Effect of Nearby Mountain on an Ideal Pendulum

In summary, the conversation discusses the use of perturbation to add a horizontal component gravitational force to a pendulum near a large mountain. The suggested approach is to determine an angle that would result in a symmetric axis and ideal pendulum, and then transform the coordinates. Another suggestion is to treat the pendulum as a 1g pendulum with the center of the swing displaced by 10^-5 times the length of the pendulum arm for a first order approximation.
  • #1
bob012345
Gold Member
2,081
914
Suppose there is a very large mountain adjacent to a pendulum such that there is a horizontal component gravitational force of ##10^{-5}g## acting on the otherwise ideal pendulum. How would one use a perturbation to add that effect to first order?

My initial thought would be to figure an angle that made the total gravitational acceleration ##g(-1z+10^{−5}x)## operating around a symmetric axis and which gives an ideal pendulum and then transform the coordinates?
 
Last edited:
Physics news on Phys.org
  • #2
If you are only looking for a 1st order approximation, treat it as a 1g pendulum with the center of the swing displaced 10^-5 A were A is the length of the pendulum arm.
 
  • Like
Likes vanhees71 and bob012345

Related to Effect of Nearby Mountain on an Ideal Pendulum

How does the presence of a nearby mountain affect the period of an ideal pendulum?

The presence of a nearby mountain affects the period of an ideal pendulum by altering the local gravitational field. The gravitational attraction from the mountain adds to the Earth's gravity, causing a slight increase in the effective gravitational acceleration. This results in a shorter period for the pendulum.

Can the effect of a nearby mountain on an ideal pendulum be quantified?

Yes, the effect can be quantified using gravitational field equations. By calculating the additional gravitational force exerted by the mountain and incorporating it into the local gravitational acceleration, the change in the pendulum's period can be determined using the formula \( T = 2\pi\sqrt{\frac{L}{g_{\text{eff}}}} \), where \( g_{\text{eff}} \) is the effective gravitational acceleration.

What factors of the mountain influence the pendulum's behavior?

The factors of the mountain that influence the pendulum's behavior include the mountain's mass, density, distance from the pendulum, and its geometric shape. A larger, denser, and closer mountain will have a more significant effect on the pendulum's period compared to a smaller, less dense, or more distant mountain.

Does the altitude of the pendulum's location relative to the mountain matter?

Yes, the altitude of the pendulum's location relative to the mountain matters. If the pendulum is at a higher altitude, the gravitational influence of the mountain might be reduced due to increased distance. Conversely, if the pendulum is closer to the base of the mountain, the gravitational effect will be more pronounced.

How significant is the mountain's effect on an ideal pendulum in practical terms?

In practical terms, the effect of a nearby mountain on an ideal pendulum is generally quite small but measurable. For most everyday applications, this effect might be negligible. However, in high-precision experiments, such as those in geophysics or metrology, the influence of nearby topographical features must be accounted for to ensure accurate measurements.

Similar threads

Component forces of a pendulum
    • Mechanics
Replies
2
Views
997
I On whether the motion of a Foucault pendulum bob is comparable to ballistics
    • Classical Physics
Replies
10
Views
1K
Effective acceleration due to gravity in non-inertial frame
    • Mechanics
Replies
6
Views
6K
Foucault Pendulum at the North Pole
    • Introductory Physics Homework Help
Replies
9
Views
943
I need some help for the verification of an assignment about pendulums
    • Introductory Physics Homework Help
Replies
2
Views
1K
Is the Angular Momentum of a Pendulum Conserved?
    • Introductory Physics Homework Help
Replies
5
Views
5K
A What is the Effect of a Lorentz Force on a Pendulum's Gyroscopic Stabilization?
    • Classical Physics
Replies
10
Views
2K
A Why are the Navier-Stokes equations inconsistent in this case?
    • Classical Physics
Replies
18
Views
1K
What is the tension in a pendulum string?
    • Introductory Physics Homework Help
Replies
2
Views
6K
Pendulum Period change due to gravitational force change
    • Introductory Physics Homework Help
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top