Southernly Deflection of a Falling Mass

In summary, the conversation discusses a problem involving a non-inertial reference frame and the deflection of a mass dropped from a height on the Earth's surface. The calculation for the eastern deflection is given, but a second order calculation for southern deflection is needed. A hint is provided to consider the Coriolis force due to a small eastward velocity.
  • #1
-Christastic-
14
0
Ok...I've struggled with this.

Let's say I'm dropping a mass from height h from the Earth's surface. Since I'm considering this as a non-inertial reference frame, I understand that there is an easternly deflection. I've done the calculation and end up with de=(1/3)(w)cos(lamda)((8h^2)/g)^(1/2) where omega is the rate of rotation of the Earth and lamda is the degree latitude.

Problem. "Repeat the calculation to second order in omega and find the southernly deflection." The easternly deflection I'm good with. I don't understand how there is any southern deflection. The calculation and explination is eluding me at this point.
 
Physics news on Phys.org
  • #2
Hi Christastic,

Here is a hint: to first order in omega, you have a small velocity to the east. Calculate the Coriolis force due to this velocity. What is its direction?
 
Last edited:
  • #3
Thanks for the hint. Will jump on it.
 

Related to Southernly Deflection of a Falling Mass

Question 1: What is Southernly Deflection of a Falling Mass?

Southernly Deflection of a Falling Mass is a phenomenon that occurs when a mass is dropped from a height and experiences a deviation from its expected trajectory due to the Earth's rotation. This deviation causes the mass to fall slightly to the south of its intended target.

Question 2: What causes Southernly Deflection of a Falling Mass?

The Coriolis effect, which is caused by the Earth's rotation, is the main factor that contributes to Southernly Deflection. As the Earth rotates, objects in motion are subject to a force that causes them to turn to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This force is what causes the deviation in the trajectory of a falling mass.

Question 3: How does the Earth's rotation affect Southernly Deflection of a Falling Mass?

The Earth's rotation plays a crucial role in Southernly Deflection of a Falling Mass. As the Earth rotates, its surface moves faster at the equator than at the poles. This difference in speed leads to a difference in the Coriolis effect, causing the deflection of falling masses to be greater at the equator and smaller at the poles.

Question 4: Is Southernly Deflection of a Falling Mass significant?

While the effect of Southernly Deflection may seem small, it can have significant consequences in certain situations. For example, in long-range artillery shooting, the Coriolis effect and Southernly Deflection must be taken into account to ensure the accuracy of the shot. In everyday life, however, the effect is negligible and not noticeable.

Question 5: Can Southernly Deflection of a Falling Mass be observed in both hemispheres?

Yes, Southernly Deflection of a Falling Mass can be observed in both the Northern and Southern Hemispheres. However, the direction of the deflection will be opposite in each hemisphere due to the direction of the Coriolis effect. In the Northern Hemisphere, the mass will be deflected to the right, while in the Southern Hemisphere, it will be deflected to the left.

Similar threads

B Eddington Exp vs Newton: Comparing Starlight Deflection
    • Special and General Relativity
Replies
6
Views
1K
How Does the Coriolis Effect Influence Falling Objects at the Equator?
    • Introductory Physics Homework Help
2
Replies
40
Views
6K
Deflection of Mass Homework Solution
    • Introductory Physics Homework Help
Replies
8
Views
1K
Why Is There No Southerly Deflection When Dropping a Particle Down a Mineshaft?
    • Advanced Physics Homework Help
Replies
1
Views
2K
I Energy Released From Dropping Things Onto Neutron Stars
    • Classical Physics
Replies
20
Views
875
I Scaling up a mass spectrometer
    • Other Physics Topics
Replies
1
Views
1K
I How to Calculate force exerted on a falling body?
    • Classical Physics
Replies
12
Views
1K
Spin-1 particle states as seen by different observers: Wigner rotation
    • Advanced Physics Homework Help
Replies
5
Views
2K
Southerly Deflection by Motion of the Earth
    • Advanced Physics Homework Help
Replies
1
Views
2K
Trying to resolve a volume calculation
    • Precalculus Mathematics Homework Help
Replies
2
Views
662

Hot Threads

Recent Insights

Back
Top