phycal sincece

Work

• Definition: Work is done when a force moves an object or changes its direction.

• Units of Work: Measured in joules.

• Equation: $ext{Work} = ext{Force} imes ext{Distance}$

Calculating Force and Distance

• Units of Force: Newtons (N).

• Units of Distance: Meters (m).

• Definition of Newton: A Newton is $ext{1 kg} imes ext{m/s}^2$.   - This shows that work is a derived unit involving mass and acceleration.   - Thus, the full equation for work is:
      $ext{Work} = ext{(kg} imes ext{m/s}^2) imes ext{m}$

• Resulting Unit for Work: Joules (J).

Relationship to Energy

• Work is closely related to energy.

• Potential Energy Equation: $ext{Potential Energy} = ext{mass} imes ext{gravity} imes ext{height}$   - Where:
      - Mass has units: Kilograms (kg).
      - Gravity has units: $ext{m/s}^2$.
      - Height has units: Meters (m).
    - All these relationships confirm that joules define both energy and work.

Conditions for Work to be Done

• Work is done when both force and movement are in the same direction.

Power

• Definition: Power is the rate at which work is done.

• Units of Power: Measured in watts (W).

• Relationship: $ext{Power} = rac{ ext{Work}}{ ext{Time}}$

Power Calculations

• Example of Power Breakdown:
    - One watt (W) is equal to one joule per second (J/s).   - Simplifying units gives:
      $1 ext{ W} = rac{1 ext{ kg} imes ext{m/s}^2 imes ext{m}}{1 ext{ s}}$     - Further breakdown results in units of:
        $ext{kg} imes ext{m} imes ext{s}^{-3}$
        - This confirms that power is also a derived unit.  

Example Problem Calculations

• Example 1:
    - Given: Weight (Force) = 30 N, Distance = 2 m.
    - Work Calculation:
      $ext{Work} = ext{Force} imes ext{Distance} = 30 ext{ N} imes 2 ext{ m} = 60 ext{ J}$

• Example 2:
    - Given: Work = 6000 J, Time = 1 minute.
    - Convert Time to Seconds: 1 minute = 60 seconds.
    - Power Calculation:
      $ext{Power} = rac{ ext{Work}}{ ext{Time}} = rac{6000 ext{ J}}{60 ext{ s}} = 100 ext{ W}$

Summary

• Work involves a force moving an object, measured in joules.

• Power is the rate of doing work, measured in watts.

• Mastery of these concepts involves understanding their relationships to units, equations, and contextual examples.