7.1 Work: The Scientific Definition
3 min read•june 18, 2024
in physics is all about and movement. It's calculated by multiplying force by in the force's direction. The unit is the , and can be positive, negative, or zero depending on how force and motion align.
Work is a key concept in transfer. It's linked to changes in and follows the principle of energy conservation. Understanding work helps us analyze how forces affect motion and energy in various scenarios.
Work: The Scientific Definition
Work calculation for applied forces
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- Work defined as product of force and in direction of force
- Formula: , where is work, is force, and is displacement
- (J) is unit of work
- 1 joule = 1 (N·m)
- Calculate work by multiplying force applied by displacement in direction of force
- If 10 N force applied to object, causing 5 m movement in force direction, work done is
- Work is quantity, only magnitude matters
- Contrast with force, vector quantity with both magnitude and direction
- is sum of work done by all forces acting on object
- , where are individual works done by each force
- Work is a form of energy transfer
Sign of work in force-displacement scenarios
- Sign of work depends on between force and displacement vectors
- Angle less than 90°, work is positive
- Angle greater than 90°, work is negative
- Angle exactly 90°, work is zero
- done when force and displacement are in same direction
- Pushing box forward across floor
- Walking uphill (force and displacement both directed upward along )
- done when force and displacement are in opposite directions
- Lowering box to ground (force is upward, but displacement is downward)
- Walking downhill (force is downward due to gravity, but displacement is upward along incline)
- done when force is perpendicular to displacement
- Carrying box horizontally at constant speed (force is upward, but displacement is horizontal)
- Orbiting satellite (gravitational force is perpendicular to velocity)
Application of work formula
- General work formula incorporates angle between force and displacement vectors
- Formula: , where is angle between and
- When force and displacement are in same direction, and , simplifying to
- When force and displacement are perpendicular, and , resulting in zero work
- Solve problems using general work formula:
- Identify force, displacement, and angle between them
- Substitute values into formula
- Calculate work done
- Person pulls sled with 50 N force at 30° angle above horizontal for 10 m. Work done is
- Block slides down incline with 30 N force parallel to incline for 2 m. If incline makes 45° angle with horizontal, work done by force is
Energy and Work
- Work is related to changes in mechanical energy (kinetic and )
- principle applies to work-energy relationships
- is the rate at which work is done or energy is transferred
Key Terms to Review (31)
Adhesive forces: Adhesive forces are the attractive forces between unlike molecules. They play a significant role in phenomena such as capillary action and the wetting of surfaces.
Angle: An angle is the measure of the rotation or inclination between two intersecting lines or planes. It represents the space between two rays or line segments that share a common endpoint, known as the vertex. Angles are fundamental in the study of geometry, physics, and various other scientific disciplines.
Conservation of Energy: Conservation of energy is a fundamental principle in physics that states the total energy of an isolated system remains constant, it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Cosine: Cosine is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle. It is one of the fundamental trigonometric functions used in various applications, including vector analysis and the calculation of work done by a force.
Displacement: Displacement is a vector quantity that refers to the change in position of an object. It has both magnitude and direction, indicating how far and in what direction the object has moved from its initial position.
Displacement: Displacement is the change in position of an object, measured from a reference point or origin. It describes the straight-line distance and direction an object has moved, without regard to the path taken.
Elastic potential energy: Elastic potential energy is the energy stored in an object when it is deformed elastically, such as when a spring is stretched or compressed. It can be calculated using the formula $U = \frac{1}{2} k x^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
Electric power: Electric power is the rate at which electrical energy is transferred by an electric circuit. It is typically measured in watts (W).
Energy: Energy is the capacity to do work or cause change. It is the fundamental currency that powers all physical and chemical processes in the universe, from the motion of subatomic particles to the dynamics of entire galaxies. Energy is a unifying concept that connects diverse areas of physics, including mechanics, thermodynamics, electromagnetism, and quantum mechanics.
Force: Force is a vector quantity that represents the interaction between two objects, causing a change in the motion or shape of one or both objects. It is a fundamental concept in physics that describes the push or pull experienced by an object due to the influence of another object or system.
