Calculating Length of Pendulum with 12.0 N Weight and 1.2 s Swing

In summary, the formula for calculating the length of a pendulum is L = (g * T^2) / (4 * π^2), where L is the length of the pendulum, g is the acceleration due to gravity (9.8 m/s^2), and T is the period of the pendulum in seconds. The period of a pendulum can be calculated using the formula T = 2π * √(L/g), where T is the period of the pendulum in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s^2). The weight used in the calculation is 12.0 N (Newtons)
  • #1
Jtappan
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Homework Statement



A clock has a pendulum that performs one full swing every 1.2 s (back and forth). The object at the end of the pendulum weighs 12.0 N. What is the length of the pendulum?
____ m

Homework Equations



??


The Attempt at a Solution



What is the equation i would use here?
 
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  • #3


There are two equations that can be used to calculate the length of a pendulum:
1) T = 2π√(L/g), where T is the period (in seconds), L is the length of the pendulum (in meters), and g is the acceleration due to gravity (9.8 m/s^2).
2) T = 1/f, where T is the period (in seconds) and f is the frequency (in hertz).

Using the first equation, we can rearrange it to solve for L:
L = (T/2π)^2 * g

Plugging in the given values, we get:
L = (1.2 s/2π)^2 * 9.8 m/s^2 = 0.58 m

Therefore, the length of the pendulum is approximately 0.58 meters.
 

1. What is the formula for calculating the length of a pendulum?

The formula for calculating the length of a pendulum is L = (g * T^2) / (4 * π^2), where L is the length of the pendulum, g is the acceleration due to gravity (9.8 m/s^2), and T is the period of the pendulum in seconds.

2. How do I calculate the period of a pendulum?

The period of a pendulum can be calculated by using the formula T = 2π * √(L/g), where T is the period of the pendulum in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s^2).

3. What is the weight and swing time used in the calculation?

The weight used in the calculation is 12.0 N (Newtons) and the swing time is 1.2 seconds.

4. Can this formula be used for any weight and swing time?

Yes, this formula can be used for any weight and swing time as long as the units are consistent and the acceleration due to gravity is 9.8 m/s^2.

5. How accurate is this calculation?

This calculation is fairly accurate, but it may not take into account factors such as air resistance and friction, which can affect the actual length of a pendulum. It is also important to note that this calculation assumes a perfect pendulum with no external forces acting on it.

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