Glossary

and are fundamental concepts in physics, shaping our understanding of how objects interact and move. These principles explain everything from pushing a box across a room to the complex motions of planets in space.

involves and , while energy represents the capacity to do work. Together, they form a powerful framework for analyzing physical systems, from to complex natural phenomena.

Work and Energy

Work by constant forces

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  • Work is the product of force and in the direction of the force calculated using W=F⋅d⋅cos⁡θW = F \cdot d \cdot \cos\theta where WW is work (J), FF is force (N), dd is displacement (m), and θ\theta is the angle between force and displacement vectors
  • When force is constant and in the same direction as displacement, work simplifies to W=F⋅dW = F \cdot d (pushing a box across a floor)
  • Work is a measured in joules (J) which is equivalent to applying 1 N of force over a distance of 1 m
  • occurs when force and displacement are in the same direction (0∘≤θ<90∘0^\circ \leq \theta < 90^\circ) such as pushing a cart forward
  • occurs when force and displacement are in opposite directions (90∘<θ≤180∘90^\circ < \theta \leq 180^\circ) like pulling a wagon uphill
  • No work is done when force is perpendicular to displacement (θ=90∘\theta = 90^\circ) as seen when carrying a heavy object horizontally at a constant speed
  • Work is a form of energy transfer, measured in the same units as energy (joules)

Work from variable forces

  • For variable forces, work is calculated by integrating force over displacement using W=∫x1x2F(x) dxW = \int_{x_1}^{x_2} F(x) \, dx where F(x)F(x) is force as a function of position xx
  • describes the force exerted by a spring as [F = -kx](https://www.fiveableKeyTerm:F_=_-kx) where kk is the (N/m) and xx is displacement from equilibrium (m)
  • Work done by a spring is W=12kx2W = \frac{1}{2}kx^2 where xx is the total displacement from equilibrium which equals the area under the for a spring
  • The work done by a spring is independent of the path taken and only depends on initial and final positions (compressing a spring 0.1 m requires the same work whether done quickly or slowly)
  • The work done on a spring changes its

Work and force-displacement curves

  • Work done by a force can be visualized as the area under the force-displacement curve (plotting force on the y-axis and displacement on the x-axis)
  • For constant forces, the area is a rectangle with width dd and height FF so W=F⋅dW = F \cdot d is equivalent to the area of this rectangle
  • For variable forces, the area under the curve can be calculated using integration with W=∫x1x2F(x) dxW = \int_{x_1}^{x_2} F(x) \, dx representing the area under the force-displacement curve between x1x_1 and x2x_2
  • The sign of work (positive or negative) depends on the direction of force relative to displacement
    • If force is in the same direction as displacement, the area under the curve is positive (pushing a lawnmower forward)
    • If force is opposite to displacement, the area under the curve is negative (pulling back on a bowstring)

Energy and Power

  • Work is related to changes in through the
  • Power is the rate at which work is done or energy is transferred, measured in watts (W)
  • The principle of states that the total energy of an isolated system remains constant
  • is the ratio of useful work output to total energy input, often expressed as a percentage

Key Terms to Review (32)

