Gravitational force from mass above you

Click For Summary
SUMMARY

The discussion centers on calculating the reduction in weight experienced by an individual standing 13 meters below the center of a spherical water tank containing 5.0×106 kg of water. The correct formula to use is Newton's law of universal gravitation, F = G(m1*m2)/r2, where G is the gravitational constant. A key error identified was the confusion between G (gravitational constant) and g (acceleration due to gravity), which led to incorrect dimensional analysis in the calculations. The discussion emphasizes the importance of correctly applying gravitational formulas to derive accurate results.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with gravitational constant (G) and acceleration due to gravity (g)
  • Basic knowledge of dimensional analysis in physics
  • Ability to perform calculations involving mass and distance in gravitational contexts
NEXT STEPS
  • Study the derivation and applications of Newton's law of universal gravitation
  • Learn about the gravitational constant (G) and its significance in physics
  • Explore dimensional analysis techniques to verify physical equations
  • Investigate real-world applications of gravitational calculations in engineering and physics
USEFUL FOR

Students in physics, educators teaching gravitational concepts, and professionals in engineering fields who require a solid understanding of gravitational forces and their calculations.

Mattyguy
Messages
1
Reaction score
0
I tried so much but I still can't figure out this question:

If you're standing on the ground 13 m directly below the center of a spherical water tank containing 5.0×106 kg of water, by what fraction is your weight reduced due to the gravitational attraction of the water?
 
Physics news on Phys.org


Mattyguy said:
I tried so much but I still can't figure out this question:

If you're standing on the ground 13 m directly below the center of a spherical water tank containing 5.0×106 kg of water, by what fraction is your weight reduced due to the gravitational attraction of the water?

You mean 5.0E6 kg?

F = gMm/r^2 = 2.90E5 m
G = gM(earth)m/R^2 = 1.44E12 m

The rest is piece of cake?
 
Last edited:


kasse said:
You mean 5.0E6 kg?

F = gMm/r^2 = 2.90E5 m
G = gM(earth)m/R^2 = 1.44E12 m

The rest is piece of cake?

On the right-hand sides of your equations you confused the gravitational constant G with g (acceleration due to gravity on the surface of Earth) here. You should have noticed that your final answers, of force per mass m, are ridiculously large (and have the wrong dimension).

Also, it's probably not a good idea to use G for the name of a force that involves gravity.

On the other hand, for calculating the ratio of two gravitational forces your first mistake doesn't matter.
 

Similar threads

Replies
6
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 16 ·
Replies
16
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
1
Views
3K
Replies
2
Views
6K
Replies
1
Views
1K