What is Work?

  • Work is the process of moving an object by applying a force

  • The object must move for work to be done

  • The force must cause the movement

  • Work is a scalar quantity

  • Units are Joules

Work in One Dimension

  • Only the force in the direction of the displacement contributes to the work done


Non-Constant Forces

  • Work done is the area under the force vs. displacement graph


Hooke's Law

  • The more you stretch or compress a string, the greater the force of the spring

  • The spring's force is opposite the direction of its displacement from equilibrium

  • Model this as a linear relationship, where the force applied by the spring is equal to a constant (the spring constant) multiplied by the spring's displacement from its equilibrium (rest) position

  • C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image078.png

  • Slope of the graph gives you the spring constant, k (in N/m)

    Force (N)

Work Done in Compressing a Spring

  • A spring obeys Hooke's Law. How much work is done in compressing the spring from equilibrium to some point x?


Work Done in Compressing a Non-Linear Spring

The force required to extend a non-linear spring is described by F(x)=O.5kx2. How much work is done in compressing the spring from equilibrium to some point x? x

Work in Multiple Dimensions


Work-Energy Theorem


Example: Velocity from an F-d Graph


  • Determine the object's final speed.


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