Lecture Notes: Kinetic Energy and Potential Energy

Introduction

• Discussion on kinetic and potential energy.

Kinetic Energy

• Definition: Energy in motion; anything that moves has kinetic energy.
  • Example: A moving ball at 5 m/s has kinetic energy.
  • A block at rest has no kinetic energy.
• Formula: $K = \frac{1}{2} mv^2$
  • Depends on mass (m) and speed (v).
  • Units: Mass in kilograms (kg), speed in meters per second (m/s), energy in joules (J).

Physics Exam Questions

• Doubling Mass:
  • Doubles the kinetic energy.
• Doubling Speed:
  • Quadruples the kinetic energy.
• Example Problem: Increase mass by factor of 3 and speed by factor of 4.
  • Kinetic energy increases by factor of 48.

Potential Energy

• Definition: Stored energy due to position.
  • Example: Object B at a higher position than object A has more gravitational potential energy.
• Formula: $PE = mgh$
  • m: Mass in kg.
  • g: Gravitational acceleration (9.8 m/s²).
  • h: Height above ground level in meters.

Example Problem

• Potential Energy Calculation:
  • 10 kg ball, 50 m above ground.
  • Potential energy: $10 \times 9.8 \times 50 = 4900$ J.
• Conversion to Kinetic Energy:
  • As the ball falls, potential energy converts to kinetic energy.
  • At ground level, all potential energy becomes kinetic.
  • Kinetic energy at ground: 4900 J.
• Speed Calculation:
  • $4900 = \frac{1}{2} \times 10 \times v^2$
  • Speed just before hitting ground: 31.3 m/s.

Conservation of Energy

• Energy conversion between potential and kinetic forms.
• Practical applications include solving physics problems.

Elastic Potential Energy

• Formula: $\frac{1}{2} kx^2$
  • k: Spring constant in Newtons per meter (N/m).
  • x: Displacement from equilibrium position in meters.
• Spring Constant:
  • Determines stiffness of spring.
  • Higher k = stiffer spring.
  • Example: 100 N/m vs 500 N/m, stiffer spring requires more force.

Other Forms of Potential Energy

• Chemical energy: Stored in chemical bonds.
• Electric potential energy: Based on position in an electric field.

Conclusion

• Summary of types and formulas of kinetic and potential energy.
• Encouragement to explore additional resources for more complex problems.

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