Kinetic Energy and Work: Physics Chapter 7

• Chapter 7 discusses work and kinetic energy and the relationship between the two.

Forms of Energy

• Energy exists in multiple forms and is converted from one form to another based on the process.
• Chemical energy is potential energy from the molecular structure of fuels such as gasoline.
• Chemical energy converts to thermal energy through oxidation.
• Electrical energy is common and easily converted to other forms for various applications.
• Thermal energy refers to the internal kinetic energy from the random motion of atoms and molecules related to an object's temperature.
• Radiant energy is electromagnetic radiation including radio, infrared, ultraviolet, X-rays, and gamma rays; all bodies radiate energy electromagnetically.
• Nuclear energy results from reactions converting mass into energy, and is converted to radiant energy in the Sun, and thermal energy in nuclear plants.
• Mechanical work is the result of transforming all forms of energy.
• World energy consumption includes fossil fuels, renewables, and nuclear, with renewable energy accounting for 19% in 2012 and still increasing.
• Solar cell arrays convert solar energy into electrical energy.
• Coursework focuses on mechanical energy, specifically kinetic energy, potential energy, and work as energy transfer.
• Energy is studied through the conservation of energy and the application of its laws to mechanical motion problems.

Work Done by a Constant Force

• Work has a specific meaning in physics, different from everyday usage.
• Work occurs when energy is transferred to an object via a force, causing displacement from one position to another.
• Vector nature and magnitude of force, and magnitude of displacement must be considered when analyzing force effects.
• Work, W, is a scalar quantity defined as magnitude, F, of force, magnitude Ar of displacement of point of application of force, and cose: W = F∆r cos θ
• θ is the angle between force and displacement vectors
• When θ = 0°, then W = F ∆r
• When θ = 90°, then W = 0, because cos 90° = 0
• The sign of work depends on the directions of F and Ar (cos θ).
• Units of work: N·m = J (joule) = kg·m²/s².
• Forces do no work when an object does not move through displacement: Ar = 0 → W = 0
• A stationary person holds a briefcase: no work is done because displacement is zero.
• A person walks horizontally while holding a briefcase: no work is done because cos θ is zero.

Work Done by Typical Forces

Norma Force

• The normal force typically does no work (θ = 90°): dWN = N · dr = 0.
• An object leaving the surface creates a situation where normal contact force is non-existent.

Kinetic Friction

• The work done by kinetic friction is negative, as kinetic friction always opposes motion (θ = 180°).
• Wfr = ∫B A fk · dr = −fk ∫B A |dr| = −fk|lAB|

Static Friction

• Static friction does no work between surfaces because there is no displacement between the surfaces.

Energy Transfer

• Energy is conserved throughout physical processes, being transferred across system boundaries.
• W is positive when energy transfers to a system as work.
• W is negative when energy transfers from the system.

Scalar Product of Two Vectors

• Scalar product (dot product) of two vectors A and B: A·B
• Scalar product: scalar quantity = product of magnitudes of two vectors and cosine of angle θ: A · B = AB cos θ
• A and B need not have identical units.

Work with Scalar Product

• Scalar product: F · ∆r = F∆r cos θ, so W = F∆r cos θ = F · ∆r
• Scalar products of unit coordinates: i · i = j · j = k · k = 1, i · j = i · k = j · k = 0
• Used to determine work by a force as an object moves along a path.

Work Done by a Varying Force

• When force varies with position, work is calculated as an integral.
• The work done by a force equals the integral of the force with respect to displacement along the path.

Work Done by a Spring

• The force exerted by a spring, Fs = -kx, where k is the spring constant measuring the stiffness of the spring.
• Hooke’s Law: Fs = −kx
• The work done by spring on attachment: Wspring, AB = ∫B A Fxdx = -k ∫B A xdx = −k x2 2 B A = 12 k(x2 A − x2 B ).
• Hooke’s Law illustrated via graph area.

Kinetic Energy Definition

• Kinetic energy defined as K = 1/2 * mv^2
• It's one-half the product of the particle's mass m and the square of its speed v.

Kinetic Energy Theorem

• Extends to systems by summing energies of constituent particles.
• It is related to momentum (p = mv): K = 1/2m(p/m)^2 = p^2 / 2m

Work–Energy Theorem

• Work done by the net force: dWnet = Fnet · dr
• The net work done Wnet.AB integrating from A to B equals a change in kinetic energy (K):Wnet = Kf – K₁ = ∆K

Power Definitions

• Power expresses the relation between work done and the time interval by introducing the concept of power.
• Average power is the work done during a time interval divided by that interval: Pavg = W/∆t.
• Instantaneous power is the limit in which the average power is approaching zero, but is referred to as just power.
• Power is the rate of doing work, or the limit of the average power for time intervals approaching zero: P = dW/dt.
• Power is valid for all means of energy transfer.
• Instantaneous power is the limiting value of average power as ∆t approaches zero, P = lim∆t→0 W/∆t = dW/dt
• Units of Power: SI unit of power: 1 W = 1 J/s = 1 kg·m²/s³
• U.S. customary system: 1 hp = 746 W
• Unit of energy (electrical transmission): 1 kWh = (10³ W)(3600 s) = 3.60×10⁶ J

Chapter 7 explores kinetic energy, work, and their relationship. It covers various forms of energy (chemical, electrical, thermal, radiant, nuclear) and how they are converted. Mechanical work results from the transformation of these energies.