Rucete ✏ AP Physics 1 In a Nutshell
4. Energy
This chapter introduces the concept of work, power, kinetic and potential energy, the work-energy theorem, and the law of conservation of energy. It also explains the role of conservative and nonconservative forces in energy transfer and provides problem-solving strategies based on energy analysis.
Work
• Work is done when a force causes displacement: W = (F cos θ)d
• Work is a scalar measured in joules (J); 1 J = 1 N·m
• θ is the angle between the force and displacement vectors.
• No work is done if displacement is zero or force is perpendicular to motion.
• Negative work occurs when force opposes motion (e.g., friction).
• Net work = sum of work by all forces → equivalent to work done by net force.
Power
• Power is the rate of doing work: P = W / t
• Units: watts (W); 1 W = 1 J/s
• For constant velocity: P = F·v
• Power depends on how quickly energy is transferred or transformed.
Kinetic Energy and the Work-Energy Theorem
• Kinetic Energy (KE): KE = ½mv²
• Work done by net external forces = change in kinetic energy: W = ΔKE
• If KE increases, work is positive; if KE decreases, work is negative.
• Useful for calculating speed changes due to force without using kinematics.
Potential Energy and Conservative Forces
Gravitational Potential Energy (PEg)
• PEg = mgh (relative to a chosen reference level)
• Depends on object’s position in a gravitational field.
Spring Potential Energy (PEs)
• PEs = ½kx², where k is the spring constant, x is displacement from equilibrium.
• Applies to ideal springs that obey Hooke’s Law: F = –kx
Conservative vs. Nonconservative Forces
• Conservative forces (e.g., gravity, springs) conserve mechanical energy.
• Nonconservative forces (e.g., friction, air resistance) convert mechanical energy into other forms like heat or sound.
• Work by conservative forces = –ΔPE
Conservation of Energy and Systems
• Mechanical energy (E) = KE + PE
• If no nonconservative forces: Einitial = Efinal
• With nonconservative forces: Wnc = ΔKE + ΔPE
• System boundaries define what forces are internal or external.
• Friction and drag reduce mechanical energy by transferring it to other forms.
Problem-Solving Strategies
• Choose a consistent zero level for potential energy.
• Use energy conservation when acceleration or force changes unpredictably.
• For motion under gravity or springs: set KE + PE at one point equal to KE + PE at another.
• For inclined planes and pulleys: use components of gravity and identify where energy is added or removed.
In a Nutshell
Energy is the ability to do work and exists in kinetic and potential forms. Work transfers energy, and power measures how quickly it is transferred. The work-energy theorem connects force and motion, while energy conservation provides a powerful tool for analyzing systems. Understanding conservative and nonconservative forces is key to applying these principles in physical problems.