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2 months ago

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A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails with a magnitu

de of 6 000 N directed toward the northwest (45 N of W). What is the magnitude of the resultant acceleration? with steps, please.

1 answer:

ValentinkaMS [3.4K]2 months ago

4 0

Respuesta:

La magnitud de la aceleración resultante es 2.2 $m/s^2$

Explicación:

La masa (m) del velero es 2000 kg

La fuerza que actúa sobre el velero debido a la marea del océano es $F_1$ = 3000N

Hacia el este significa que se da a lo largo de la dirección positiva del eje x

Entonces $F_{1x}$ = 3000N y $F_{1y}$ = 0

La fuerza del viento que actúa sobre el velero es $F_2$ 6000N dirigida hacia el noroeste, lo que significa a un ángulo de 45 grados sobre el eje negativo x

Luego

$F_{2x}$ = -(6000N) cos 45 grados = -4242.6 N

$F_{2y}$ = (6000N) cos 45 grados = 4242.6 N

Por lo tanto, la fuerza neta que actúa sobre el velero en la dirección x es

$F_x = F_{1x}+ F_{2x}$

= - 3000 N + 4242.6 N

= - 3000 N +4242.6 N

= 1242.6N

La fuerza neta que actúa sobre el velero en la dirección y es

= 0+ 4242.6N

= 4242.6N $F_y = F_{1y}+ F_{2y}$ La magnitud de la fuerza resultante =

Usando el teorema de Pitágoras de 1243 N y 4243 N

4420.8 N $\sqrt{(1242.6)^2 + (4242.6)^2$ F = ma

$\sqrt{(1544054.76) + (17999654.8)}$

$\sqrt{(19543709.5)^2}$

= 2.2

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