Work Done by a Variable Force (Leaving Cert Applied Maths): Flashcards

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Work Done by a Variable Force
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Work formula for constant force

W=FdW = Fd

Tool for variable force work calculation

Integration/calculus

Formula for work by variable force

W=∫ABF(x)dxW = \int_A^B F(x)dx

What does F(x)F(x) represent in variable force formula?

Force as a function of distance xx

Law that elastic strings follow

Hooke's Law

How does force vary with extension in Hooke's Law?

Linearly

Hooke's Law when xx is extension only

F=kxF = kx

Hooke's Law when xx is total string length

F=k(l−l0)F = k(l - l_0) or F=k(x−l0)F = k(x - l_0)

Do both position variable methods give same result?

Yes, identical results

PE gained vs work done from natural length

They are equal

Does reference point choice affect final answer?

No, it doesn't affect the answer

Sign of work when stretching elastic string

Positive

What must integration limits match?

Your chosen variable definition

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