p ch7 2017 Dasch

Chapter 7 - Circular Motion and Gravitation

Section 1 - Circular Motion

Radial acceleration and Radial force

Section 2 – BIG G gravity

where did little g come from?

Section 3 – Orbits and Periods Kepler’s law, T2 _{= r}3

Section 1 - Circular Motion

- even if something is traveling at a constant speed, it is accelerating if it is changing direction!

- this acceleration is called the centripetal or RADIAL acceleration

- centripetal acceleration is calculated using

a_c = v2_{/r OR a}

c = r(dθ/dt)2 c

if given tangential velocity OR If given radial velocity (use radians)

e.g.1) A toy swings at the end of a 0.45 m long string, at a speed of 2.0 m/s. What is its acceleration?

e.g.2) How fast would the toy in the previous problem be moving if the toy's acceleration doubles?

Radial Force (F_c):

- the force that causes the change of direction of motion, the centripetal acceleration

- must be equal to the net force

F_c = mv2_/r

* note: should NOT be put on the free-body diagram since it is the net force!

e.g.3) What is the centripetal force experienced by the toy in the previous three examples if its mass is 250 g? How must the radius be changed to double each answer?

Practice Problems:

Homework 1:

page 226 Practice A #1, 3, (4) page 228 Practice B #1, 2, 3, (4)

Practice A:

#1. 2.5 m/s #3. 1.5 m/s2 _{(#4) 58.4 m}

Practice B:

#1. 29.6 kg #2. 40.0 m #3. 40.0 N (#4) 35.0 m/s

After you finish, you need to make sure you have the following equations written in your notebook:

1: get from y (release height) to t (time in air) to velocity of the stooper you sling(assuming zero wind resistance)

2: get from velocity of stopper at release to a_c

Section 2 - Universal Gravitation:

- Newton developed the idea of the gravitational force and also his Universal Law of gravitation

 F = Gm₁m₂ G = 6.67x10-11 _Nm2_/kg2

 r2

- The force of gravity applies to all objects in the universe, including you and your neighbor in this classroom!

 e.g.5) What is the force of gravity felt by a 60 kg person at an elevation of 300 km above the earth's surface? How far above Earth's surface must the person be in order to experience the same gravitational force as his weight on Mercury?

 e.g.6) Show that the acceleration due to gravity experienced at the surface of Earth is 9.8 m/s2_{. What is the acceleration due to gravity 5000 km}

from the Earth's surface? 50000 km from Earth's surface?

Homework:

Homework:

page 232 Practice C #1-3

1. 0.692 m 2. 9.4 x 106 _m

Practice Problems

DUE Tuesday, 1/30/18

:

1. Calculate the force of gravity the Earth exerts on the Sun.

2. Calculate your weight on Mars.

3. A child jumps from a platform 2.0 m tall on Pluto. How long is he in the air if he jumps vertically at 4.0 m/s? If he jumps at an angle of 20 degrees above the horizontal?

4. How far away from each other do two 500 kg objects need to be held in order to make the gravitational force between them equal to 1.0 N?

Physics Quiz

G = 6.67 x 10-11 _Nm2_/kg2

On the given piece of paper...

1. Calculate the acceleration due to gravity an object experiences when it is at the given location.

2. Calculate the elevation above Earth at which a 10 kg object must be held in order to experience a gravitational force of 49N.

Name Mass (kg) Average Radius (m) Mean distance from Sun (m)

Sun 1.99 x 1030 _{6.96 x 10}8 _n/a

Earth 5.97 x 1024 _{6.38 x 10}6 _{1.50 x 10}11

(moon) 7.35 x 1022 _{1.08 x 10}3 _{2.40 x 10}5

Neptune 1.02 x 1026 _{2.48 x 10}7

4.50 x 1012

Saturn 5.69 x 1026 _{6.03 x 10}7

1.43 x 1012

Pluto 1.5 x 1022 _{1.15 x 10}6

5.91 x 1012

Mercury 3.30 x 1023 _{2.44 x 10}6

5.79 x 1010

Mars 6.42 x 1023 _{3.40 x 10}6

Physics Quiz

On the given piece of paper...

FRONT SIDE:

1. Calculate the acceleration due to gravity an object experiences when it is at the given location.

REVERSE SIDE:

Section 3 - Kepler's Laws

 1) The paths of planets are elliptical, with the sun at one focus

 2) The area covered by an imaginary line between the sun and the planet is constant for any given time interval

 3) A planet's period and average orbital radius are related mathematically,

  e.g.9) What is the period of Pluto (in years)? Of Venus?

 e.g.10) The period of a given proposed dark mater object in our solar system is 528 days. How far must this planet orbit, on average, from the sun?

Homework:

page 262 (chapter review section!) # 25 (explain!), 27, 28

Answers:

25) Twice as big

27) 1630 m/s ; 5.78 x 105 _s

Section 3 - Motion in Space

Kepler’s law is nice and all, but what about non-planetary objects orbiting other heavinly bodies?

We need to add Newton's Law of Universal Gravitation:

  - assuming that the orbit of a planet in our solar system in relatively

circular, we can say that the force of gravity exerted on a planet by the sun is equal to the centripetal force required to keep the planet in a circular path

 relevant results:

v = √(Gm/r)

T = 2π√(r

_/Gm)

* Mass is the mass of the CENTER body, and radius is from the center of mass of each body.

  e.g.7) At what average speed does the Earth move along its orbital path? The Moon?

  e.g.8) What is the period of Pluto? Of Venus?

Homework: page 241 Practice D #1, 2

Answers:

#1.  Earth: 7690 m/s; 5510 s  Jupiter: 42000 m/s; 10800 s  Moon: 1530 m/s; 8630 s

#2. 1.90 x 106 _m

More examples:

 e.g.11) What is the period (in seconds) of the entity formerly-known as the planet Pluto?

 e.g.12) What is the weight of a person who lands on the planet Venus? Assume the person has a weight of 550 N on Earth.

  e.g.13) What force of gravity is exerted on a 2.0 kg mass that is 10 m away from a 5.0 kg mass? Assume their radii are negligible.