EE1 Particle Kinematics : Newtons Legacy "If I see further, it is because I stand on the shoulders o

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EE1 Particle Kinematics Newtons
Legacy"If I see further, it is because I stand
on the shoulders of giants,"
Motion Forces Energy Momentum
Conservation Circular Motion Gravity

Chris Parkes
http//ppewww.ph.gla.ac.uk/parkes/teaching/PK/PK.
html
October 2005
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Motion
x
e.g

• Position m
• Velocity ms-1
• Rate of change of position
• Acceleration ms-2
• Rate of change of velocity

dx
0
t
dt
v
0
t
a
0
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Equations of motion in 1D

• Initially (t0) at x0
• Initial velocity u,
• acceleration a,

sut1/2 at2, where s is displacement from
initial position vuat
Differentiate w.r.t. time
v2u22 as
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2D motion vector quantities
Scalar 1 number Vector magnitude direction,
gt1 number

• Position is a vector
• r, (x,y) or (r, ? )
• Cartesian or cylindrical polar co-ordinates
• For 3D would specify z also
• Right angle triangle
• xr cos ?, yr sin ?
• r2x2y2, tan ? y/x

Y
r
y
?
x
0
X
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vector addition

• cab
• cx ax bx
• cy ay by

y
b
a
c
can use unit vectors i,j i vector length 1 in x
direction j vector length 1 in y direction
x
scalar product
a
?
finding the angle between two vectors
b
a,b, lengths of a,b
Result is a scalar
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Velocity and acceleration vectors

• Position changes with time
• Rate of change of r is velocity
• How much is the change in a very small amount of
  time ?t

Y
r(t)
r(t?t)
Limit at ?t?0
x
0
X
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Newtons laws
We described the motion, position, velocity,
acceleration, now look at the underlying causes

• First Law
• A body continues in a state of rest or uniform
  motion unless there are forces acting on it.
• No external force means no change in velocity
• Second Law
• A net force F acting on a body of mass m kg
  produces an acceleration a F /m ms-2
• Relates motion to its cause
• F ma units of F kg.m.s-2, called Newtons
  N

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• Third Law
• The force exerted by A on B is equal and opposite
  to the force exerted by B on A

Fb

• Force exerted by block on table is Fa
• Force exerted by table on block is Fb

Block on table
Fa
Weight (a Force)
Fa-Fb
(Both equal to weight)
Examples of Forces
For this course
weight of body from gravity (mg), tension,
compression Friction,
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Tension Compression

• Tension
• Pulling force - flexible or rigid
• String, rope, chain and bars
• Compression
• Pushing force
• Bars
• Tension compression act in BOTH directions.
• Imagine string cut
• Two equal opposite forces the tension

mg
mg
mg
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Friction

• A contact force resisting sliding
• Origin is chemical forces between atoms in the
  two surfaces.
• Static Friction (fs)
• Must be overcome before an objects starts to move
• Kinetic Friction (fk)
• The resisting force once sliding has started
• does not depend on speed

N
fs or fk
F
mg
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Questions
From Benson, University Physics, Revised Addition

• Topics Covered
• Vector addition and dot product, descriptions of
  motion, Newtons 3 laws, Friction.