Work is defined as:

Work = Fparallel component *Displacement

The component of the Force used is the one that is parallel to the Displacement. You are expected to be able to:

• Explain whether the work is positive, negative, or zero by referring to the directionof the Force and Displacement vectors.
• Calculate the amount of work done on an object by a particular force.

Is the Work +, - or 0? Identify all the forces that act on the object.

For each force listed:

• Draw a coordinate system with one axis in the direction of motion. Identify the positive direction.
• Draw the force vector on the coordinate system and break it into components.
• Find the component of the force that is parallel to the displacement.
• Assign a sign for the Force component and for the displacement based on your coordinate system.
• Use the definition of work equation to decide if the work done is positive, negative, or zero.

What is the value of the Work?

• Plug the value of the Force component and the displacement into the equation for work and solve.
• For example: What is the work done by a Force of 10 N directed at 30 degrees on an object that moves 5 m to the left?
  • Draw a coordinate system that is horizontal to the left. Add in the vertical axis.
  • Draw the Force vector with its tail at 0,0.
  • Find the x-component of the Force.
  • Fx = 10Ncos(30)
  • Fx = 8.67N
  • Work = (8.67N)(-5m)
  • Work = =43.3 J

For extra practice there is a spreadsheet that recalculates for finding Work given a Force and a displacement: Practice Work Calculations