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Universal Gravitation and Central

Net Force

supplemental

Gravity

• Newton’s Universal Law of Gravitation

• Inverse square law (all field forces are inverse

squares)

– Why?

– Our universe has 3 dimensions of space, as you

move outward – you encounter 3 dimensional

spheres of gravitational field – the surface area of

a sphere is 4πr2, so each new sphere of field

(influence) decreases by a r2 term.

• All massive objects put gravitational forces on other massive objects

• You have mass, and so does the person next you

• Yes, you are attracted to the person sitting next to you

• You are also attractive so someone living in another galaxy, but the force is so small it can’t be measured

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7 173

• The equation is where little g comes from

• mg = GMm/r2

• Cancel the little m’s and you find

• g = GM/r2

• where the mass of the Earth is 5.972 x 1024 kg

• Where the radius of the Earth is 6.371 x 106 m

• Big G is 6.67 x 10-11

• Multiple it out and g = 9.8 N/kg, tada!

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Assignments on gravity

• Volume of a sphere:

• Density:

3

3

4rV π=

V

mD =

• The nature of orbits

• Throw a ball, projectile motion (a parabola)

• Throw it harder and the projectile motion is the same just a longer parabola

• Throw it so hard that it makes it to the horizon before it hits the ground that it will enter into a constant state of falling toward the center of the earth but never hitting it

• People in ISS are not floating, they are falling –continuous state of sky-diving– https://www.youtube.com/watch?v=3bCoGC532p8

• http://stuffin.space/

• https://www.youtube.com/watch?v=cfSaztUiw5s

• http://www.windows2universe.org/kids_space/sat.html

• http://neo.jpl.nasa.gov/

• https://www.youtube.com/watch?v=sl_RknL9G-Q

• https://www.youtube.com/watch?v=dpmXyJrs7iU

• https://en.wikipedia.org/wiki/Chicxulub_crater#Effects

Centripetal vs centrifugal

• In order to accelerate, you need an unbalanced force in the direction of acceleration.

• When you take the round-about at middle road too fast, you have to be accelerated into the circle (inward), but you feel like you are being thrown outward because of your inertia wanting to keep you in the path of your motion

• Centrifugal vs. centripetal motion (centri meaning center and petal meaning seeking like a bee seeks a flower petal). Centrifugal is not real, it is the feeling of inertia.

• Silly Silo at Adventureland example

Curves, Centrifugal, Centripetal Forces

• Going around a curve smushes you

against window

– Understand this as inertia:your body wants to

keep going straight

but the car is accelerating

towards the center of the curve

The Car accelerates

→ you think you’re being accelerated

Centripetal, Centrifugal Forces, continued

• The car is accelerated toward the center of the curve by a

centripetal (center seeking) force

– The name for the “net force toward the center of the circle” that causes circular motion to occur

– NOT a separate force. Can use Fnet to represent it.

• In your reference frame of the car, you experience a “fake”, or

fictitious centrifugal “force”– Not a real force, just inertia relative to car’s acceleration

Centripetal Force

on car velocity of car

(and the way you’d rather go)

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Centripetal Force

What provides it?

Car Around a Curve - Friction

If there isn’t enough friction (icy or wet road),

the car doesn’t make the curve!

Silly Silo – the wall provides the

centripetal force!

• Vertical drum rotates, you’re pressed against wall

– Friction force against wall matches gravity

– Seem to stick to wall, feel very heavy

Real Forces:

Friction; up

Centripetal; inwards

Gravity (weight); down

Lab – How do mass, velocity and

radius affect centripetal force?

• Three investigations

– Fc versus velocity

– Mass versus velocity

– Radius versus velocity

• Some values are filled in already

• Circular Motion w/ a sparkler https://youtu.be/ID0R43My4Co

• How do we create artificial gravity

– Circularly moving space stations

• The Martian (movie)

• Interstellar (movie)

• 2001 Space Oddyssey (movie)

• Halo (video game)

• Elysium (movie)

How differentials work

• How differentials work

– https://www.youtube.com/watch?v=K4JhruinbWc

• 2001 Space Odyssey

– https://www.youtube.com/watch?v=1wJQ5UrAsIY

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• How do trains turn?

– https://www.youtube.com/watch?v=agd8B-31bjE

– http://i.imgur.com/skXgNKK.gif

• Baffling balloon behavior

– https://www.youtube.com/watch?v=FjuMvUbT8g

A

– https://www.youtube.com/watch?v=y8mzDvpKzfY

Which direction does the net

force (centripetal force) point for

an object moving in a uniform

circular motion?

Which of the following is true for an

object traveling in a circular path at

constant speed?

a) its speed is constant, so its acceleration is zero.

b) both its speed and velocity are constant.

c) its speed is constant, but its velocity is changing.

d) both its velocity and acceleration are constant.

Fnet

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A 1500-kg car goes around a curve with a radius of 50.0-m at a speed of 8.0 m/s.

a) How much Fc is needed?

Nr

mvFc 19001920

0.50

)0.8)(1500( 22

====

A 50.0-g cork on a 1.00-m string twirls at 3.00 rev/s. The string can hold only 20.0-N. Will it break?

NF

smv

c7.17

1

)8.18(0500.

/8.18333.0

)1(2

2

==

=Π

=

IT WILL HOLD!!!

A classmate swings a rock on a string in an

overhead circle. Suppose that the string breaks

at the point shown. Draw a line to show the

path of the rock.

Two identical boats race around a semi-circular turn,both are traveling at the same speed.

a. Which boat takes longer to complete the turn?b. Which boat has a greater acceleration in the turn?

c. Which boat has the greater net force on it?

Unit 6

Universal Gravitation and

Central Net Force Model

Recap/Review

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Fnet

How do I figure this out? Try it out but make it easy on yourself. Substitute in easy #s to work with, like 1 and 2 and find out!