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April 1

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April 1

B Day – Alg– Wrapping Up Ch. 12

“Radius” (r), “distance” (d), “from the center”…all mean THE SAME THING!

(The bottom part of the equation!)

1. 1

12

2 . 1

12

= 2

1

= 2

Gravity is TWICE as much!

1. 1

12

1. 1

22

= 1

4

= ¼ OR 0.25

Gravity is ¼ as much!

2 . 2

12

= 4

1

= 4

Gravity is 4x as much!

1. 1

(0.5)2

= 1

.25

= 4

Gravity is 4x as much!

1. 1

( ½ )2

= 1

¼

= 4

Yes

- Is weight a force?
- Suppose I told you that you can calculate your weight with this equation (you can!) What do you think F, m1, m2, and r would have to be for the above equation in this specific case?
- F specifically represents
- m1 specifically represents
- m2 specifically represents
- r specifically represents

Your weight

Your Mass

Earth’s Mass

Distance b/t you and

center of Earth

4 . 1

12

= 4

1

= 4

- If you were 4 times as massive, by how much would your weight change?
- If Earth were half as massive, by how much would your weight change?
- What happens to the force between 2 objects one mass is tripled, and the distance does not change?

Gravity is 4x as much!

1. ½

12

= ½

1

= ½ (or 0.5)

Gravity is HALF as much!

1. 3

12

= 3

1

= 3

Gravity is 3 times as much!

6. If you were 2 times as massive and Earth were 4 times as massive (but you both were still the same size), by how much would your weight change?

7. What is the relationship between mass and force? (Be as specific as possible!!! Are they proportional? How?)

2 . 4

12

= 8

1

= 8

Gravity is 8 times as much!

Directly proportional!!!

8. If you double both of the masses, and quadruple the distances between them, what happens to the force? <<- GO back to this one later!

9. If Earth was 3 times as wide but the same mass (in other words, the diameter of Earth was 3x larger, and therefore the radius of Earth was 3x larger), by how much would your weight change?

1. 1

32

= 1 or 0.11

9

Gravity is 1/9as much!

1. 1

22

= 1

4

OR 0.25

- If you stood on an impossibly tall ladder so you were twice as far from Earth’s center, by how much would your weight change?
- If you halve the distance between 2 masses, what happens to the force? (mass is not changed)
- What is the relationship between distance and force? (Be as specific as possible!!! Are they proportional? How?)

Gravity is ¼ as much!

Gravity is 4 times as much!

1. 1

(½) 2

= 1

¼

or 1

0.25

OR 1. 1

(0.5) 2

Force is INVERSELY PROPORTIONAL to the SQUARE of the distance!

13. CHALLENGE! If Earth was 2 times as wide AND your mass was 4x greater, by how much would your weight change?

= 4

4

= 1…

4 . 1

22

Gravity is the SAME!!!

14. CHALLENGE! Determine what happens to the gravitational force between two objects if you double one of the masses, make the other eight times as much, and quadruple the distances between them.

= 1

2 . 8

42

OR = 16

16

Gravity is the SAME!

15. CHALLENGE- If you double one of the masses, and halve the distances between them, what happens to the force?

= 2

(¼ )

OR = 2

(0.25)

2 . 1

(½ )2

OR = 2 . 1

(0.5)2

Gravity is 8 times as much!

2 . 2

42

= 4

16

= ¼

OR

0.25

Gravity is ¼ as much!

CHALLENGE! Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 2 meters.

(6.67 * 10 -11) 70. 2000

22

(6.67 * 10 -11) 140,000

4

(6.67 * 10 -11) 35000

2.33 * 10 -6 N

Answers for HW due last class:

#8-12– NOT in order…check them!!!

