A machine carries a 5.0 kg package from a initial position of d_i^vector_i = (0.

Question

A machine carries a 5.0 kg package from a initial position of d_i^vector_i = (0.8 m)i^cap + (0.78 m)j^cap + (0.25 m)l^cap at t = 0 at a final position of d_f^vector = (8.5 m)i^vector + (12.0 m)j^cap + (8.2 m)k^cap at t = 13.0 s. The constant force applied by the machine on the package is F^vector = (4.0 N)i^cap + (8.0 N)j^cap + (10.0 N)k^cap. For that displacement, find (a) the work done on the package by the machine's force and (b) the average power of the machine's force on the package. (a) Number ________________ Units (b) Number _______________ Units

Explanation / Answer

Work in the i direction
(8.5-0.8)*4 = 30.8

Work in the j direction
(12-0.78)*8 = 89.76

Work in the k direction
(8.2-0.25)*10 = 79.5

a) Add the three together
200.06 J

b) Power is
200.06/13 watts
15.3892 watts

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