GRAVITATIONAL FORCE AND FIELD

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1 POINT AND FORCES A. POINT AND FORCES A FACT: Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of their distances. Source: Physics Course Companion, Kirk and Hodgson

2 WHAT THIS REALLY MEANS: A. POINT AND FORCES

3 A. POINT AND FORCES

4 A. POINT AND FORCES Verify the values in the table:

5 A. POINT AND FORCES Don t believe it? EXAMPLE 1 Using the following data.. m earth = 5.98 x kg r earth = 6378 km determine the force of gravity between a 200 g apple and the Earth.

6 RELATING NEWTON S LAW OF GRAVITATION TO A. POINT AND FORCES Source: Physics for the IB Diploma, 5 th Ed, Tsokos

7 Remember, g = GM e R e 2 A. POINT AND FORCES Source: Physics, 8 th Ed, Cutnell & Johnson

8 A. POINT AND FORCES EXAMPLE 2 Find the acceleration due to gravity (the gravitational field strength) on a planet 10 times as massive as the Earth and with a radius 20 times as large.

9 A. POINT AND FORCES EXAMPLE 3 Find the acceleration due to gravity at a height of 300 km from the surface of the Earth.

10 EXAMPLE 4 Using the following data: m earth = 5.98 x kg A. POINT AND FORCES r earth = 6378 km a) Complete the following table by determining the gravitational force on a mass at different distances from the center of the Earth. DISTANCE (m) GRAVITATIONAL FORCE (N) r 100 2r 3r 4r 5r 6r 7r 8r b) Make a graph of gravitational force on the mass and distance from the center of the Earth. On your distance axis, make your scale go to d = 0 m (at the center of the Earth). Linearize your graph from part (b) and find the slope. What does the slope represent?

11 FORCE S REMEMBER: FORCE (F) = something that can move, deform, stretch, rotate, or compress something. = something that can cause a velocity change (so an acceleration). = a push or a pull. UNIT = Newton (N), a vector quantity, so F. 1 N = 1 (kg m)/s 2 What gives rise to a force naturally? A. POINT AND FORCES

In mathematics, you have probably only really dealt with 2-dimensional space A. POINT AND FORCES + y To understand force fields, you have to think in 3-D. which is the space you actually LIVE IN.

12 In mathematics, you have probably only really dealt with 2-dimensional space A. POINT AND FORCES + y To understand force fields, you have to think in 3-D. which is the space you actually LIVE IN. - x + z - z + x Instead of x and y coordinates, in 3-D space we deal with x, y, and z coordinates. Each set of axes is perpendicular to one another ( orthogonal, at right angles). Source: http//answers.com - y Every point in 3-D space can be described as a set of coordinates (x, y, z) in that order.

13 EXAMPLE 5 Plot the point (2, 3, 2) on the following 3-D coordinate system. A. POINT AND FORCES (2, 3, 2) (x, y, z) Source:

14 When working in 3-D space, we need to have a way to show vectors going into and out of the board/page. A. POINT AND FORCES

15 A. POINT AND FORCES

16 THE GRAVITATIONAL DUE TO ONE POINT MASS A. POINT AND FORCES

17 THE GRAVITATIONAL AT THE SURFACE OF A PLANET A. POINT AND FORCES

18 THE GRAVITATIONAL DUE TO TWO OR MORE POINT This can get complicated! A. POINT AND FORCES The field in the Earth-Moon system: Source: Physics for the IB Diploma, Hamper

Newton's Law of Universal Gravitation

Section 2.17: Newton's Law of Universal Gravitation Gravity is an attractive force that exists between all objects that have mass. It is the force that keeps us stuck to the earth and the moon orbiting