Final answer:
The acceleration due to gravity at the pendulum's location is calculated using the formula g = (4π²L) / T². Given the pendulum's length and the time for 7 swings, the acceleration due to gravity is found to be approximately 9.81 m/s².
Step-by-step explanation:
Calculating the Acceleration Due to Gravity
To find the acceleration due to gravity at the location of the pendulum, we can use the formula that relates the period of a pendulum (T) to the length (L) of the pendulum and the acceleration due to gravity (g), which is:
T = 2π√(L/g)
We can solve for acceleration due to gravity by rearranging the formula:
g = (4π²L) / T²
Given that the pendulum makes 7.0 complete swings in 37.0 s, we first find the period of one swing:
Period of one swing (T) = Total time / Number of swings = 37.0 s / 7.0 swings = 5.2857 s
Now, we plug the values for L and T into the formula:
g = (4π² × 2.6 m) / (5.2857 s)²
After calculating, we find:
g = 9.81 m/s² (approximated to two decimal places)
This is the acceleration of gravity at the pendulum's location.