Work and Energy - MCAT Physics Lecture

Topics Covered

• Work and its components
• Pressure-volume graphs
• Power and work-energy theorem
• Mechanical advantage

Key Concepts

Work

• Work Definition: Measure of energy transfer via application of force and displacement.
• Forms of Energy Transfer: Work and heat.
• Work Formula:
  • Work (W) = Force (F) · Displacement (D) · cos(θ)
  • F: Magnitude of applied force
  • D: Magnitude of displacement
  • θ: Angle between force vector and displacement vector
• SI Unit: Joule (J)

Pressure-Volume (PV) Graphs

• Used to analyze gas systems with movable pistons.
• Gas Expansion: Work done by gas is positive.
• Gas Compression: Work done on gas is negative.
• Work and PV Graphs: Area under the curve represents work done.
• Processes:
  • Isovolumetric/isochoric: Constant volume, no work done.
  • Isobaric: Constant pressure, work = Pressure x ∆Volume.
  • Graph C: Varying pressure and volume, calculate work by summing areas (triangle + rectangle).
  • Graph D: Closed cycle, calculus required.

Power

• Definition: Rate of energy transfer from one system to another.
• Formula: Power (P) = Work (W) / Time (T)
  • Also P = Change in Energy / Time.
• SI Unit: Watt (W) = Joules/second.

Work-Energy Theorem

• Expression: Work_net = ∆Kinetic Energy
  • Work_net = K_final - K_initial
• Kinetic Energy Changes: Positive work if final velocity > initial velocity, negative if opposite.

Mechanical Advantage

• Definition: Ratio of output force to input force in a simple machine.
• Formula: Mechanical Advantage = Force_out / Force_in
• Examples: Inclined planes, levers, pulleys.
• Effects: Reduces necessary force, increases distance.

Example Problems

Work-Energy Theorem Problem

• Scenario: Lead ball mass 0.125 kg, initial velocity 30 m/s.
• Objective: Calculate work done by gravity at maximum height.
• Approach:
  • Use Work-Energy Theorem: Work_net = K_final - K_initial
  • Final velocity = 0 at max height, solve for work as -1/2 mv_initial^2.

Mechanical Advantage Problem

• Scenario: Block weighs 100 N, pushed up incline.
• Objectives:
  • Minimum force to push block.
  • Work done by force.
  • Force and work if lifted vertically.
• Incline Analysis:
  • Draw free body diagram, resolve forces.
  • Calculate using mg sin(θ) and work = force x displacement.

Pulley System Problem

• Pulley Efficiency: 80%
• Objectives:
  • Distance effort must move.
  • Effort required to lift load.
  • Work done by person.
• Approach:
  • Calculate using efficiency equation.
  • Account for number of pulleys, distance increased for mechanical advantage.

Conclusion

• Discussed various concepts of work and energy including power and mechanical advantage.
• Importance of understanding work-energy relationships and calculations using PV graphs.
• More practice problems to follow in next session.