Top Banner
Gravity
34

Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Dec 27, 2015

Download

Documents

Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravity

Page 2: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Newton’s Universal Law of Gravitation

Newton’s conceptual leap in understandinggravity was his realizationthat the same force governs the motion of a falling objecton Earth & the motion of the

Moon in its orbit around the Earth.

Page 3: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Universal Law of Gravitation

• Every mass attracts every other mass through gravity.

• The force of attraction between any 2 objects is directly proportional to the product of their masses.

• Doubling the mass of 1object doubles Fg between the 2 objects.

Page 4: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Inverse Square

• Doubling distance between two objects weakens force of gravity by a factor of 22 (or 4).

• Fg drops off by ¼.

Page 5: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

NEWTON’S UNIVERSALLAW OF GRAVITATION

Fg =GMm

r2

Page 6: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

G is universal gravitation constant.

G = 6.67 x 10-11 N m2. kg2.

m1 m2 are mass of objects in kg.

r is distance between ctrs m.

Page 7: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravity and Weight• Definition: The weight of an object is a measure

of the Fg one object feels in the presence of another.

• Weight Fg = mg. Where g is known.

Page 8: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Mass can be measured in 2 ways

• Inertial mass - the mass of a body as determined by its momentum, as opposed to gravitational mass. How it accelerates

• m = Fnet/a

• Gravitational mass -the mass of a body determined by its response to the force of gravity.

Page 9: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

1. Prove that the acceleration of gravity g = GM/r2, where M is the mass of a planet or star r is its radius.

Page 10: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Fg = m2g = GM1m2. r2.

g = GM1 is accl due to gravity r2.

Mass of the object cancels out.Acceleration depends only on the mass of the

planet (or star).

Page 11: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

• Is heavier body attracted to the Earth with more force than a light body.

•Does the heavier object free fall faster?

•Explain.

Questions: Raise Hands.

Page 12: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Newton’s Universal Law of Gravitation

• Fg = GMm.

R2.

Describes Force btw point masses.What is a point mass?

Page 13: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravitational Field deals with space around the mass.

Page 14: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravitational Field Strength/Intensity -Force per unit mass experienced by a

small “test mass” in space.

Page 15: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravitational Field Linesdrawn in direction of acceleration of small

mass.

Page 16: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Gravitational Field = g.

The value for acceleration, g, is also called the gravitational field. Set the weight equal the Fg. The units of the gravitational field are N/kg.

Since mg = GMm. The small mass m cancels

r2.

Grav Field g = GM units N/kg. r2.

Use to find acceleration or gravitational field.

Page 17: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

2. What is the gravitational field strength due to Earth at a point

450 km above the surface?

Page 18: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

• g = GM r2.

• (6.67 x 10-11)(6 x 1024kg)(6.4 x 106m + 450 x 103m)2.

• 4 x 1014.(6 850 000)2.

• 4 x 1014.

4.7 x 1013. 8.5 N/kg

Page 19: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Fields are vectors. Forces resulting from more than 1 field is the sum of the field strengths.

Page 20: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Ex 3. Two spheres lie along a straight line. The sphere on the left has m = 1000-kg, and the right on the right has m = 100-kg. The distance between their centers is 5-m.

Point A lies between the spheres at 2.5-m from the center of each.

Calculate the field strength at point A.

Page 21: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

9.63 x 10 – 9 N/kg left

Page 22: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Rd Hamper 127 – 129 do pg 129 - 131.Purple boxes #1 – 5.Show all work.

Page 23: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Einstein vs. Newton9.5 min

• http://www.youtube.com/watch?v=4yyb_RNJWUM

Page 24: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Orbits Maintained By Gravity

Page 25: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

4. Derive an equation to express the minimum

velocity a satellite must have to stay in orbit.

Page 26: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

v = (GMe)1/2. (r) 1/2.

Fg keeps the satellite in orbit.

Set Fc equal to gravitational force.

Fg = Fc

GMem = mv2. r2 r

Page 27: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

5. What is the velocity needed for a satellite to stay in orbit 200 km above the Earth’s surface?

Page 28: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

First find the total distance between their centers.

Page 29: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

6.37 x 106 m.

2.0 x 105 m.

6.57 x 106m total r.

Page 30: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

v = (GMe)1/2. (r) 1/2.

(6.67x10-11)(5.98x1024 kg)1/2

(6.57 x 106m )1/2.

7790 m/s.

Page 31: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Cavendish Torsion Balancemeasurement of G.

Page 32: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

Einstein vs. Newton9.5 min

• http://www.youtube.com/watch?v=4yyb_RNJWUM

Page 33: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

http://www.phy.ntnu.edu.tw/java/projectileOrbit/projectileOrbit.html• Newton’s Cannon Launch Satellite

• Apparent weightlessness. Satellites are in freefall around the Earth! That is why astronauts appear weightless. They are constantly falling toward Earth. Their rate of fall is balanced by their tangential momentum.

Page 34: Gravity. Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion.

The universe season 2 Gravity, Roller Coasters, Space Travel & PEg.

https://www.youtube.com/watch?v=EiljzeDL0co 45 minutes