Find the length of a simple pendulum that has a period of 5.00s . Assume g = 9.81 m/s2.
Express your answer to three significant figures and include the appropriate units.
T = 2 pi sqrt(L/g)
5 = 2 pi sqrt(L/9.81)
L/9.81 = .63326
L = 6.21 meters
The period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the period is given as 5.00s and the acceleration due to gravity is 9.81 m/s^2.
Plugging in these values into the formula, we can solve for L:
5.00 s = 2π√(L / 9.81 m/s^2)
Simplifying the equation, we have:
1.25 = π√(L / 9.81)
Squaring both sides of the equation, we get:
1.5625 = π^2(L / 9.81)
Multiplying both sides by 9.81, we have:
15.309525 = π^2L
Dividing both sides by π^2, we can solve for L:
L = 15.309525 / π^2
Using a calculator, we find:
L ≈ 1.55 m
Therefore, the length of the simple pendulum is approximately 1.55 meters.
To find the length of a simple pendulum that has a period of 5.00s, we can use the formula for the period of a simple pendulum:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Rearranging the formula, we have:
L = (T^2 * g) / (4π^2)
Let's substitute the given values:
T = 5.00s
g = 9.81 m/s^2
Now we can calculate the length:
L = (5.00s)^2 * 9.81 m/s^2 / (4π^2)
L = (25.00s^2 * 9.81 m/s^2) / (4π^2)
L = 245.25 m^2/s^2 / (4π^2)
L ≈ 1.96 m
Therefore, the length of the simple pendulum that has a period of 5.00s is approximately 1.96 meters.