Glossary
Conservative Forces
Conservative forces are forces for which the work done on an object is independent of the path taken, depending only on the initial and final positions. Gravity and the spring force are prime examples.
Example:
When a ball falls from a certain height, the conservative force of gravity does the same amount of work on it, regardless of whether it falls straight down or slides down a ramp.
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.
Example:
Gravity is a conservative force; the work done by gravity on a falling apple is the same whether it falls straight down or rolls down a ramp.
Dot Product
A mathematical operation between two vectors that results in a scalar, used in work calculations to find the component of force parallel to displacement.
Example:
To calculate the work done by a force applied at an angle, you use the dot product of the force vector and the displacement vector.
Force-Displacement Graph
A force-displacement graph plots the force applied to an object against its displacement. The area under the curve of this graph represents the total work done on the object.
Example:
To find the work done by a varying force, you would calculate the area under the force-displacement graph.
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion. It depends on the object's mass and its speed squared.
Example:
A speeding bullet has a large amount of kinetic energy due to its high velocity.
Kinetic energy
The energy an object possesses due to its motion, directly proportional to its mass and the square of its speed.
Example:
A fast-moving baseball has significant kinetic energy, which allows it to do work on whatever it hits.
Mechanical Energy
Mechanical energy is the sum of an object's kinetic energy and potential energy. In the absence of nonconservative forces, total mechanical energy is conserved.
Example:
A roller coaster at the top of a hill has high gravitational potential energy, which converts to mechanical energy as it speeds down the track.
Negative Work
Negative work is done when the force acting on an object has a component opposite to the object's displacement, resulting in energy being removed from the system.
Example:
When a car brakes, the friction force from the road does negative work on the car, slowing it down by removing kinetic energy.
Negative Work
Work done when energy is removed from a system, typically when the force has a component opposite to the direction of displacement.
Example:
Air resistance does negative work on a falling skydiver, reducing their acceleration.
Nonconservative Forces
Nonconservative 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:
Pushing a box across a rough floor, the nonconservative force of friction does more work if you push it in a winding path compared to a straight line.
Nonconservative forces
Forces for which the work done on an object depends on the path taken, often dissipating mechanical energy from the system.
Example:
Friction is a nonconservative force; the work it does on a sliding object increases with the distance the object slides.
Parallel Component of Force
The parallel component of force is the portion of a force vector that acts in the same direction as the object's displacement. Only this component does work on the object.
Example:
When pulling a suitcase with a handle, only the parallel component of force (the part pulling horizontally) contributes to moving the suitcase forward.
Perpendicular Component of Force
The perpendicular component of force is the portion of a force vector that acts at a 90-degree angle to the object's displacement. This component changes the direction of motion but does no work.
Example:
When a car turns a corner, the centripetal force acts as a perpendicular component of force, changing the car's direction but not its speed (and thus not doing work).
Positive Work
Positive work is done when the force acting on an object has a component in the same direction as the object's displacement, resulting in energy being added to the system.
Example:
Lifting a book upwards does positive work on the book because the lifting force is in the same direction as the book's upward displacement.
Positive Work
Work done when energy is added to a system, typically when the force has a component in the direction of displacement.
Example:
A rocket's thrust does positive work on the rocket, increasing its kinetic energy.
Potential Energy
Potential energy is stored energy associated with the position or configuration of an object, typically due to the action of conservative forces. It can be converted into kinetic energy or other forms of energy.
Example:
A stretched rubber band possesses potential energy that can be released to launch a small projectile.
Potential energy
Energy associated with the configuration of a system, specifically linked to conservative forces.
Example:
A stretched spring stores elastic potential energy that can be converted into kinetic energy when released.
Scalar Quantity
A scalar quantity is a physical quantity that has magnitude but no direction. Work, energy, mass, and time are examples of scalar quantities.
Example:
The temperature outside is 25°C; this is a scalar quantity because it only has a magnitude (25) and a unit (°C), but no direction.
Scalar quantity
A physical quantity that has magnitude but no direction.
Example:
Work is a scalar quantity, meaning it only describes the amount of energy transferred (e.g., 50 Joules), not a direction.
Spring Force
The spring force (or elastic force) is a conservative force exerted by a spring that tends to restore it to its equilibrium position. It is proportional to the displacement from equilibrium.
Example:
When you compress a toy dart gun, the spring force stores potential energy, which then propels the dart forward.
Thermal Energy
Thermal energy is the internal energy of a system associated with the random motion of its atoms and molecules. It is often generated from the dissipation of mechanical energy due to nonconservative forces like friction.
Example:
When you rub your hands together, the friction converts mechanical energy into thermal energy, making your hands feel warm.
Work
Work is the transfer of energy to or from an object by means of a force acting on it over a displacement. It is a scalar quantity that quantifies how much energy is added to or removed from a system.
Example:
When you push a shopping cart across the store, you are doing work on the cart, transferring energy to it and increasing its speed.
Work
Work is the process by which energy is transferred into or out of a system when a force acts over a distance.
Example:
When you push a heavy box across a room, you are doing work on the box, transferring energy to it.
Work Formula ($W = Fd \cos heta$)
This formula calculates the work (W) done by a constant force (F) acting on an object over a displacement (d), where θ is the angle between the force and displacement vectors.
Example:
To calculate the work done by a rope pulling a sled, you'd use the formula W = Fd cos θ, considering the angle at which the rope is pulled.
Work by Variable Forces
The calculation of work done when the applied force is not constant, requiring the use of integration over the displacement.
Example:
Determining the work by variable forces done by a spring as it is compressed requires integrating the spring force over the compression distance.
Work-Energy Theorem
The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy. It provides a direct link between work and changes in motion.
Example:
If a pitcher throws a baseball, the Work-Energy Theorem tells us that the work done by the pitcher's arm on the ball equals the ball's final kinetic energy.
Work-Energy Theorem
A fundamental principle stating that the net work done on an object equals its change in kinetic energy.
Example:
If the net work-energy theorem done on a car is 50,000 J, its kinetic energy will increase by exactly that amount.
Zero Work
Zero work is done when the force acting on an object is perpendicular to its displacement, or when there is no displacement. In this case, no energy is transferred to or from the system by that force.
Example:
If you hold a heavy backpack stationary, you are exerting a force, but since there is no displacement, you are doing zero work on the backpack.
Zero Work
Work done when there is no energy change in the system due to a particular force, often when the force is perpendicular to displacement or there is no displacement.
Example:
When you carry a heavy backpack horizontally at a constant velocity, the force of gravity does zero work on the backpack.