Work, Power & Energy Quiz

Work

• Defined as the product of force and displacement in the direction of that force.
• Work is classified as a scalar quantity, which means it has magnitude but no direction.
• Mathematically represented by the equation:
  ( W = F \cdot S = |F| |S| \cos \theta )

Units and Dimensions of Work

• The unit of work is Newton-meter (Nm) or Joule (J).
• The dimensional formula for work is ( ML^2T^{-2} ).

Cases of Work

• Force in the Direction of Displacement (θ = 0°):
  Work is maximized, calculated as:
  ( W = F \cdot S \cos 0° = F \cdot S )

• Force Perpendicular to Displacement (θ = 90°):
  No work is done since the direction of force does not contribute to displacement:
  ( W = F \cdot S \cos 90° = 0 )

• Force Opposite to Displacement (θ = 180°):
  Work is negative, indicating that the force opposes motion:
  ( W = F \cdot S \cos 180° = -F \cdot S )

Example Calculation of Work

• Problem concerns a mass of 10 kg with a displacement of 5 m.

• External Force: 50 N with an angle of 0° to the displacement.
  Work done by external force is calculated as:
  ( W_{ext} = 50 \times 5 \times 1 = 250 , J )

• Frictional Force: 10 N with an angle of 180° to the displacement.
  Work done by frictional force is calculated as:
  ( W_{friction} = 10 \times 5 \times (-1) = -50 , J )