Glossary
Acceleration due to gravity (g)
The acceleration experienced by objects near the Earth's surface due to gravity, approximately 9.8 m/s².
Example:
When you drop a ball, it accelerates downwards at acceleration due to gravity (g), ignoring air resistance.
Change in Height (Δy)
The vertical displacement of an object from an initial position to a final position, used in calculating gravitational potential energy near Earth's surface.
Example:
When a climber ascends a mountain, their change in height directly relates to the gain in their gravitational potential energy.
Change in potential energy (ΔU)
The difference in potential energy between two states of a system, which is determined by the start and end points, not the path taken.
Example:
When a spring is compressed, the change in potential energy (ΔU) is positive, indicating energy is stored.
Conservation of Energy
A fundamental principle stating that the total energy of an isolated system remains constant over time, though it may transform from one form to another.
Example:
In a frictionless roller coaster, the conservation of energy means that the sum of kinetic and potential energy at any point remains the same.
Conservative Forces
Forces for which the work done on an object is independent of the path taken, depending only on the initial and final positions. These forces allow for the storage of potential energy.
Example:
Gravity is a conservative force; the work done lifting a book to a shelf is the same whether you lift it straight up or take a winding path.
Conservative Forces
Forces for which the work done on an object is independent of the path taken, meaning the net work done in a closed loop is zero.
Example:
Gravity is a conservative force; the work done lifting a book to a shelf is the same whether you lift it straight up or in a zigzag path.
Displacement (Δx for springs)
The change in length of a spring from its natural, unstretched, or uncompressed equilibrium position.
Example:
When you sit on a pogo stick, the spring undergoes a displacement as it compresses.
Displacement from equilibrium (Δx)
The distance a spring is stretched or compressed from its natural, relaxed length.
Example:
If a spring is stretched 5 cm from its resting position, its displacement from equilibrium (Δx) is 5 cm.
Elastic Potential Energy
Energy stored in a deformable elastic object, such as a spring, when it is stretched or compressed from its equilibrium position.
Example:
A stretched slingshot stores elastic potential energy that can launch a projectile.
Elastic Spring Potential Energy
The potential energy stored in a spring when it is stretched or compressed from its equilibrium position, calculated as U_s = (1/2)k(Δx)².
Example:
A toy dart gun stores elastic spring potential energy when its spring is compressed, ready to launch the dart.
Gravitational Constant (G)
A fundamental physical constant that quantifies the strength of the gravitational force between any two objects with mass.
Example:
The value of the gravitational constant is used to calculate the force of attraction between planets.
Gravitational Field (g)
The strength of gravity at a particular location, representing the acceleration experienced by an object due to gravity.
Example:
On Earth, the gravitational field is approximately 9.8 m/s², causing objects to accelerate downwards.
Gravitational Potential Energy (General)
The potential energy associated with the gravitational interaction between two masses, dependent on their masses and the distance between their centers.
Example:
The gravitational potential energy between the Earth and the Moon keeps the Moon in orbit.
Gravitational Potential Energy (Near Earth's Surface)
The potential energy an object possesses due to its height above a reference point near the Earth's surface, calculated as mass times gravitational field times height.
Example:
A diver on a high platform has significant gravitational potential energy before jumping into the pool.
Gravitational Potential Energy (Near Earth's Surface)
The potential energy of an object due to its height above a reference point near Earth's surface, calculated as ΔU_g = mgΔy.
Example:
A book lifted onto a shelf gains gravitational potential energy (near Earth's surface) proportional to its mass and the height it's raised.
Gravitational Potential Energy (Point Masses)
The potential energy associated with the gravitational interaction between two point masses, inversely proportional to their separation distance and always negative.
Example:
The gravitational potential energy (point masses) between Earth and the Moon keeps them bound in their orbital dance.
Gravitational constant (G)
The universal constant that determines the strength of the gravitational force between two masses, appearing in Newton's Law of Universal Gravitation.
Example:
The gravitational constant (G) is a fundamental constant that allows us to calculate the attractive force between any two objects with mass.
Multiple-Object Systems (Potential Energy)
The total potential energy of a system composed of multiple interacting objects, calculated as the sum of the potential energies for all unique pairs of interacting objects.
Example:
In a system with three planets, the multiple-object systems (potential energy) would be the sum of the gravitational potential energies between planet 1 and 2, 1 and 3, and 2 and 3.
