Two physical pendulums (not simple pendulums) are made from meter sticks that are suspended from the ceiling at one end. The sticks are uniform and are identical in all respects, except that one is made of wood (mass = 0.17 kg) and the other of metal (mass = .85 kg). They are set into oscillation and execute simple harmonic motion. Determine the period of a) the wood pendulum and b) the metal pendulum.
The period is independent of mass, so the periods should be the same.
http://hyperphysics.phy-astr.gsu.edu/hbase/penrod.html#c1
To determine the period of the two pendulums, we need to use the formula for the period of a physical pendulum. The period of a physical pendulum is given by:
T = 2πsqrt(I/mgh)
Where:
T = Period of the pendulum
π = Pi
I = Moment of inertia of the pendulum
m = Mass of the pendulum
g = Acceleration due to gravity
h = Length of the pendulum
To find the period of the wood pendulum:
1. Determine the length of the wood pendulum:
The length of the pendulum is the length of the meter stick. Assuming the pendulum is swinging from the center of the meter stick, the length is 1/2 meter or 0.5 m.
2. Calculate the moment of inertia (I) of the wooden pendulum:
The moment of inertia for a pendulum is given by the formula I = (1/3)ML^2, where M is the mass of the pendulum and L is the length of the pendulum.
For the wooden pendulum, M = 0.17 kg and L = 0.5 m.
Plugging these values into the formula, we get I = (1/3)(0.17 kg)(0.5 m)^2.
3. Calculate the period (T) of the wooden pendulum:
Using the formula T = 2πsqrt(I/mgh), where g is the acceleration due to gravity (9.8 m/s^2), and h is the length of the pendulum, we can calculate the period of the wood pendulum.
To find the period of the metal pendulum:
1. Determine the length of the metal pendulum:
Assuming the metal pendulum has the same length as the wood pendulum, the length is also 0.5 m.
2. Calculate the moment of inertia (I) of the metal pendulum:
Using the same formula as before, I = (1/3)(0.85 kg)(0.5 m)^2.
3. Calculate the period (T) of the metal pendulum:
Using the formula T = 2πsqrt(I/mgh), with the same values of g and h as before, we can calculate the period of the metal pendulum.
By following these steps and plugging in the given values, you can determine the periods of both the wood and metal pendulums.