Pendulum A is 20 cm long and has a 5 g mass on it. Pendulum B is 30 cm long and has a 10 g mass on it. Which one has a faster period?
Pendulum B has a faster period.
To determine which pendulum has a faster period, we can use the formula for the period of a simple pendulum, which is given by:
T = 2π√(L/g)
Where:
T is the period,
π is Pi (approximately 3.14),
L is the length of the pendulum in meters, and
g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Let's calculate the periods of Pendulum A and Pendulum B:
For Pendulum A:
Length (L) = 20 cm = 0.2 m
Mass (m) = 5 g = 0.005 kg
Acceleration due to gravity (g) = 9.8 m/s^2
T(A) = 2π√(0.2/9.8)
≈ 2π√(0.02/1)
≈ 2π√0.02
≈ 2π × 0.1414
≈ 0.886 seconds
For Pendulum B:
Length (L) = 30 cm = 0.3 m
Mass (m) = 10 g = 0.01 kg
Acceleration due to gravity (g) = 9.8 m/s^2
T(B) = 2π√(0.3/9.8)
≈ 2π√(0.03/1)
≈ 2π√0.03
≈ 2π × 0.1732
≈ 1.089 seconds
Comparing the two periods, we see that Pendulum B has a faster period with a period of approximately 1.089 seconds, while Pendulum A has a period of approximately 0.886 seconds.
The period of a pendulum is the time it takes for one complete back-and-forth motion, also known as a swing. The factors that affect the period of a pendulum are the length of the pendulum and the acceleration due to gravity, but not the mass of the pendulum.
To determine which pendulum has a faster period, we need to calculate the period for each pendulum using their respective lengths.
The formula to calculate the period of a pendulum is:
T = 2π√(L/g),
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).
For Pendulum A:
T_A = 2π√(L_A/g),
where L_A = 20 cm = 0.2 m.
T_A = 2π√(0.2/9.8),
T_A ≈ 2π√(0.02041),
T_A ≈ 2π * 0.1429,
T_A ≈ 0.8990 s (rounded to four decimal places).
For Pendulum B:
T_B = 2π√(L_B/g),
where L_B = 30 cm = 0.3 m.
T_B = 2π√(0.3/9.8),
T_B ≈ 2π√(0.03061),
T_B ≈ 2π * 0.1749,
T_B ≈ 1.1004 s (rounded to four decimal places).
Comparing the two periods, we can see that Pendulum B has a longer period (1.1004 seconds) compared to Pendulum A (0.8990 seconds). Therefore, Pendulum A has a faster period.