Question

When a weight is tied on the end of a string and is pulled back and released, it creates a pendulum. The time it takes for the pendulum to swing out and return to its original position is called the period, and depends on the length of the string. For small release angles, like the one in the video, we can use the equation T = 2 π √ L g , where T is the period of the swing, in seconds L is the length of the string, in meters g is gravity, about 9.8 m/s2 My stopwatch estimated the period to be 1.36 seconds. Use this to determine the length of the string, in meters, to at least 3 decimal places meters

Answer 1

The length of the string for a pendulum with a period of 1.36 seconds is approximately 0.369 meters.

Step-by-step explanation:

The period of a simple pendulum can be calculated using the equation T = 2π√(L/g), where T is the period in seconds, L is the length of the string in meters, and g is the acceleration due to gravity (approximately 9.8 m/s²).

To find the length of the string in this case, we can rearrange the equation to solve for L: L = (T^2*g)/(4π^2). Plugging in the given period of 1.36 seconds, we get L = (1.36^2*9.8)/(4π^2) ≈ 0.369 meters.

Therefore, the length of the string is approximately 0.369 meters.

Answer 2

The length of the string is approximately 0.899 meters.

Step-by-step explanation:

The period of a simple pendulum is given by the equation T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity. In this case, the period is given as 1.36 seconds. To determine the length of the string, we can rearrange the equation as follows:

T = 2π√(L/g)

1.36 = 2π√(L/9.8)

To solve for L, we divide both sides by 2π and square both sides:

(1.36 / 2π)² = L/9.8

Plugging in the values and solving for L:

L = (1.36 / 2π)² * 9.8

Using a calculator, we find that L is approximately 0.899 meters.