Neutral Equilibrium
A state where a system, if displaced from its position, remains in its new position without experiencing a restoring or pushing force, corresponding to a flat region on a potential energy curve.
Example:
A ball on a flat, level surface is in neutral equilibrium; it stays wherever it's placed.
Non-Conservative Forces
Forces for which the work done on an object depends on the path taken, typically dissipating mechanical energy from the system, often as heat.
Example:
Friction is a non-conservative force; pushing a box across a rough floor requires more work than across a smooth one due to energy loss.
Non-Conservative Forces
Forces that dissipate mechanical energy, often as heat, and for which the work done depends on the path taken.
Example:
Non-conservative forces like air resistance cause a thrown ball to lose mechanical energy as it flies through the air.
Potential Energy
Energy stored within a system due to the positions or configurations of objects, representing the capacity to do work.
Example:
When you stretch a rubber band, you are storing potential energy in it, ready to be released.
Potential Energy Slope and Forces
In one dimension, the conservative force acting on an object is equal to the negative of the slope of the potential energy curve at that position.
Example:
If a potential energy slope and forces graph shows a steep negative slope, it indicates a strong positive force pushing the object.
Potential Energy and Work
The change in potential energy of a system is equal to the negative of the work done by conservative forces acting within that system.
Example:
When gravity does positive work on a falling object, the object's potential energy and work relationship dictates its potential energy decreases.
Potential energy
Stored energy within a system due to the positions or configurations of its components, representing the system's capacity to do work.
Example:
A roller coaster at the top of a hill has maximum potential energy before it begins its descent.
Relative Positions
The positions of objects in relation to each other within a system, which determine the system's potential energy.
Example:
The relative positions of a magnet and a metal object determine their magnetic potential energy.
Relative positions
The spatial arrangement of objects within a system with respect to each other, which determines the system's potential energy.
Example:
The relative positions of two magnets determine their magnetic potential energy; closer like poles have higher potential energy.
Scalar
A physical quantity that has only magnitude and no direction.
Example:
Temperature is a scalar quantity; it only tells you how hot or cold something is, not a direction.
Scalar quantity
A physical quantity that has magnitude but no direction.
Example:
Temperature, mass, and scalar quantity like potential energy are described by a single numerical value.
Spring Constant (k)
A measure of the stiffness of a spring, indicating how much force is required to stretch or compress it by a certain distance.
Example:
A car's suspension system uses springs with a specific spring constant to absorb shocks from the road.
Spring constant (k)
A measure of the stiffness of a spring, representing the force required to stretch or compress the spring by a unit distance.
Example:
A high spring constant (k) indicates a very stiff spring, requiring a large force to deform it.
Stable Equilibrium
A state where a system, if slightly displaced from its position, experiences a restoring force that brings it back to that position, corresponding to a local minimum on a potential energy curve.
Example:
A ball resting at the bottom of a bowl is in stable equilibrium; if nudged, it rolls back to the center.
Stored Energy
A general term for energy held within a system that can be converted into other forms of energy or used to do work.
Example:
A battery holds stored energy in chemical form, which can be converted to electrical energy.
Stored energy
Energy held within a system that has the potential to be converted into other forms of energy or to do work.
Example:
A stretched rubber band contains stored energy that can be released when it snaps back.
Total Potential Energy
The sum of all forms of potential energy present in a system, often including gravitational and elastic potential energy.
Example:
For a system with a mass on a spring, the total potential energy would be the sum of its gravitational and elastic potential energies.
Unstable Equilibrium
A state where a system, if slightly displaced from its position, experiences a force that pushes it further away, corresponding to a local maximum on a potential energy curve.
Example:
A pencil balanced on its tip is in unstable equilibrium; a tiny nudge will cause it to fall over.
Work-Energy Theorem
States that the net work done on an object is equal to the change in its kinetic energy.
Example:
If a force does positive work on a car, the work-energy theorem tells us the car's kinetic energy will increase.
Zero Potential Energy
An arbitrary reference point chosen for convenience where the potential energy of a system is defined as zero.
Example:
For a roller coaster, the bottom of the first hill might be chosen as the point of zero potential energy.
Zero potential energy
An arbitrary reference point chosen for convenience, where the potential energy of a system is defined as zero.
Example:
For gravitational potential energy, the ground is often chosen as the zero potential energy reference point.