1

Honors Physics Review 2

Chapter 4 - 7

2

Newton’s Three Laws of Motion

2 : nd

tn

eF ma

3rd: When one object exerts a force on a second object, the second object also exerts a force on the first object that is equal in magnitude but opposite in direction.

1st: When An object with no net force acting on it remains at rest or moves with constant velocity in a straight line.direction.

3

Tension

Tension is along the line. Tension points away from the object.

T

4

Normal Force (N or FN)

Normal force points from surface to object. Normal force is always perpendicular to the surface in

contact. (Normal = perpendicular) If there is no tendency for the object to go into the

surface, there is no normal force.

N

N

N

Fapp

5

Weight and Apparent Weight

Apparent weight is the normal force or tension.

T

Weight is force of gravity of Earth pulling on the object.

W mgN

6

Free-Body Diagram (Force Diagram)

Draw all the forces acting on the object of consideration. Ignore all forces the object acting on other objects (reaction

forces) Draw all forces starting from center of the object for simplicity.

(frictional force normally is drawn at surface of contact.)

N T

Wf

7

Adding Vectors: Head-to-Tail

Head-to-Tail method:A

B

A

BA+B

– Draw vector A– Draw vector B starting

from the head of A– The vector drawn from the

tail of A to the head of B is the sum of A + B.

Example: A + B

8

Vector Components

cos

sinx

y

a a

a a

x

y

a

is the angle between the vector and the +x axis.

ax

ay

9

Vector magnitude and direction

The magnitude and direction of a vector can be found if the components (ax and ay) are given:

2 2magnitude: x ya a a

is the angle from the +x axis to the vector.

1 directi : non ta y

x

a

a

a

ax

ay

x

y

tan y

x

a

a

10

Friction

Friction: force opposing the motion or tendency of motion between two rough surfaces that are in contact

s sf N

k kf N

Static friction is not constant and has a maximum:

Kinetic (or sliding) friction is constant:

,maxs sf N

11

Equilibrium and Equilibrant Force

Concurrent forces: forces acting on the same object at the same time.

Equilibrium: Fnet = 0 Equilibrant Force: A force that produce equilibrium

when applied to an object.

12

Independence of Motion

From observation:– The horizontal motion and the vertical motion are

independent of each other; that is, neither motion affects the other.

Connection:– Both horizontal and vertical motions are functions of

time. Time connects the two independent motions. – Though these two motions are independent, they

are connected to each other by time.

13

Initial Velocity

x

vi

y

i

ix

iy

v

v

vix

viy

Initial velocity: vi at angle i with the horizontal

cosi iv

sini iv

14

Projectile Motion Breakdown

Projectile: Object launched into the air Horizontal:

ix

x ix

x v t

v v

0netF 0netFa

m Constant velocity

15

Projectile Motion Breakdown (2)

Similarly, Vertical: Constant acceleration (ay = g,

downward) ay = g if downward is defined as +y direction

ay = -g if upward is defined as +y direction

21

2i iy y

y iy y

y y v t a t

v v a t

16

Symmetry of Trajectory (2)

vx

vx

vy

vy

v

v

Velocity at any moment is tangent to the actual path. Velocity is horizontal at the top of the trajectory.

17

Projectile Motion

2 2sin

2i iv

Hg

vy = 0

vx = vix = vi cos i

Maximum Height is

Minimum speed at top, but 0

min cosi iv v

x

y

2 sin 2i ivR

g

Horizontal Range Only when initial and final heights are the same.

2

2tan2 cos

i

i i

gxy x

v

Equation of Path

18

Centripetal Acceleration and Force

Direction of acceleration is always toward the center of circle (or circular arc)

2va

r

a

a

a

v

v

v

for uniform circular motion at any time.a v

2

c c

vF ma m

r

19

Direction of Acceleration

a in the same direction as v:

a opposite to v:

a v:

Speed: increases

Speed: decreases

Speed: does not change

Direction of velocity: changing

20

Uniform Circular Motion

Period: Time for one complete cycle

2 rT

v

1f

T

Frequency: Number of cycles per unit time

21

Relative Velocity

Velocity of A relative to B Velocity of A measured by B Velocity of A at reference frame B

VA,B

, ,A C A Bv v

Bv

,C

22

Kepler’s Three Laws of Planetary Motion

1st: The paths of the planets are ellipses with the center of the sun at one focus.

2nd: An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Thus, planets move fastest when closest to the sun slowest when farthest away.

3rd: 2 3

A A

B B

T r

T r

23

Newton’s Law of Universal Gravitation

m1 and m2 are masses of the two objects

r = distance between m1 and m2, center to center Gravitational force is always attractive, pointing from

center to center.

1 22

GmmF

r

211

26.67 1where 0

N mG

kg

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Using Newton

F

2 2

3

4T

r GM

cF 2v

mr

22 r

Tmr

Mm

r

2

GMm

r

cma

GMv

r

3

2r

TGM

2 3

A A

B B

T r

T r