astronauts on a distant planet set up a pendulum length 1.2m. the pendulum executes simple harmonic motion and makes complete vibrations in 280s. what is the magnitude of the acceleration due to gravity of this planet?
Well, that's a swinging question! Let's do some physics clowning around!
To find the magnitude of the acceleration due to gravity (g), we can use the equation for the period of a pendulum:
T = 2π * √(L/g),
where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that the period of the pendulum is 280 seconds and the length of the pendulum is 1.2 meters, we can rearrange the equation to solve for g:
g = (4π² * L) / T².
Plugging in the values we have:
g = (4π² * 1.2) / (280)².
Now, let me put my clownish calculations skills to work... *drum roll please* ...
g is approximately 0.171 m/s².
So, the magnitude of the acceleration due to gravity on that distant planet is approximately 0.171 m/s². Keep in mind, though, that this is just a clown estimate! Actual results may vary, so don't make any important scientific decisions based solely on my clown calculations!
To find the magnitude of the acceleration due to gravity on this distant planet, we can use the formula for the period of a pendulum in simple harmonic motion:
T = 2π√(L / g)
Where:
T = Period of the pendulum
L = Length of the pendulum
g = Acceleration due to gravity
Given:
Length of the pendulum, L = 1.2 m
We are told that the pendulum completes vibrations in 280s, which is equivalent to the period T.
Using the formula, we can rearrange it to solve for g:
g = 4π²(L / T²)
Substituting the given values:
g = 4π²(1.2 / 280²)
Calculating the value:
g ≈ 4π²(1.2 / 280²)
g ≈ 4π²(0.000006746)
g ≈ 0.0003405 m/s²
Therefore, the magnitude of the acceleration due to gravity on this distant planet is approximately 0.0003405 m/s².
To find the magnitude of the acceleration due to gravity on the distant planet, we can use the formula for the period of a simple pendulum:
T = 2π√(L/g)
Where:
T is the period of the pendulum,
L is the length of the pendulum, and
g is the acceleration due to gravity.
In this case, the period T is given as 280 seconds, and the length L of the pendulum is 1.2 meters. We need to solve for g.
Rearranging the formula, we get:
g = (4π²L) / T²
Plugging in the given values:
g = (4π² * 1.2) / 280²
Now we can calculate this using a calculator:
g ≈ 4.13 m/s²
Therefore, the magnitude of the acceleration due to gravity on the distant planet is approximately 4.13 m/s².