physics 1710—warm-up quiz in the movie “armaggedon” a comet “the size of texas’” (800...

Physics 1710Physics 1710—Warm-up Quiz—Warm-up QuizIn the movie “Armaggedon” a comet “the size of In the movie “Armaggedon” a comet “the size of Texas’” (800 miles or 1250 km in diameter) was Texas’” (800 miles or 1250 km in diameter) was heading for Earth. If the density were 800 kg/mheading for Earth. If the density were 800 kg/m33, the , the mass would be about 8.x10 mass would be about 8.x10 2020 kg. How far would a ball kg. How far would a ball on the surface fall in 1.0 second?on the surface fall in 1.0 second?

A B C D

4% 2%

16%

78%A.A. About 5 m About 5 m B.B. About 7 cmAbout 7 cmC.C. About 2 cmAbout 2 cmD.D. None of the aboveNone of the above

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GravitationGravitation

g =G M/ RG M/ R22

g=(6.67x10g=(6.67x10-11-11 N m N m22/kg/kg22)(8x10)(8x102020 kg)/(625x10kg)/(625x1033 m) m)22

g = 0.14 N/kgg = 0.14 N/kg

d = ½ g t d = ½ g t 22 = 0.5 (0.14 m/s = 0.5 (0.14 m/s22)(1 sec))(1 sec)22

= 0.0 7 m = 7 cm= 0.0 7 m = 7 cm

Physics 1710Physics 1710—C—Chapter 12 Apps: Gravityhapter 12 Apps: Gravity

11′′ Lecture Lecture

•The gravitational force constant g is equal to The gravitational force constant g is equal to g = G M/(R+h) g = G M/(R+h) 22, , M and R are the mass and radius of the planet.M and R are the mass and radius of the planet.

•The The gravitation fieldgravitation field is the force divided by the is the force divided by the mass.mass.

•The The gravitation potential energygravitation potential energy for a point for a point mass is proportional to the product of the masses mass is proportional to the product of the masses and inversely proportional to the distance between and inversely proportional to the distance between their centers.their centers.

•The The escape velocityescape velocity is the initial velocity at the is the initial velocity at the surface required to leave a body.surface required to leave a body.

vvescape escape = = √[ 2GM/R]√[ 2GM/R]


No Talking!No Talking!

Think!Think!

Confer!Confer!

Peer Instruction Peer Instruction TimeTime

Does the position of the moon affects us as astrology claims?


Does the position of the moon affects us as astrology claims?

A B C D

17%

2%

23%

58%A.A. Yes, I strongly agree Yes, I strongly agree

B.B. Yes, I AgreeYes, I Agree

C.C. No, I disagreeNo, I disagree

D.D. No, I strongly disagreeNo, I strongly disagree

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Astrology: Does the moon affect us? Astrology: Does the moon affect us?

F = - G M m/ d F = - G M m/ d 22


d moon=3.84x108 m

M = 7.36x1023 kg; d = 3.84x108 m

|F/m|= (7x10-11)(7x1023)/(4x108)2 = 3x10-4 N/kg ~ 30 μ g

M =7.36x1023 kg

Gravitational Potential EnergyGravitational Potential Energy

U = -U = -∫∫∞∞RR F•F•d d rr

U = -U = -∫∫∞∞RR G Mm/r G Mm/r 2 2d rd r

U = GMm/R = mgRU = GMm/R = mgR

U = 0 as r U = 0 as r →∞→∞


FF

d d rr

Escape VelocityEscape VelocityIf K is such that E = 0 as r If K is such that E = 0 as r →∞→∞, then, then

KKRR = ½ m v = ½ m v 2 2 = U = URR = GMm/ R = GMm/ Randand

vvescape escape = = √[ 2GM/R] = √[2gR] √[ 2GM/R] = √[2gR]


K = ½ m vK = ½ m v 2 2

UU∞∞ = 0 = 0UURR = GMm/R = GMm/RKK∞∞ = 0 = 0

Were the astronauts in danger of jumping off the Were the astronauts in danger of jumping off the “Armaggedon” comet? (“Armaggedon” comet? (Hint: What is the escape Hint: What is the escape velocity from our “Armaggedon” comet? M = velocity from our “Armaggedon” comet? M = 8x108x102020 kg, R =6.25x10 kg, R =6.25x10 55 m, g = 0.14 N/kg) m, g = 0.14 N/kg)

A B C D

13%

4%

35%

48%A.A. Yes. Definitely.Yes. Definitely.B.B. Maybe. Maybe.

