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AP Physics Exam 2 Review

Chapter 5-8

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Newton’s Three Laws of Motion

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

2nd:

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.

F ma

Action and reaction forces always exist together.

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Free Body (Force) Diagram

Draw all forces acting on the object being considered– Ignore all forces this object acting on other objects– Draw forces starting from center of object or at

points of action– Make sure each force giver can be identified

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Normal Force (N, but not Newton)

Given by the surface in contact to support the object.

NN

N

Fapp

• No contact No normal force• No tendency to move into surface No normal force

Always perpendicular to the surface in contact. Points from surface to the object

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Tension

Tension is along the string and points away from the object of consideration.

T

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Weight and Apparent Weight

Apparent weight is either tension or normal force.

T

W mgN

Weight or gravity: gravitational force the Earth pulling on object around it

Always straight downward.

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Two kinds of frictions

Static friction: ,maxs sf N

k kf N Kinetic (or sliding) friction:

s sf N

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Examples of centripetal forces

Rounding a curve in a car

max sv Rg

tanv Rg

Max velocity w/o skidding

– Flat curve:

– Banked curve:

Orbiting the Earth (Sun or other object)– Gravity

N

f

W

Static friction provides the centripetal force (when no skidding)

a component of Normal force (net force)

Rear View

N

W

No friction2

1tanv

Rg

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Kinetic Energy, K

Kinetic Energy: ability to do work due to motion

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2K mv

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Work Done by A Constant Force

W F d ����������������������������

W: a scalar, no direction W < 0 if > 90o.

cosFd x x y y z zF d F d F d

F

d

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Work-Kinetic Energy Theorem

The total work done on an object is equal to the change in the kinetic energy of that object

W K f iK K

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Work (Wg) Done by Weight (Fg)

cosgW mgd

gW mg h

cosW Fd

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Work Done by a Variable Force

W Fd 1-D

or: Area under curve of

Force-position graph

( )f

i

x

x

W F x dx

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Spring Force and Work

Hook’s Law: Spring force is given by

Notice that this force is the force exerted by the spring, not the force you apply to compress or stretch the spring.

o r F F kk x x ����������������������������

sW 2 21 1

2 2s i fW kx kx f

i

x

xFdx f

i

x

xkx dx

Work done by spring force:

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Power

Average Power: WP

t

dWP

dt F v

cosFv or x x y y z zF v F v F v

Instantaneous Power:

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Potential Energy U (Ug or Usp)

Gravitational Potential Energy:

gU mgy

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2spU kx

Spring (Elastic) Potential Energy:

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Force and Potential Energy

dUF

dx

For each potential energy, there is a conservative force associated with it.

U W

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(Total) Mechanical Energy, E

Sum of kinetic and potential energy:

mecE K U

E K U

or simply,

g sK U U

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Conservation of Mechanical Energy

When only conservative forces are doing work within a system, the kinetic energy and potential energy can change. However, their sum, the mechanical energy E of the system, remains unchanged.

i fE E

i i f fK U K U 0E K U

K U

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Work Done By External Force

Work done by external force will change the total mechanical energy of the system:

ext mecW E

If there is also kinetic friction,

ext f mecW W E ext mec thW E E

where is the heat gain (change in thermal energy) f kthE W f d

Total Energy: inttot mec thE E E E

Eint = Chemical Energy & Nuclear Energy

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Work and Energy Change

ext mecW E

Total work done by __________________________.

W K

Total work done by _______________________________.

Work-Kinetic Energy Theorem:

all external forces (excluding spring force and gravity)

all external forces, normally including spring force and gravity.