A varying force is given by F=Ae ^-kx, where x is the position; A and I are constants that have units of N and m^-1, respectively. What is the work done when x goes from 0.10 m to infinity?

Question

Physics

Lorena Heath

17 April, 04:32

A varying force is given by F=Ae ^-kx, where x is the position; A and I are constants that have units of N and m^-1, respectively. What is the work done when x goes from 0.10 m to infinity?

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Answers (1)

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Karsyn Stewart · Answer 1

W = ∫ (x from 0.1 to + oo) F dx

= ∫ (x from 0.1 to + oo) A e^ (-kx) dx

= A/k x [ - e^ (-kx) ] (between 0.1 and + oo)

= A/k x [ 0 + e^ (-k * 0.1) ]

= A/k x e^ (-k/10)