Cheat Sheet: Work Energy And Simple Machines

1. Introduction

1.1 Scope

• Introduces work, energy, power, and simple machines as analytical tools for motion with variable/complex forces.
• Simple machines change magnitude or direction of applied force to make tasks easier without reducing total work.

1.2 Central concept

• Energy is the capacity to do work.

2. Work Done by a Constant Force

2.1 Observations leading to scientific concept

• Work increases proportionally with force when displacement is fixed.
• Work increases proportionally with displacement when force is fixed.
• Work for multiple identical tasks is additive.

2.2 Force-displacement graph

• Work for constant force equals area of rectangle under force-displacement graph.
• For variable force, work equals area under the force-displacement graph between initial and final positions.

2.3 Zero, positive, negative work (concepts only)

• Work is zero when force = 0, or displacement = 0, or when force is perpendicular to displacement.
• Positive work: displacement in same direction as force.
• Negative work: displacement opposite to direction of force.

3. Work-Energy Theorem

3.1 Statement

• Work done on an object equals the change in its energy.
• The theorem applies to a system of objects and to variable forces.

3.2 Energy transfer modes (brief)

• Mechanical work is one way to transfer energy; other modes include heat, radiation, electric currents, sound, and nuclear reactions.

4. Forms of Energy

4.1 List of forms

• Mechanical energy - due to motion or position of objects.
• Thermal energy - makes things warm or hot.
• Light energy - allows us to see.
• Sound energy - energy of vibrations of air or other molecules.
• Electrical energy - related to position or motion of charges.
• Chemical energy - stored in fuels and food as chemical bonds.
• Nuclear energy - stored in nuclei of atoms.

5. Mechanical Energy

5.1 Components

• Mechanical energy is the sum of kinetic and potential energies (E = K + U).

5.2 Kinetic and potential (concepts)

• Kinetic energy: energy possessed by an object due to its motion.
• Potential energy: energy stored due to deformation or relative positions within interacting systems.
• Gravitational potential energy: energy due to position relative to Earth; increases with height above ground.

5.3 Conservation and examples (concepts)

• Mechanical energy remains constant if no external forces (friction, air resistance) act on the object or system.
• Pendulum: at extreme positions KE ≈ 0 and PE maximum; at lowest point KE maximum and PE minimum; KE↔PE interchange conserves total ME if nonconservative forces absent.

6. Power

6.1 Concept

• Power is the rate at which work is done.
• Greater work in same time increases required power; same work in less time increases required power.

6.2 Units and alternative unit

• Watt is the SI unit of power; horsepower is an alternative unit (1 hp = 746 W).

7. Simple Machines

7.1 Key terms

7.2 Pulley, inclined plane, lever (descriptions)

• Fixed pulley: changes direction of force; does not reduce magnitude (MA = 1 for a fixed pulley).
• Movable pulley or pulley systems: provide MA > 1 to reduce required effort.
• Inclined plane: moves load to higher level using smaller force over larger distance; longer/shallower incline gives greater MA.
• Lever: rigid bar rotating about a fulcrum; effort acts at effort arm and load at load arm; changing arm lengths changes required effort.

8. Summary: At a Glance

• Work: force acting on an object causes displacement in direction of the force.
• Energy: capacity to do work.
• Work-Energy Theorem: work done on an object equals change in its energy.
• Kinetic energy: energy due to motion.
• Gravitational potential energy: energy due to height above Earth's surface.
• Mechanical energy: sum of kinetic and potential energies; conserved if no external nonconservative forces act.
• Power: rate of doing work.
• Simple machines change magnitude or direction of force but do not reduce total work; MA relates load and effort.

9. Key Formulas at a Glance

9.1 Units: name origins