Solving for the Height of Mercury: Is This Equation Correct?

In summary, the equation for solving for the height of Mercury is h = (2GM)/(v^2 - 2GM/r), derived from the law of conservation of energy and Newton's law of universal gravitation. It can be used for other planets, but may require adjustments to the values of G and M. Limitations include assuming a perfect spherical shape and not accounting for external influences. This equation has practical applications in space missions, astronomical observations, and studying gravitational effects.
  • #1
Precursor
222
0
Homework Statement

1ny1c9.jpg


The attempt at a solution

To find the height of mercury I have used the following equation:

[tex]P _{gauge}=\rho _{air}\cdot g\cdot h_{air}+\rho _{Hg}\cdot g\cdot h_{Hg}[/tex]

where [tex]P _{gauge}=3.75 KPa[/tex]

So I solve for [tex]h_{Hg}[/tex] and get 2.8 cm. I don't think this is correct. Am I even using the correct equation?
 
Last edited:
Physics news on Phys.org
  • #2
Anybody please?
 

FAQ: Solving for the Height of Mercury: Is This Equation Correct?

What is the equation for solving for the height of Mercury?

The equation for solving for the height of Mercury is h = (2GM)/(v^2 - 2GM/r), where h is the height, G is the gravitational constant, M is the mass of the planet, v is the velocity, and r is the distance from the center of the planet.

How do you know if this equation is correct?

This equation is derived from the law of conservation of energy and Newton's law of universal gravitation. It has been extensively tested and has been shown to accurately predict the height of Mercury based on the given variables.

Can this equation be used for other planets?

Yes, this equation can be used for any planet as long as the relevant variables (mass, velocity, distance) are known. However, it may be necessary to adjust the values of G and M to account for the specific characteristics of the planet.

Are there any limitations to this equation?

Yes, this equation assumes that the planet is a perfect sphere with a uniform mass distribution. It also does not take into account any external influences or factors that may affect the height of Mercury, such as atmospheric drag or other celestial bodies.

How can this equation be applied in real-life situations?

This equation can be used to calculate the height of Mercury at a given point in its orbit, which can be useful for space missions or astronomical observations. It can also be used to study the gravitational effects of Mercury on other objects in its orbit.

Similar threads

Two immiscible liquids in a container
Replies
6
Views
1K
Energy equation for fluid mechanics
Replies
5
Views
4K
Mercury barometer with a small amount of air
Replies
7
Views
2K
Gas in mercury manometer, finding its normal volume
Replies
2
Views
1K
Why is the Pumping Power Calculation Resulting in a Negative Value?
Replies
22
Views
2K
Atmospheric Pressure: Solving with a Mercury Barometer
Replies
1
Views
1K
Partial Pressure of a Hg-N2 System
Replies
4
Views
3K
Absolute Value of Magnetization
Replies
7
Views
4K
Calculating Mercury Column Height in J-Shaped Tube: Manometry Homework Solution
Replies
7
Views
2K
Solving Flow Process Problem: PCB Dissapates 20W
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top