What is the free-fall acceleration in a location where the period of a 2.03 m long pendulum is 2.86 s s? Answer in units of m/s squared
To find the free-fall acceleration, you can make use of the formula for the period of a simple pendulum:
T = 2π * sqrt(L/g)
Where:
- T is the period of the pendulum
- L is the length of the pendulum
- g is the acceleration due to gravity
Rearranging the formula, we have:
g = (4π² * L) / T²
Now, let's substitute the given values into the equation. The length of the pendulum is 2.03 m, and the period is 2.86 s.
g = (4π² * 2.03) / (2.86)²
To solve this equation, we need to compute the right-hand side:
g = (4 * 3.14² * 2.03) / (2.86)²
g = (4 * 9.86 * 2.03) / (8.1796)
g ≈ 9.81 m/s²
Therefore, the free-fall acceleration in this location is approximately 9.81 m/s².