Final answer:
The maximum speed of a simple pendulum with a 100 g mass released from a 30° angle is found using conservation of energy principles. The potential energy at the release point converts to kinetic energy at the lowest point, resulting in a calculated speed of approximately 1.62 m/s.
Step-by-step explanation:
To calculate the maximum speed of the mass on a simple pendulum of length 1.00 m with a mass of 100 g released from a 30° angle, we can use the principle of conservation of energy. The potential energy (PE) at the release point is transformed into kinetic energy (KE) at the lowest point of the swing. The PE at the release point is given by PE = mgh, where m is the mass, g is the acceleration due to gravity (9.81 m/s²), and h is the height change. The height can be found using the equation h = l(1 - ), where l is the pendulum length and θ is the angle from the vertical. The KE at the lowest point, where the pendulum has its maximum speed (v), is given by KE = 0.5mv². By equating the initial PE to the KE at the lowest point, we can solve for v.
First, we calculate the height: h = l(1 - ) h = 1.00 m (1 - cos(30°)) h ≈ 1.00 m (1 - 0.866) h ≈ 0.134 m
Now, PE at the release point is: PE = mgh = 0.1 kg × 9.81 m/s² × 0.134 m PE ≈ 0.13134 J
Since PE = KE, we have: 0.13134 J = 0.5 × 0.1 kg × v² Solving for v: v² = <(2 × 0.13134 J) / (0.1 kg)> v² ≈ 2.6268 m²/s² v ≈ √2.6268 m²/s² v ≈ 1.62 m/s
The maximum speed of the mass at the bottom of its arc is approximately 1.62 m/s.