Newtons laws

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Newtons laws
Whats a force and whats it do? What are
Newtons three laws of motion? What are they
good for? Rosencrantz Heads. Heads.
Heads. Heads. Rosencrantz and Guildenstern are
Dead by Stoppard
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What Newton said

• 1 Objects have inertia
• Motion under no force does not change
• momentum is constant
• 2 F ma aka (force) (mass)?(acceleration)
• if you push on something you can change its
  motion
• decrease, increase or re-direct the momentum
• 3 Each (action) force causes and equal and
  opposite reaction
• F (A on B) - F (B on A)

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Vectors

• There is more than one spatial direction
• Write boldface
• or symbols with arrows
• F
• Position r (or whatever)
• Velocity v
• Acceleration a
• Force F

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Remedial Vector Vocabulary

• Cartesian components (the x, y and z or direction
  of it)
• Length or amplitude (the amount of it)

Add them head to tail graphically Or r1
Dr r2 and v vx vy ivx jvy
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An example

• Pop fly chased by Ozzie Smith
• Horizontal speed is constant
• Vertical speed changes
• Acceleration is down
• And constant

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Now back to Newtons laws

• Newton 2 F ma

Force is gravity or weight and constant here
y
So (drum roll..)
Acceleration is constant its 9.8m/s2 it points
down
x
Only vy changes, vx is constant
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More of the example
Velocity v v0 aDt

• For constant acceleration

Horizontal component x x0 vxDt
y
Vertical component y y0 vyDt ay (Dt)2/2
Both components r r0 vDt a(Dt)2/2
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Physics is problems solving

• How high does the ball go if the initial vy is
  30m/s ?

• How long is the ball in the air?

• How far does Ozzie run to catch it if the initial
  vx is 10m/s ?

• Is Ozzie amazing or what?

• How can you solve these kinds of questions?

1. Write down the definitions (what does vy
mean?)
2. Write down the principles (F ma for
example)
3. Analyze the problem to get the answer
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Lets try one

• How high does the ball go?

1. Write down the definitions vy Dy/Dt
a vy Dvy/Dt
2. Write down the principles y y0 v0yDt
ay(Dt)2/2 v v0 aDt, which means vy
v0y ayDt
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Now analyze the problem

• Use what we know to get what we want (in stages)

We know v0y (30m/s) and ay (-10m/s2), but not
vy and Dt
So we can use vy v0y ayDt to get Dt And then
use y y0 v0yDt ay(Dt)2/2 to get y at the
top of the arc
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How long is the ball in the air?

• Can do more calculations or can think for a
  moment.

• Equations for motion are the same going up and
  coming down.

• So from symmetry, expect time to come down to be
  the same.

• Total time in the air is 3 3 6 sec

• Symmetry is a new principle.

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How far does Ozzie run?

• I did not tell you enough to answer this one.
  You dont know where he starts or where the ball
  is headed

• At most, he runs for 6 sec at 10 m/sec (world
  record speed)

• Probably less depending on where the ball was hit
  on the field.

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Klee (Speaking of amazing!!)

• This guys work is so rich

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Newton 3

• For every reaction, there is an equal,
• opposite reaction

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Lazy mule or smart mule

• Mule to farmer Its impossible because of Newton
  3

• Farmer to mule Quit stalling around and use the
  force

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Please carry my piano upstairs.

• The mammoth is in no danger here

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Work and Potential Energy

• Work required to lift something
• W (force) ? (distance)

W (mg) ? (h)
This process stores energy as potential
energy PE mgh
Potential energy can be converted into
work (hydroelectric plants, waterwheels, etc)
Potential energy can be converted kinetic
energy
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Potential and Kinetic Energy

• Potential Energy energy stored among forces
  that want to accelerate an object
• eg gravity pulling down on the boulder
• or the bucket of icewater balanced on the
  nerds door.

Kinetic Energy energy stored in motion of an
object eg baseball before it hits Ozzies
glove or speeding cars just before the
head-on collision
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Ramps allow work to be spread out

• Work to lift the boulder is (W)(Dy) mg(y-y0)

Youre tired at the top of the ramp because you
gave your energy to the boulders potential
energy
The mammoths headache comes from releasing that
potential energy as kinetic energy
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Take home messages

• Newton 2 (and 3)
• Equations of motion
• HOW TO SOLVE PROBLEMS !!!!
• Definitions
• Principles
• Analysis
• Ramps and mechanical advantage
• Potential energy
• Kinetic energy