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Una maquina lleva un paquete de 14 kg desde una posicion inicial de di = (1.5i + 1.75j + 1.2k) m en t = 0 a una posicion final df = (8.5i + 13j + 8.2k) m en t = 12 s. La fuerza constante que la maquina ejerce sobre el paquete es F = (2i + 4j + 6k) N. Para ese desplazamiento, encuentre (a) el trabajo que realiza la fuerza de la maquina sobre el paquete y (b) la potencia promedio de la fuerza de la maquina sobre el paquete

Sagot :

LammettHash

(a) Calculate the displacement r :

r = (8.5 i + 13 j + 8.2 k) m - (1.5 i + 1.75 j + 1.2 k) m

r = (7 i + 11.25 j + 7 k) m

The work W done by F in the direction of this displacement is

W = F • r = (2 i + 4 j + 6 k) N • (7 i + 11.25 j + 7 k) m

W = (2×7 + 4×11.25 + 6×7) Nm = 101 J

(b) The average power P of the machine is then

P = W / ∆t = (101 J) / (12 s)

P = 101/12 J/s ≈ 8.42 W

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