Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Work and Energy ↓


work done by the force


In the field of physics, understanding the concept of work done by a force is central to the study of energy. This fundamental concept serves as a bridge between forces acting on an object and the energy changes that result. Throughout this explanation, we will explore the definition of work, delve deeper into the mathematical formulation, and examine various scenarios where the concept of work applies.

What is the work?

In everyday language, "work" means a variety of tasks and activities. However, in physics, work has a very specific definition. Work is done when a force is applied to an object to move it in the direction of the force. Two essential components are implicit in this definition: a force must be applied, and there must be motion or displacement in the direction of that force.

Mathematical definition of work

Mathematically, the work done by a force is defined using the following equation:

W = F · d · cos(θ)

Where: - W represents the work done by the force, in joules (J). - F is the magnitude of the applied force, measured in newtons (N). - d is the displacement of the object in the direction of the force, measured in meters (m). - θ (theta) is the angle between the force vector and the direction of displacement.

If the direction of the force and displacement are the same, then θ is 0 degrees, and the equation simplifies to:

W = F · d

Understanding the components of the task

Force and its direction

A force applied to an object can be viewed as a vector, which has both magnitude and direction. This vector representation is important because work is done only by the component of the force that acts in the direction of displacement.

Consider a block being pushed along a surface:

F D

In the above illustration, a block is acted upon by a force F which is moving it along a horizontal surface with displacement d.

Displacement

The concept of displacement in physics refers to the change in position of an object due to an applied force. It is important to note that only the displacement in the direction of the force is a factor in calculating work.

Angle between force and displacement

The angle θ is between the direction of the applied force and the displacement made. The cosine of this angle gives us the ratio of the force that is effectively acting to the displacement that is being made.

For example, if the force is applied at an angle to the displacement, a different calculation is used to determine the work done, accommodating only the parallel component of the force that helps move the object.

F D θ

Positive and negative actions

The work done by a force can be positive, negative, or zero, depending on the direction of the force relative to the direction of displacement.

Affirmative action

When the applied force has a component in the direction of displacement, the work done is positive. For example, consider a person who is pushing a box on the floor. If the direction of the push coincides with the direction of motion, positive work is done.

Positive Work: θ = 0°, W = F · d

Negative functions

Negative work occurs when the force applied is in the opposite direction of the displacement. This usually means that the force is acting against the motion, such as friction or air resistance. A practical example is a car braking force acting in the opposite direction of its motion.

Negative Work: θ = 180°, W = -F · d

In such cases, the force results in the object slowing down, removing energy from the system.

Zero work

If the force is perpendicular to the displacement, no work is done by the force on the object. This scenario can be seen with an object moving in a circle under the influence of centripetal force. The force is perpendicular to the direction of motion, resulting in no work being done.

Zero Work: θ = 90°, W = 0

Work done by variable forces

So far, the discussion has focused on constant forces. However, in real-world applications, forces often vary in magnitude and/or direction. Calculating the work done in such cases requires integration. This means adding up infinite amounts of work done over small displacements.

Mathematical approaches

The work done by a variable force can be calculated using the integral form of the work equation:

W = ∫ F(x) · dx

where F(x) is the varying force in the direction of displacement, and dx is the differential displacement element.

Examples of work done in everyday life

The concept of work done by a force can be illustrated in various common scenarios:

Work done by gravity

The force of gravity works on an object when it moves under the influence of the force of gravity. When an apple falls from a tree, gravity does positive work on it, turning potential energy into kinetic energy.

W_gravity = m · g · h

Where m is the mass of the object, g is the acceleration due to gravity, and h is the height from which it falls.

Work done by the spring force

Another example is the work done by spring forces, where Hooke's law applies. The work done in compressing or extending a spring can be given as follows:

W_spring = 1/2 · k · x²

Here, k is the spring constant, and x is the compression or extension measured from the equilibrium position.

The work done in pulling or pushing an object

When a person pulls a cart with a rope on a horizontal plane at an angle to the horizontal, the work done is determined by taking into account both the force applied and the angle with the plane, which requires vector decomposition in the calculation.

For example, suppose a force of 50 N is applied to pull a cart 5 m, where the force makes an angle of 30° with the horizontal direction, then:

W = 50 · 5 · cos(30°) = 50 · 5 · √3/2 = 125√3 J

Conclusion

Understanding the work done by a force enriches our understanding of energy transformations in various physical processes. It provides a basis from which other energy principles such as conservation of energy derive. Its applications range from simple mechanical systems to more complex phenomena seen in engineering and technology.

From a deeper perspective, function as a primary concept facilitates progress in understanding more advanced topics of physics, including force, energy, momentum, and their interrelationships, paving the way for the unhindered exploration of the physical laws that govern our universe.


Undergraduate → 1.3.1


U
username
0%
completed in Undergraduate

← Prev (1.3)
Work and Energy
Next (1.3.2) →
Work–energy theorem

Comments 



work done by the force

https://www.physicsflow.com/ug/1.3.1?pfal=en