Physics of Technology PHYS 1800

Circular Motion and Gravitational Force

Introduction Section 0 Lecture 1 Slide 1

Lecture 11 Slide 1

INTRODUCTION TO Modern Physics PHYX 2710

Fall 2004

Physics of Technology—PHYS 1800

Spring 2009

Physics of TechnologyPHYS 1800

Lecture 11




Lecture 11 Slide 2


Fall 2004


Spring 2009

PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet

*Homework Handout

Date Day Lecture Chapter Homework Due Jan 5 6 7 9

M T W F*

Class Admin: Intro.Physics Phenomena Problem solving and math Units, Scalars, Vectors, Speed and Velocity

1 App. B, C 1 2

-

Jan 12 14 16

M W F*

Acceleration Free Falling Objects Projectile Motion

2 3 3

1

Jan 19 21 23

M W F*

Martin Luther King Newton’s Laws Mass and Weight

No Class 4 4

2

Jan 26 28 29 30

M W Th F

Motion with Friction Review Test 1 Circular Motion

4 1-4 1-4 5

3

Feb 2 4 6

M W F*

Planetary Motion and Gravity Energy Harmonic Motion

5 6 6

4

Feb 9 11 13

M W F*

Momentum Impulse and Collisions Rotational Motion

7 7 8

5

Feb 16 17 18 19 20

M Tu W H F*

Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure

No Class 8 5-8 5-8 9

-

Feb 23 25 27

M W F*

Flotation Fluids in Motion Temperature and Heat

9 9 10

6

Mar 2 4 6

M W F*

First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change

10 10 -

7

Mar 9-13 M-F Spring Break No Classes Mar 16 18 20

M W F*

Heat Engines Power and Refrigeration Electric Charge

11 11 12

8

Mar 23 25 26 27

M W H F*

Electric Fields and Electric Potential Review Test 3 Electric Circuits

12 13 9-12 13

-

Mar 30 Apr 1 3

M W F

Magnetic Force Review Electromagnets Motors and Generators

14 9-12 14

9

Apr 6 8 10

M W F*

Making Waves Sound Waves E-M Waves, Light and Color

15 15 16

10

Apr 13 15 17

M W F*

Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes

17 17 17

11

Apr 20 22 24

M W F

Review Seeing Atoms The really BIG & the really small

1-17 18 (not on test) 21 (not on test)

No test week 12

May 1 F Final Exam: 09:30-11:20am



Lecture 11 Slide 3


Fall 2004


Spring 2009

Physics of TechnologyPHYS 1800

Lecture 11


Introduction and Review



Lecture 11 Slide 4


Fall 2004


Spring 2009

Describing Motion and Interactions

Position—where you are in space (L or meter)

Velocity—how fast position is changing with time (LT-1 or m/s)

Acceleration—how fast velocity is changing with time (LT-2 or m/s2)

Force— what is required to change to motion of a body (MLT-2 or kg-m/s2)

We will focus on a special kind of force, termed a central forces [e.g., gravity, Coulombic (charge) or centripetal forces].

Important: Velocity, acceleration and force are VECTORS!!!



Lecture 11 Slide 5


Fall 2004


Spring 2009

The Math Approach• We are going to explore a different kind of force that is no

longer constant, but is proportional to 1/r.

20

0

21

222

2222

attvtvvtvvd

tvvtvv

tvv

tvd

tvv

aoratvv

ga

ofoo

ooofofavg

off

k/r



Lecture 11 Slide 6


Fall 2004


Spring 2009

Newton’s Laws in Review

• 1st Law —a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless

a force acts on the object.

• 2nd Law (and 1st Law)—How motion of a object is effected by a force.– The acceleration of an object is directly

proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force.

• 3rd Law —Forces come from interactions with other objects.• For every action (force), there is an equal but

opposite reaction (force).

F ma

units : 1 newton = 1 N = 1 kgm s2



Lecture 11 Slide 7


Fall 2004


Spring 2009

It is the total force or net force that determines an object’s acceleration.

If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions.

Fstring 10 N (to the right)

ftable 2 N (to the left)

Fnet 10 N 2 N

8 N (to the right)

a Fnet

m8 N

5 kg

1.6 m s2 (to the right)

Net Forces



Lecture 11 Slide 8


Fall 2004


Spring 2009

Free Body Diagrams

• Fancy Science: Vector analysis of complex force problems is facilitated by use of a free body diagram.

• Common Sense: A picture is worth a 100 words. (A scale picture is worth an A!)

• Key is to:• Isolate a single body and draw all the forces acting on it. • Add up all the arrows (vectors).• What’s left is the net force.• Net force (and masses) a.• A plus initial conditions motion!



Lecture 11 Slide 9


Fall 2004


Spring 2009

... have anything in

common with circular motion

on Earth?

Does the circular motion of the moon around the Earth ...



Lecture 11 Slide 10


Fall 2004


Spring 2009

A ball is whirled on the end of a string with constant speed when the string breaks. Which

path will the ball take?

a) Path 1b) Path 2c) Path 3d) Path 4

Path 3, in the direction of the tangent to point A. Neglecting gravity, the body would move in the direction it was moving when the force disappeared, in accordance with the first law.



Lecture 11 Slide 11


Fall 2004


Spring 2009

If the string breaks, the ball flies off in a straight-line path in the direction it was traveling at the instant the string broke.

• If the string is no longer applying a force to the ball, Newton’s First Law tells us that the ball will continue to move in a straight line.

• Circular motion is called centripetal motion, with the string providing a centripetal force.



Lecture 11 Slide 12


Fall 2004


Spring 2009

Centripetal Acceleration

• Centripetal acceleration is the rate of change in velocity of an object that is associated with the change in direction of the velocity.– Centripetal

acceleration is always perpendicular to the velocity.

– Centripetal acceleration always points toward the center of the curve

(It’s a central force!).

ac v 2

r

F~1/r

A central force!



Lecture 11 Slide 13


Fall 2004


Spring 2009

Centripetal Acceleration• Centripetal acceleration is the rate of

change in velocity of an object that is associated with the change in direction of the velocity.

– Centripetal acceleration is always perpendicular to the velocity.

– Centripetal acceleration always points toward the center of the curve.

• The centripetal force refers to any force or combination of forces that produces a centripetal acceleration.

ac v 2

r

Fc mac



Lecture 11 Slide 14


Fall 2004


Spring 2009

• The horizontal component of T produces the centripetal acceleration.

• The vertical component of T is equal to the weight of the ball.

• At higher speeds, the string is closer to horizontal because a large horizontal component of T is needed to provide the required centripetal force.

A Simple Demonstration of Centripetal Force(with commentary by Newton)



Lecture 11 Slide 15


Fall 2004


Spring 2009

Centripetal Forces—Negotiating a Flat Curve

• The centripetal force is the total force that produces a centripetal acceleration.– The centripetal force may be due to one or more individual forces,

such as a normal force and/or a force due to friction.

• The Static force of friction is the frictional force acting when there is no motion along the surfaces.– No skidding or sliding

• The Kinetic force of friction is the frictional force acting when there is motion along the surfaces.



Lecture 11 Slide 16


Fall 2004


Spring 2009

• The friction between the tires and road produces the centripetal acceleration on a level curve.

• On a banked curve, the horizontal component of the normal force also contributes to the centripetal acceleration.

Centripetal Forces—Leaning Into a Curve



Lecture 11 Slide 17


Fall 2004


Spring 2009

What forces are involved in riding a Ferris wheel?

Depending on the position:

• Weight of the rider• Normal force from seat• Gravity

Physics of Technology PHYS 1800

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