Table of Contents

Work

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Definition

  • action done on an object that displaces the object.
  • Work is the dot product of force and displacement. It is a scalar quantity.
  • Work can be ± and if it is -, then the work done is opposite of the direction of the displacement.
  • it can also be defined as a change in energy.
  • Work is done only when a force succeeds in moving the body upon which it acts.
    • Work is only done if displacement occurs.
  • The SI Unit of work is Joules (J) which is in Nm.
  • only the component of force parallel to the displacement counts towards work.

Formula

  • Formula: W=Fd
    • where the F is the magnitude of the applied force.
    • d is the displacement of the object.
  • More detailed formula: W=Fd cos(θ)
  • If the work done is inconsistent and you want to get the total amount of work done within a given time period then:
W=x1x2F(x)dx
  • where x1 is the first position of the object.
  • where x2 is the last position of the object.

Deriviation

  • Other Formulas
W=ΔEkW=ΔEp
  • Deriviation for general:
W=t1t2Fvdt=t1t2Fdsdtdt=CFds=FCds=Fs
  • Deriviation with angle θ:
W=CFds=Fs cosθ

References

Date: August 18, 2023

Author: Paul Gerald D. Pare

Emacs 29.1 (Org mode 9.6.6)