Lecture 12

Newton’s Laws of Motion

Amount that the IRS has spent since 2006 on an outsourced program to

collect unpaid taxes: $87,000,000

Amount the contractors have collected during that time:

$50,000,000

QUIZ

• Find this vector’s magnitude and angle with respect to the positive x axis and draw it

• Find the x- and y-components of the vector

20 / 40 /x yv m s v m s

0(2 ,45 below +x-axis)d km

What Causes Motion?

In the absence of any forces acting on it, an object will continue moving forever. Motion needs no “cause.”

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Seat Belts: An Application of Newton’s First Law

Catalogue of Forces

Spring Force Fsp

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Tension Force T

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Normal Force n

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Friction fk and fs

Drag and Thrust D

Fthrust

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Example

A block is dragged uphill by a rope. Identify all forces acting on the block.

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Exercise

A ball, hanging from the ceiling by a string, is pulled back and released. Identify the forces acting on it just after its release.

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Newton’s Second Law

• Physics added to motion:

NETF F ma

Example

An elevator, lifted by a cable, is going up at a steady speed. • Identify the forces acting on the elevator. • Is T greater than, equal to, or less than w? Or is there not

enough information to tell?

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Free body diagrams

• Make diagram of object showing all forces acting on it (as vectors). For now object will be represented by a point.

• Decide on the x and y-axes• Find x- and y-components of each force• Find

• Show FNET on diagram

, 1 2

, 1 2

...

...NET x x x

NET y y y

F F F

F F F

Problems due Today

• 3: 26, 28, 30, 33, 70, 72

Problems due Friday

• Reading: 4: 5-8• Problems: 4: CQ1, MC21, 4, 7, 8, 9, 10, 11