Energy, Work and Potential Energy

Energia

• Energia is reviewed.

Trabalho

• The work done by a constant force on an object equals the force times the object's displacement in the force's direction.
• Formula: W = F ⋅ d ⋅ cos(θ), where W is work in Joules, F is force in Newtons, d is displacement in meters, and θ is the angle between force and displacement.
• Work is scalar and can be positive (motor), negative (resistant), or zero.

Energia Cinética

• Kinetic energy is the energy of an object due to its motion.
• Formula: K = (1/2)mv², where K is kinetic energy in Joules, m is mass in kg, and v is velocity in m/s.
• The work-energy theorem says total work on an object equals its kinetic energy change.
• Formula: Wtotal = ΔK = Kf - Ki

Energia Potencial

• Potential energy is stored energy due to position or configuration.

• Types include gravitational and elastic potential energy.

  Energia Potencial Gravitacional:

  • Formula: Ug = mgh, where Ug is gravitational potential energy in Joules, m is mass in kg, g is acceleration due to gravity (9.8 m/s² on Earth), and h is height relative to a reference point in meters.

  Energia Potencial Elástica:

  • Formula: Ue = (1/2)kx², where Ue is elastic potential energy in Joules, k is spring constant in N/m, and x is spring displacement from equilibrium in meters.

Conservação de Energia

• In an isolated system, total energy (kinetic + potential) stays constant.
• Formula: Etotal = K + U = constant, where Etotal is total system energy, K is total system kinetic energy, and U is total system potential energy.
• Energy conservation is key in physics, applied in projectile motion, oscillations, and collisions.

Potência

• Power is the rate of work or energy transfer.
• Formula: P = W/Δt = ΔE/Δt, where P is power in Watts, W is work in Joules, Δt is time interval in seconds, and ΔE is energy change in Joules.

Impulso, Quantidade de Movimento e Colisões

• Impulse, momentum, and collisions are overviewed.

Impulso

• Impulse is the force multiplied by the time it acts.
• Formula: I = F ⋅ Δt, where I is impulse in N.s, F is force in Newtons, and Δt is the time interval in seconds.
• Impulse is vectorial, with the same direction as the force.

Quantidade de Movimento

• Momentum is the mass times velocity of any object.
• Formula: p = m ⋅ v, where p is momentum in kg.m/s, m is mass in kg, and v is velocity in m/s.
• Momentum is vectorial, with the same direction as velocity.

Teorema do Impulso-Quantidade de Movimento

• Net impulse on an object equals its momentum change.
• Formula: I = Δp = pf - pi

Conservação da Quantidade de Movimento

• In a closed system, total momentum remains constant.
• Formula: ptotal = constant

Colisões

• Interations between two or more objects are Collisions where there are interchanges of energy and momentum.

• Types of collisions include elastic (kinetic energy conserved) and inelastic (kinetic energy not conserved).

• In all collisions, total system momentum is conserved without external forces.

  Coeficiente de Restituição (e):

  • Formula: e = |vsegregation|/|vapproach|
  • e = 1 for elastic collision
  • 0 < e < 1 for inelastic collision.
  • e = 0 for perfectly inelastic collision

Estática

• Reviews the principles of statics.

Condições de Equilíbrio

• For static equilibrium:
  • Net force must be zero: ∑F = 0
  • Net torque must be zero: ∑τ = 0

Torque

• Torque indicates a force's tendency to cause rotation around an axis.
• Formula: τ = r ⋅ F ⋅ sin(θ), where τ is torque in N.m, r is distance to rotation axis in meters, F is force in Newtons, and θ is the angle between force and position vector.
• Torque is a vector quantity, perpendicular to the plane formed by position vector and force.

Centro de Gravidade

• The center of gravity is the point where all gravitational force affects an object.
• For homogeneous, symmetrical objects, the center of gravity is the geometric center.
• Object stability depends on the position of its center of gravity relative to its support base.