- Gravity is REALLY weak!!!
- As the distance increases, gravity decreases by the inverse square of the distance
- Gravity is universal – it’s everywhere – it’s not unique to Earth
- 1/25 as much (4% the weight); 1/100 as much (1% the weight)
- Your mass, earth’s mass, and the distance between you and the center of earth

- Groups of 1 – 4 (Individual or Team Quiz)
- Out of 20 points (like a quiz grade).
- 2 points per problem correct…getting 10 problems correct earns you a 20/20
- BUT extra credit can be earned for every correct question in addition to first 10.
- Potential for 40/20 on this!!!

- Spread out so other teams can’t hear you.
- 1 sheet of loose leaf per team
- All team member names & ID’s at the top
- # each answer (you only need to write answers, not questions)
- If your answer is unclear, no credit will be earned!

- Be COMPLETE in your answer – give as MUCH DETAIL as possible! (Do not need to use full sentences)

THERE IS GRAVITATIONAL FORCE BETWEEN ALL OBJECTS, INCLUDING PLANETS…

1. How would the gravitational force between a pair of planets be altered if:

The mass of one planet is doubled?

2. . How would the gravitational force between a pair of planets be altered if:

The planets are TWICE as far apart?

SHOW ALL WORK IN ORDER TO GET FULL CREDIT

3. How would the gravitational force between a pair of planets be altered if:

The planets are 3 TIMES as far apart?

4. How would the gravitational force between a pair of planets be altered if:

The masses of both planets are doubled AND they are TWICE as far apart?

SHOW ALL WORK IN ORDER TO GET FULL CREDIT

6. Venus is called Earth’s “sister” planet because it is almost the same size (mass & diameter) as Earth. BUT – Venus is closer to the Sun. Does the Sun have a STRONGER or WEAKER gravitational pull on Venus than it does on Earth? EXPLAIN:

7. The earth’s gravity is pulling on you. Are you pulling on the earth? And if so, which force is stronger – earth pulling you, or you pulling earth? Explain your reasoning.

8. Gravity is a force of attraction between objects based on their mass and their distance apart. Why aren’t other objects, like your pencil, being pulled towards you? Explain your reasoning.

- Why do you think the Earth orbits the sun, not the other way around (sun orbiting Earth?? )
Use what you have learned this chapter and PREVIOUSLY to EXPLAIN!!!

10. Consider a pair of binary stars that pull on each other with a certain force. Would the force be larger or smaller if the mass of each star were three times as great & their distance apart is three times as far?

- Show what the new force will be compared to the ﬁrst one… show MATHEMATICAL REASONING …
SHOW YOUR WORK!

- (*Binary Stars are ‘twin’ stars that are locked in the same circular orbit)

- 11. show MATHEMATICAL REASONING …
- SHOW YOUR WORK!

TRUE or FALSE or NOT ENOUGH INFO… EXPLAIN: (*Explanation determines if you get these right!*)12. Planets very far away from the sun exert less gravity than Earth exerts 13.Planets with thin atmospheres (or no atmospheres!) have very little to no gravity

14. What would happen to YOUR WEIGHT if:

The masses of both you and earth are doubled?

15. What would happen to YOUR WEIGHT if:

You are 10x as farther away from the center of Earth?

16. What would happen to YOUR WEIGHT if:

The mass of Earth is doubled AND you are 2x as far away from Earth’s center?

SHOW ALL WORK IN ORDER TO GET FULL CREDIT

Calculate the force of gravity between two objects that have masses of 100 kilograms and 2,000 kilograms separated by a distance of 12 meters.

SHOW ALL WORK IN ORDER TO GET FULL CREDIT

- The Moon has a radiusthat is approx. 0.27 that of Earth’s, and a massthat is approx. 0.012that of Earth’s. Would you weigh more or less on the Moon, and by how much?
- Mars has a radiusthat is approx. ½that of Earth’s, and a massthat is approx. 0.1 that of Earth’s. Would you weigh more or less on Mars, and by how much?
- The Sun has a radiusthat is approx. 100times that of Earth’s, and a massthat is approx. 333,000that of Earth’s. Would you weigh more or less on the Sun, and by how much?