Worked Example: Work and Energy
This worked example illustrates the relationship between mechanical work and potential energy, showing how energy is transferred when a force moves an object over a distance.
Loading Component...
This worked example illustrates the relationship between mechanical work and potential energy, showing how energy is transferred when a force moves an object over a distance.
A crane lifts a concrete block with a weight (force due to gravity) of 12,000 N vertically upwards through a distance of 15 meters. Calculate the mechanical work done by the crane and the resulting change in the block's potential energy.
Mechanical Work: Work () is defined as the force () applied multiplied by the distance () moved in the direction of the force:
Potential Energy: The work done against gravity is stored as gravitational potential energy (). Therefore, the change in potential energy is equal to the work done:
The 180 kJ of work represents the energy the crane's motor must output (ignoring mechanical losses) to lift the load. This energy is conserved and stored as potential energy in the block, which would be released back as kinetic energy if the block were dropped.
Calculate the work done by the crane: Since 1 Joule (J) is equivalent to 1 :