Conservation Law Fundamental Forces Estimation Of Distances L-2
CONSERVATION LAWS, FUNDAMENTAL FORCES, ESTIMATION OF DISTANCES
Conservation Law Fundamental Forces Estimation Of Distances L-2
Gravitation
It is assumed that the applied force is known.
Case of simple harmonic motion: F=−kx.
Case of electrostatic interaction: F=r2e2r^ = 4πϵ0r21e1e2r^
Conservation Law Fundamental Forces Estimation Of Distances L-2
Work done
F acts in a particle and the body moves.
W=∫t1t2F⋅ds.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Work done
- We say that a Force is Conservative, if the work done is independent of the path.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Work done
∫F⋅ds the component of the force along the direction of the displacement.
Total Work done is zero.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Work done
F=−drdV(r)
This is the statement of conservation of energy.
⇒21mv2+V(r) = Constant
- 21mv2 = Kinetic Energy
V(r) = Potential Energy
Conservation Law Fundamental Forces Estimation Of Distances L-2
Fundamental Forces
- Gravitation
- Electromagnetic
- Nuclear
- Weak
Conservation Law Fundamental Forces Estimation Of Distances L-2
Fundamental Forces
| Interaction | Range | Strength |
|---|---|---|
| Gravitation | ∞ | ≈10−37 |
| Electromagnetic | ∞( screened $) | ≈10−2 |
| Nuclear Forces | 10−15 m | ≈1 |
| Weak Forces | <10−17 m | ≈10−7 |
Conservation Law Fundamental Forces Estimation Of Distances L-2
Screening Effect
FG∼r21
FE∼r21
FE can be positive and negative.
Every positive charge likes to get surrounded by negative charges vice-versa.
Because of this screening, the effective interaction between objects, is very weak compared to the gravitational force.
The range of electromagnetic forces become smaller.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Nuclear Force
- Using Einstein's mass energy equivalents you can find how much energy is liberated in a nuclear reactor.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Gravitational Force
FG=+r2GMm
Gravitational Force is attractive in nature.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Universal Constant
A particle of mass m is moving in the field of the sun's gravitational force.
Determine the universal constant.
ma=r2GMm
mass of A = m
mass of B = M
where, M >> m
Conservation Law Fundamental Forces Estimation Of Distances L-2
Distances and Masses
- Size of the Earth
- Size of the Moon
- The Earth Moon distance
- The Earth Sun distance
- Masses of (i) The Earth, (ii) The Moon, and (iii) The stars
Conservation Law Fundamental Forces Estimation Of Distances L-2
Radius of the Earth
Use trigonometry to find the radius of earth.
If we know the angle and distance, we should be able to estimate the radius of earth.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Radius of the Earth
Simple Example
If the earth were flat your range of vision would be infinite.
We make a simple model and estimate what the radius of the earth.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Radius of the Earth Observation and Inference 4th Century BC
- Eratosthenes found good methods of estimating the radius of the earth.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Radius of the Earth
Point corresponds to Alexandria.
Point corresponds to Aswan.
A well in Aswan and well contains water.
Distance between Alexandria and Aswan is known.
The distance is 50 stadium.
s=Rθ
R=θs = 800 km
C=2πR= 40,000 km
Conservation Law Fundamental Forces Estimation Of Distances L-2
Earth-Moon Distance
Euclidean distance, not the shortest distance.
The sum of the angles of a triangle to be 180 degrees.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Earth Sun and Moon Distance
The distance earth,moon and sun can find by trigonometry.
The new moon when the moon is completely on the opposite side of the earth.
The orbit of the moon is slightly inclined to this plane.
The moon would come between the earth and the sun. There would have been a solar eclipse.
Half moon is the eighth day, that day the moon is a perfect semicircle.
Conservation Law Fundamental Forces Estimation Of Distances L-2
Thank You
Conservation Law Fundamental Forces Estimation Of Distances L-2 CONSERVATION LAWS, FUNDAMENTAL FORCES, ESTIMATION OF DISTANCES $\rightarrow$ $\rightarrow$ CONSERVATION LAWS, FUNDAMENTAL FORCES, ESTIMATION OF DISTANCES $\rightarrow$ Gravitation $\rightarrow$ Work done