Pendulum A is 20 cm long and has a 5 gram mass on it. Pendulum B is 30 cm long and has a 10 gram mass on it. Which one has a faster period?
To determine which pendulum has a faster period, we need to understand the factors that affect the period of a pendulum.
The period of a pendulum is the time it takes for the pendulum to complete one full swing (back and forth). It is determined by the length of the pendulum and the acceleration due to gravity.
The period of a pendulum can be calculated using the formula:
T = 2π√(L/g)
Where:
T = Period of the pendulum
π ≈ 3.14 (pi)
L = Length of the pendulum
g = Acceleration due to gravity (approximately 9.8 m/s² on Earth)
Let's calculate the period for pendulum A and pendulum B separately:
For Pendulum A:
Length (L) = 20 cm = 0.2 m
Mass (m) = 5 grams = 0.005 kg (convert grams to kilograms by dividing by 1000)
For Pendulum B:
Length (L) = 30 cm = 0.3 m
Mass (m) = 10 grams = 0.01 kg
Using the formula, we can calculate the periods for both pendulums:
For Pendulum A:
T = 2π√(0.2/9.8)
T ≈ 2π√0.02041
T ≈ 2π * 0.1429
T ≈ 0.8975 seconds
For Pendulum B:
T = 2π√(0.3/9.8)
T ≈ 2π√0.03061
T ≈ 2π * 0.1745
T ≈ 1.0966 seconds
Comparing the periods, we can conclude that Pendulum A has a faster period of approximately 0.8975 seconds, while Pendulum B has a slower period of approximately 1.0966 seconds. Pendulum A swings back and forth faster than Pendulum B.