Glossary
Conservative Forces
Conservative forces are forces for which the work done on an object depends only on the initial and final positions, not on the path taken. Gravity and spring forces are prime examples.
Example:
The work done by conservative forces like gravity on a roller coaster car is the same whether it takes a steep drop or a gradual slope, as long as the vertical displacement is identical.
Displacement
Displacement is the change in an object's position, representing the straight-line distance and direction from its initial to its final point. It is a vector quantity crucial for calculating work.
Example:
If you walk 5 meters east and then 5 meters west, your total distance traveled is 10 meters, but your displacement is zero because you returned to your starting point.
Kinetic Energy (KE)
Kinetic energy is the energy an object possesses due to its motion. It depends on both the object's mass and its speed, calculated as one-half times mass times velocity squared.
Example:
A bowling ball rolling down the lane has significant Kinetic Energy (KE), which it transfers to the pins upon impact.
Non-conservative Forces
Non-conservative forces are forces for which the work done on an object depends on the path taken. Friction and air resistance are common examples, often leading to energy dissipation.
Example:
When a car brakes, the non-conservative forces of friction between the tires and the road do negative work, converting the car's kinetic energy into heat and sound.
Variable Force
A variable force is a force whose magnitude or direction changes as an object moves. The work done by such a force is found by integrating the force over the displacement, or by finding the area under a force-position graph.
Example:
The force exerted by a spring is a variable force; it increases as the spring is stretched or compressed further from its equilibrium position.
Work
Work is the transfer of energy that occurs when a force causes a displacement of an object. It is a scalar quantity, calculated as the product of the force component parallel to the displacement and the magnitude of the displacement.
Example:
Lifting a heavy box onto a shelf requires you to do positive work against gravity, transferring energy to the box.
Work-Energy Theorem
This fundamental principle states that the net work done on an object is equal to its change in kinetic energy. It provides a powerful link between force, displacement, and an object's motion.
Example:
When a car accelerates from rest, the net Work-Energy Theorem tells us that the work done by the engine and other forces directly translates into the car gaining kinetic energy.