Incline: An incline is a sloping surface or a gradual rise in elevation. It is a fundamental concept in physics, particularly in the study of work and energy, as it influences the amount of force required to move an object up or down a surface against the force of gravity.
Internal kinetic energy: Internal kinetic energy is the sum of the kinetic energies of all particles within a system. It plays a crucial role in understanding how energy is distributed and conserved during elastic collisions.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It measures 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. The joule is a fundamental unit that connects various topics in physics, from work and energy to thermodynamics and electricity.
Kinetic Energy: Kinetic energy is the energy of motion possessed by an object. It is the energy an object has by virtue of being in motion and is directly proportional to the mass of the object and the square of its velocity. Kinetic energy is a crucial concept in physics, as it relates to the work done on an object, the conservation of energy, and various other physical phenomena.
Law of conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The total energy in an isolated system remains constant over time.
Mechanical Energy: Mechanical energy is the sum of kinetic energy and potential energy in a system, representing the total energy available for performing work. This concept encompasses various forms of energy related to motion and position, and is crucial for understanding how objects interact under the influence of forces.
Negative Work: Negative work refers to the work done by a force that opposes the motion of an object. It occurs when the force and displacement are in opposite directions, resulting in a decrease in the object's mechanical energy.
Net Work: Net work is the total amount of work done on an object, calculated by summing up all the individual work done on the object. It represents the net effect of all the forces acting on the object, and determines the object's change in kinetic energy.
Newton-Meter: A newton-meter (N⋅m) is a unit of torque, which is a measure of the rotational force that causes an object to rotate about an axis, fulcrum, or pivot. This unit combines the units of force (newton) and distance (meter), representing the product of force and the perpendicular distance from the axis of rotation to the line of action of the force. The newton-meter is a fundamental unit in the study of rotational dynamics and equilibrium conditions.
Newton-meters: A newton-meter (N·m) is the unit of torque in the International System of Units (SI). It measures the amount of force applied over a distance, typically represented as the rotational equivalent of work.
Positive Work: Positive work is a concept in physics that refers to the work done on an object when the force applied and the displacement of the object are in the same direction. This means that the work done is positive, as it increases the energy of the object.
Potential Energy: Potential energy is the stored energy an object possesses due to its position or state, which can be converted into kinetic energy or other forms of energy. This term is central to understanding various physical phenomena and energy transformations in the context of introductory college physics.
Power: Power is the rate at which work is done or energy is transferred. It is the measure of the amount of energy expended per unit of time. Power is a fundamental concept in physics that is essential for understanding various topics, including work, energy, and simple machines.
Scalar: A scalar is a physical quantity that has only magnitude and no direction. Examples include mass, temperature, and electric potential.
Scalar: A scalar is a physical quantity that has only a magnitude, or numerical value, and no direction. Scalars are contrasted with vectors, which have both a magnitude and a direction. Scalars are commonly used in physics to describe various physical properties and quantities.
Useful work: Useful work is the component of work that results in a desired outcome or effective energy transfer. It excludes any energy dissipated as waste, such as heat.
Work: Work is the transfer of energy that occurs when a force is applied to an object over a distance. It is calculated as the product of the force and the displacement in the direction of the force.
Work: Work is a measure of the energy transferred by a force acting on an object as it is displaced. It is the product of the force applied and the distance moved in the direction of the force. Work is a fundamental concept in physics that is central to understanding energy, power, and the laws of motion.
Work-Energy Theorem: The Work-Energy Theorem states that the work done by all forces acting on an object equals the change in its kinetic energy. This relationship highlights how work and energy are interchangeable; when work is done on an object, it results in a change in that object's energy state. Understanding this theorem is crucial because it connects the concept of work with energy, showing how forces impact motion and energy transformations.
Zero Work: Zero work is a fundamental concept in physics that describes a situation where no work is done on an object, even if the object experiences a change in position or state. This term is particularly relevant in the context of understanding the scientific definition of work, as outlined in the topic 7.1 Work: The Scientific Definition.