Understanding the Concepts
* Potential Energy: When the pendulum is held horizontally, all its energy is in the form of potential energy (due to its height).
* Conservation of Energy: As the pendulum swings, potential energy converts into kinetic energy (energy of motion). The total mechanical energy (potential + kinetic) remains constant.
* Angle and Potential Energy: The potential energy of the pendulum depends on its height above its lowest point. This height changes as the angle with the vertical changes.
Calculations
1. Initial Potential Energy (Horizontal Position):
* Height (h) = Length of pendulum (L) = 1 m
* Potential energy (PE) = mgh = (0.1 kg) * (9.8 m/s²) * (1 m) = 0.98 Joules
2. Potential Energy at 0°:
* Height (h) = 0 (pendulum at its lowest point)
* Potential energy (PE) = 0
3. Potential Energy at 30°:
* Height (h) = L - L*cos(30°) = 1 m - 1 m * cos(30°) ≈ 0.134 m
* Potential energy (PE) = mgh = (0.1 kg) * (9.8 m/s²) * (0.134 m) ≈ 0.131 Joules
4. Kinetic Energy at 0°:
* Since all potential energy converts to kinetic energy at the lowest point, kinetic energy (KE) = 0.98 Joules
5. Kinetic Energy at 30°:
* Using conservation of energy:
* KE at 30° = Initial PE - PE at 30°
* KE at 30° ≈ 0.98 Joules - 0.131 Joules ≈ 0.849 Joules
Summary
* Kinetic energy at 0°: 0.98 Joules
* Kinetic energy at 30°: ≈ 0.849 Joules
Important Notes:
* We're assuming no energy loss due to friction or air resistance.
* The angle is measured from the vertical.
* This calculation uses the basic principles of conservation of energy and potential/kinetic energy relationships.
