Gravitational field strength at latitude

[zohapmkoftid]

This figure is captured from my physics textbook and it is about the gravity at latitude

http://pix.gogobox.com.tw/out.php?i=567045_.JPG

I want to know the difference between mg0 and mg(theta). Which one is the weight of the object? Thank you!

 

[Doc Al]

Looks to me like mg₀ is the gravitational force on the object and mg_θ is the apparent weight of the object at latitude θ. The apparent weight is the gravitational force minus the centripetal force. (If you hung an object from a string, the string would end up parallel to the apparent weight.)

 

[zohapmkoftid]

Is gθ called 'apparent gravity'?

 

[Doc Al]

Is gθ called 'apparent gravity'?

That's what I would call it, but it is also called the local value of g as a function of θ. It's somewhat a matter of semantics. What does your textbook call it? (What text are you using?)

 

[zohapmkoftid]

It is a Hong Kong textbook called New Way PHYSICS for Advanced Level
In the book, gθ is called gravitational field strength at latitude θ
I think the author uses the wrong name
The gravitational field strength at latitude θ should be g₀, right?

Here is the related page from my textbook
http://uploadpie.com/bHHsD

 

[Doc Al]

I think the author uses the wrong name
The gravitational field strength at latitude θ should be g₀, right?

No, the author's terminology is reasonable. When they talk about 'gravitational field strength at latitude θ' they are lumping together the strictly gravitational component (g₀) with the effect due to rotation. Think of it as the 'net' or 'apparent' gravitational field strength. (It is a bit confusing, but commonly done.)

 

[zohapmkoftid]

gravity = g₀
apparent gravity / gravity at latitude = g_θ
weight = mg₀
apparent weight = mg_θ

I hope I don't understand wrongly

So when we measure our body weight, the reading of the balance = mg_θ rather than mg₀

 

[Doc Al]

gravity = g₀
apparent gravity / gravity at latitude = g_θ
weight = mg₀
apparent weight = mg_θ

I hope I don't understand wrongly

So when we measure our body weight, the reading of the balance = mg_θ rather than mg₀

Looks good to me. (Of course, this is just a simple model of the Earth as a sphere, ignoring various complications.)