a) The period of a simple pendulum is T = 2𝜋L/g where L is the length of the pendulum and g is the acceleration due to gravity at the pendulum's location. Thus, if a pendulum has a period of T = 1.9 s on Earth where gEarth = 9.8 m/s2, its length isLEarth = gEarthT24𝜋2 = m/s2 s 2 4𝜋2 = m = cm
Question
a) The period of a simple pendulum is T = 2𝜋L/g where L is the length of the pendulum and g is the acceleration due to gravity at the pendulum's location. Thus, if a pendulum has a period of T = 1.9 s on Earth where gEarth = 9.8 m/s2, its length isLEarth = gEarthT24𝜋2 = m/s2 s 2 4𝜋2 = m = cm
Solution
To find the length of the pendulum on Earth, we can rearrange the formula for the period of a simple pendulum to solve for L:
L = gT^2 / 4π^2
Substituting the given values:
L = (9.8 m/s^2 * (1.9 s)^2) / 4π^2
Now, we just need to calculate the right side of the equation to find the length of the pendulum.
Let's do the calculation:
L = (9.8 * 1.9^2) / (4 * π^2)
L = 0.908 meters
To convert this to centimeters, we multiply by 100 (since there are 100 centimeters in a meter):
L = 0.908 m * 100 = 90.8 cm
So, the length of the pendulum on Earth is approximately 90.8 cm.
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