Action-at-a-distance force: An action-at-a-distance force is a force exerted by an object on another object that is not in physical contact with it, acting over a distance through space. Examples include gravitational, electromagnetic, and nuclear forces.
Conservation of Energy: The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. This fundamental concept links various phenomena, illustrating how mechanical, kinetic, and potential energies interconvert while keeping the total energy constant in a closed system.
Displacement: Displacement is a vector quantity that refers to the change in position of an object. It is measured as the straight-line distance from the initial to the final position, along with the direction.
Displacement: Displacement is the change in position of an object relative to a reference point. It is a vector quantity, meaning it has both magnitude and direction, and is used to describe the movement of an object in physics.
Efficiency: Efficiency is a measure of the performance or output of a system in relation to the input or resources used. It represents the ability to achieve maximum productivity or output with the minimum amount of effort, time, or resources expended.
Energy: Energy is the fundamental quantity that describes the ability to do work or cause change. It is the driving force behind all physical and chemical processes in the universe, from the smallest subatomic interactions to the largest-scale cosmic events. Energy can take many forms, such as kinetic, potential, thermal, electrical, and more, and it is conserved in the sense that it cannot be created or destroyed, only transformed from one type to another.
F = -kx: The equation F = -kx represents Hooke's law, which describes the relationship between the force (F) applied to a spring and the displacement (x) of the spring from its equilibrium position. The negative sign indicates that the force is in the opposite direction of the displacement, acting to restore the spring to its equilibrium state.
Force: Force is a vector quantity that represents the interaction between two objects, causing a change in the motion or shape of the objects. It is the fundamental concept that underlies many of the physical principles studied in college physics, including Newton's laws of motion, work, energy, and more.
Force-displacement Curve: A force-displacement curve is a graphical representation of the relationship between the force applied to an object and the resulting displacement or deformation of that object. It is a fundamental tool in the analysis of mechanical systems and the study of the behavior of materials under various loading conditions.
Hooke's Law: Hooke's law is a fundamental principle in physics that describes the linear relationship between the force applied to an elastic object and the resulting deformation or displacement of that object. It is a crucial concept that underpins the understanding of various physical phenomena, including work, conservative and non-conservative forces, potential energy diagrams and stability, stress, strain, and elasticity, as well as simple harmonic motion.
Inclined plane: An inclined plane is a flat surface tilted at an angle to the horizontal. It is used to facilitate raising or lowering a load with less effort.
Inclined Plane: An inclined plane is a flat surface that is tilted or angled relative to the horizontal. It is a simple machine that is used to lift or move objects by applying a force parallel to the surface, rather than perpendicular to it. The inclined plane is a fundamental concept in physics, with applications across various topics.
James Prescott Joule: James Prescott Joule was a British physicist who made significant contributions to the understanding of energy and its transformations. He is best known for establishing the relationship between mechanical work and the generation of heat, which led to the formulation of the principle of the conservation of energy.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It represents the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
Joule: The joule (J) is the standard unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter.
Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object.
Negative Work: Negative work refers to the work done by an external force that opposes the motion of an object, resulting in a decrease in the object's mechanical energy. This occurs when the force and the displacement of the object are in opposite directions.
Net work: Net work is the total work done on an object, accounting for all forces acting on it. It determines the change in the object's kinetic energy.
Newton: Newton is the standard unit of force in the International System of Units (SI), named after the renowned English physicist and mathematician, Sir Isaac Newton. It is a fundamental unit that is essential in understanding and describing the behavior of objects under the influence of various forces, as well as in the study of mechanics, dynamics, and other related areas of physics.
Positive Work: Positive work is the work done by a force when the force and the displacement of the object are in the same direction. It represents the transfer of energy to the object, increasing its total mechanical energy.
Potential Energy: Potential energy is the stored energy possessed by an object due to its position or state, which can be converted into kinetic energy or other forms of energy when the object is moved or transformed. This term is central to understanding various physical phenomena and the conservation of energy.
Scalar Quantity: A scalar quantity is a physical quantity that is fully described by a single numerical value and a unit. It has magnitude, or size, but no direction associated with it. Scalar quantities are often contrasted with vector quantities, which have both magnitude and direction.
Simple Machines: Simple machines are basic mechanical devices that can be used to multiply or transfer force, allowing for the accomplishment of work with less effort. They are the fundamental building blocks of more complex machines and mechanisms.
Spring Constant: The spring constant, often denoted as 'k', is a measure of the stiffness of a spring. It quantifies the force required to stretch or compress a spring by a unit distance, and it is a fundamental property of a spring that is crucial in understanding its behavior in various physical contexts.
W = ∫F(x)dx: The term W = ∫F(x)dx represents the mathematical expression for calculating the work done by a force F(x) acting on an object as it moves through a displacement. It is the integral of the force function F(x) with respect to the position x, which gives the total work performed over the given displacement.
W = ½kx²: W = ½kx² is the formula used to calculate the work done by a spring when it is displaced from its equilibrium position. The work done is directly proportional to the square of the displacement of the spring from its equilibrium position, and the spring constant, which is a measure of the stiffness of the spring.
W = F * d: The equation W = F * d, known as the work equation, states that the work (W) done on an object is equal to the force (F) applied to the object multiplied by the displacement (d) of the object in the direction of the force. This equation is a fundamental concept in the study of physics and is particularly relevant in the context of the topic of work.
Work: Work is the energy transferred to or from an object via the application of force along a displacement. It is mathematically defined as the dot product of force and displacement vectors.
Work: Work is a physical quantity that describes the energy transferred by a force acting on an object as the object is displaced. It is the product of the force applied and the displacement of the object in the direction of the force.
Work (W = F * d * cos θ): Work is a scalar quantity that represents the amount of energy transferred by a force acting on an object as it moves in the direction of that force. It is calculated as the product of the force applied, the distance moved in the direction of the force, and the cosine of the angle between the force and the displacement.
Work-energy theorem: The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Mathematically, it is expressed as $W_{net} = \Delta KE$.
Work-Energy Theorem: The work-energy theorem is a fundamental principle in physics that states the change in the kinetic energy of an object is equal to the net work done on that object. It establishes a direct relationship between the work performed on an object and the resulting change in its kinetic energy, providing a powerful tool for analyzing and solving problems involving energy transformations.
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