To determine the period of a pendulum, we will use the formula for the period of a simple pendulum, which is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the period of the pendulum (the time it takes for the pendulum to complete one full swing back and forth)
- \( L \) is the length of the pendulum
- \( g \) is the acceleration due to gravity
- \( \pi \) is the mathematical constant Pi (approximately 3.14159)
The mass of the pendulum bob (4 kg in this case) does not affect the period; it is the length of the pendulum that is important, so we can ignore the mass.
Given the length \( L = 2.6 \) meters and using the standard value for the acceleration due to gravity on Earth, \( g = 9.81 \) m/s², we plug these values into the formula:
\[ T = 2\pi \sqrt{\frac{2.6}{9.81}} \]
Now let's calculate this step by step:
1. Divide the length of the pendulum by the acceleration due to gravity:
\[ \frac{2.6}{9.81} \approx 0.265 \]
2. Take the square root of the resulting number:
\[ \sqrt{0.265} \approx 0.5148 \]
3. Multiply by \( 2\pi \) to find the period \( T \):
\[ T \approx 2 \times 3.14159 \times 0.5148 \]
\[ T \approx 6.28318 \times 0.5148 \]
\[ T \approx 3.2336 \]
So, the period of a pendulum that is 2.6 meters long is approximately 3.23 seconds.
