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A constant force of 12.5 N in the positive x direction acts on an object as it moves from the origin to the point open parenthesis space 6 i with hat on top minus 8 j with hat on top space close parentheses m. How much work is done by the given force during this displacement

Respuesta :

Kazeemsodikisola

Answer:

Explanation:

Given that

Force is acting in the positive x direction,

Then F = 12.5 •i

The displacement is given as

d = 6 •i — 8 •j

Then,

Work done?

Work done is given as the dot product of force and displacement

W = F•d

W = 12.5i •(6i — 8j)

Note that,

i•i = j•j = 1

i•j = j•i = 0

Then,

W = (12.5×6)(i•i) —(12.5×8)(i•j)

W = 75 —0

W = 75J

work is done by the given force during this displacement is 75J

onyebuchinnaji

The work done by the given force during this displacement is 75 J.

The given parameters:

  • Applied force, F = 12.5 i N
  • Displacement of the object, s = (6i - 8j)

The work done by the given force during this displacement is calculated as follows;

W = F.s

W = 12.5 i . (6i - 8j)

W = (12.5 x 6)i² - (12.5 x 8)(i.j)

W = 75 - 0

W = 75 J

Thus, the work done by the given force during this displacement is 75 J.

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