

El momento de cada pieza se calcula de la siguiente manera:

p = m · v

Donde:

p = momento.

m = masa.

v = velocidad.

El momento es un vector. La pieza de 200 g se mueve a lo largo del eje x, por lo que su momento será:

p = (m · v, 0)

p = (0.200 kg · 82.0 m/s, 0)

p = (16.4 kg m/s, 0)

La pieza de 300 g se mueve a lo largo del eje y. Su vector momento será:

p =(0, m · v)

p = (0, 0.300 kg · 45.0 m/s)

p = (0, 13.5 kg m/s)

El momento total es la suma de cada momento:

Momento total = (16.4 kg m/s, 0) + (0, 13.5 kg m/s)

Momento total = (16.4 kg m/s + 0, 0 + 13.5 kg m/s)

Momento total = (16.4 kg m/s, 13.5 kg m/s)

La magnitud del momento total se calcula de la siguiente manera:

$|p| = \sqrt{(16.4 kgm/s)^2+(13.5 kg m/s)^2}= 21.2 kg m/s$

La dirección del vector de momento se calcula utilizando trigonometría:

cos θ = px/p

Donde px es el componente horizontal del momento total y p es la magnitud del momento total.

cos θ = 16.4 kg m/s / 21.2 kg m/s

θ = 39.3 (39.5° si no redondeamos la magnitud del momento total)

<pFinalmente, la magnitud del momento total es 21.2 kg m/s y su dirección es 39.5° respecto al eje x.

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11 days ago