C.C. No. Definitely not.No. Definitely not.

D.D. Not enough information.Not enough information.

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Escape VelocityEscape Velocity

vvescape escape = = √[ 2GM/R] = √[2gR] √[ 2GM/R] = √[2gR] = √[2(0.14 N/kg)(625 km)] ~ 400 m/s= √[2(0.14 N/kg)(625 km)] ~ 400 m/s

~ 900 mph. Safe!~ 900 mph. Safe!


vvescape escape = = √[ 2GM/R] = √[ 2GM/R] = √[2gR]?? √[2gR]??

Escape Velocity of Earth?Escape Velocity of Earth?vvescape escape = = √[ 2GM/R] = √[2gR] √[ 2GM/R] = √[2gR]

= √[2(9.8 N/kg)(6.3 x10 = √[2(9.8 N/kg)(6.3 x10 6 6 m)] ~ 11,000 m/sm)] ~ 11,000 m/s25,000 mph. Stuck!25,000 mph. Stuck!


vvescape escape = = √[ 2GM/R] = √[ 2GM/R] = √[2gR]?? √[2gR]??

Total Energy Total Energy for Gravitationally Bound Massfor Gravitationally Bound Mass

E = K + UE = K + U

E = ½ m v E = ½ m v 22 – GMm/r – GMm/r

E = LE = L22/2mr/2mr 2 2 – GMm/r – GMm/r

Bound orbit if E Bound orbit if E ≤ 0 and ≤ 0 and

- dE/dr - dE/dr ||rroo= 2 (= 2 (LL22/2mr/2mroo) - GMm = 0 ) - GMm = 0

E = - GMm/2rE = - GMm/2roo


Total Energy Total Energy for Gravitationally Bound Massfor Gravitationally Bound Mass

E = K + UE = K + UE = - GMm/2rE = - GMm/2roo


E < 0 < 0

rro o = - 2E/(GMm) = - 2E/(GMm)

LL22

/2m

r /

2m

r 2 2 –

GM

m/r

–

GM

m/r

r

SummarySummary::

• The force of attraction between two bodies The force of attraction between two bodies with mass M and m respectively is proportional with mass M and m respectively is proportional to the product of their masses and inversely to the product of their masses and inversely proportional to the distance between their proportional to the distance between their centers squared.centers squared.

F = - G M m/ r F = - G M m/ r 22

• The proportionality constant in the Universal The proportionality constant in the Universal Law of Gravitation G is equal to 6.673 x 10 Law of Gravitation G is equal to 6.673 x 10 –11–11 N N mm22 /kg /kg22 . .


Summary:Summary:•The gravitational force constant g is equal to The gravitational force constant g is equal to G M/(R+h) G M/(R+h) 22, R is the radius of the planet., R is the radius of the planet.

• Kepler’s LawsKepler’s Laws–The orbits of the planets are ellipses.The orbits of the planets are ellipses.–The areal velocity of a planet is constant.The areal velocity of a planet is constant.–The cube of the radius of a planet’s orbit The cube of the radius of a planet’s orbit is proportional to the square of the period.is proportional to the square of the period.

• The gravitation field is the force divided by the The gravitation field is the force divided by the mass.mass.

g g = = FFgg / m / m


Summary:Summary:

• The gravitation potential energy for a point mass is The gravitation potential energy for a point mass is proportional to the product of the masses and proportional to the product of the masses and inversely proportional to the distance between their inversely proportional to the distance between their centers:centers:

U = GMm / rU = GMm / r

• The escape velocity is the minimum speed a The escape velocity is the minimum speed a projectile must have at the surface of a planet to projectile must have at the surface of a planet to escape the gravitational field.escape the gravitational field.

vvescape escape = = √[ 2GM/R]√[ 2GM/R]

• Total Energy E is conserved for two body Total Energy E is conserved for two body geavitational problem; bodies are bound for E ≤ 0geavitational problem; bodies are bound for E ≤ 0

E = LE = L22/2mr/2mr 2 2 – GMm/r – GMm/r


physics 1710—warm-up quiz in the movie “armaggedon” a comet “the size of texas’” (800...

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