Question

For the following exercises, use the model for the period of a pendulum, t, such that t = 2π/√l/g, where the length of the pendulum is l and the acceleration due to gravity is g. if the acceleration due to gravity is 9.8 m/s^2 and the period equals 1 s, find the length to the nearest cm (100cm = 1m).

Answer 1

To find the pendulum length with a 1-second period, the formula t = 2π/√(l/g) is rearranged to solve for l. Given g = 9.8 m/s², the length is calculated and converted to centimeters, resulting in approximately 25 cm.

Step-by-step explanation:

To find the length (l) of the pendulum with a period (t) of 1 second using the model t = 2π/√(l/g), we can rearrange the formula to solve for l, given the acceleration due to gravity (g) is 9.8 m/s2. First, we square both sides of the equation to eliminate the square root:

t2 = (2π)2 (l/g)

Next, multiply both sides by g and then divide by (2π)2 to isolate l:

l = (t2 × g) / (2π)2

Plugging in the values for t and g:

l = (12 × 9.8 m/s2) / (2π)2 ≈ 0.2487 meters

To find the length to the nearest cm, we convert meters to centimeters:

l ≈ 0.2487 m × 100 cm/m ≈ 24.87 cm

Therefore, the length of the pendulum is approximately 25 cm when rounded to the nearest centimeter.