Physics with Technology Gravity Patterns Physics with Technology

How to Measure Distance: Always measure from CENTER to CENTER. r

RATIOS: r M M r 4M M r 4M ½ M r 4M 6M How does the mass of each object affect the force of gravity between them? The first picture starts with two equal masses (M) separated by a distance (r). The force of gravity between them was initially 100 N. In each picture, ONE thing has been changed from the picture above it. See if you can spot the pattern between MASS and GRAVITY. r GRAVITY = 100 N M M r 4M M GRAVITY = 400 N r GRAVITY = 200 N 4M ½ M r 4M 6M GRAVITY = 2400 N

PATTERN: Gravity is directly proportional to BOTH masses. (As the mass of either object got bigger, gravity got bigger. So if either mass changes by a factor of x, then so will gravity.) If you double ONE mass then the force of gravity will ________________. If you double BOTH masses then the force of gravity will _____________. double quadruple

RATIOS: r M M 2r M M 1/3 r M M 1/4 r M M How does the distance between the objects affect the force of gravity? The first picture starts with two equal masses (M) separated by a distance (r). The force of gravity between them was initially 100 N. Then the distance was changed. Compare each distance with the original distance, and each new force with the original force. See if you can spot the pattern between DISTANCE and GRAVITY. r GRAVITY = 100 N M M 2r M M GRAVITY = 25 N 1/3 r M M GRAVITY = 900 N 1/4 r M M GRAVITY = 1600 N

PATTERN: The force of gravity is inversely proportional to the distance squared. (As the distance between the objects got bigger, the force of gravity got smaller.) If the distance doubles then the force of gravity will ________________. 1/4

PRACTICE: r M M 2 r M 3M 1/2 r 2M 2M 1.5 r ½ M 2M Let’s try changing both factors at the same time. Try completing the following scenarios: r GRAVITY = 100 N M M 2 r M 3M GRAVITY = 1/2 r 2M 2M GRAVITY = Better to write this out for them. 1.5 r ½ M 2M GRAVITY = If you double everything (both masses and the distance) then the force of gravity will _____________________. stay the same

PRACTICE: Let’s try problems with real numbers instead of letters. CHANGE RATIO = New Gravity = final / initial Old Gravity x M1 ratio x M2 ratio / r2 ratio GRAVITY = 100 N 10 m 4 4 GRAVITY = 5 m 16 2 20 m GRAVITY = 8 12 Better to write this out for them (makes it less confusing). 7 m GRAVITY = 10 5

ACTUAL EQUATION: Gravity is directly proportional to both masses. MASS: DISTANCE: Build an Equation: Means: M1 M2 top Gravity is inversely proportional to distance squared. Means: r2 bottom Just a pattern not equation. M1 M2 r2

If the MASS of planet Earth doubled then I would weigh __________ times as much. If the MASS of myself doubled then I would weigh _________ times as much. If the MASS of BOTH planet Earth AND myself doubled then I would weigh __________ times as much. If the RADIUS of planet Earth doubled then I would weigh __________ times as much. If the RADIUS of Earth shrunk to 1/5 the current size (but same mass) then I would weigh ________times as much. 2 2 4 1/4 25

Gravity Equation: https://www.youtube.com/watch?v=p_o4aY7xkXg

How much would I weigh inside a Cave? Atoms above you pulling you up. Less. Atoms below you pulling you down.

How much would I weigh at the center of the Earth? Nothing.

What would happen if I jumped into a tube going through the whole Earth? You would fall back and Forth forever as gravity keeps switching directions. https://www.youtube.com/watch?v=jN-FfJKgis8

GRAVITATIONAL CONSTANT: Pattern from yesterday: Turn it into an equation: Gravitational Constant: M1 M2 r2 Fg = GM1 M2 r2 G = 6.67x10-11 Nm2 Kg2 To make life easier, program this into your Calculator.

GRAVITATIONAL CONSTANT: Type in the number Hit Enter Hit Sto Hit Alpha Hit G

How did we figure out the gravitational constant? Cavendish Demo: Have a student bring a bowling ball close to you and then turn toward the bowling ball. “By measuring the angle of the rod and knowing the twisting force of the wire for a given angle, Cavendish was able to determine the force between the pairs of masses. Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the density of the earth to be calculated, using Newton’s law of gravitation.” Wikipedia.

Using the Gravity Equation: Let’s try calculating the force of gravity between Bob (75 kg) and Betty (65 kg) if they are sitting 3 meters apart in Physics class. Let’s calculate how much a 5 kg watermelon would weigh on planet Earth. What about a 14 kg crate? What about a 1200 kg car?

Gravitational Field: GM2 r2 Acceleration of any object on this planet. Fg = field x M1 (W = mg) Plug in Earth: (6.67x10-11)(5.98x1024) (6.37x106)2 = 9.829878576 m/s2 So… 9.8 m/s2

Gravitational Field: GM2 r2 Let’s calculate how much a 3 kg cat, a 524 kg horse, and a 76 kg chimpanzee would weigh on the moon. To save time, calculate the gravitational field on the moon: Now you can calculate all three very quickly:   What if we took those same animals to Neptune

Why does gravity depend on the distance SQUARED? Particle Theory – Gravitons (massless particles that contribute to the force of gravity). Spray Paint Example To find the density: Density = mass volume Paint area Paint πr2 = area of a circle (Use the area of a circle because it is 2D.) Image From: www. vecteezy.com Image From: www. vecteezy.com Image From: www.foxnews.com Image From: www.foxnews.com