Dynamics: Newtons Laws of Motion

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Dynamics Newtons Laws of Motion

• Newtons Laws of Motion

Newtons 1st Law A body will continue in its
state of rest or uniform motion in a straight
line as long as no net force acts on it. Also
called the Law of Inertia.
Newtons 2nd Law The acceleration of an object
is directly proportional to the net force on the
object and inversely proportional to its
mass. nFma kg.m.s-2
Newtons 3rd Law If two bodies interact the
force exerted by 1 on 2 is equal and opposite, to
the force exerted by 2 on 1. F12-F21
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Application of Newtons Laws

• 1. Draw a simple diagram.

2. Isolate the objects of interest separately,
draw a free body diagram showing all the forces
on the body.
3. Resolve the forces according to the chosen
coordinate sytem.
3. Solve equations for the unknowns.
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Application of Newtons Laws

• Example A traffic light is suspended by cables
  as shown. Calculate the tension in the cables.
  Assume the weight of the light is 100 N.

There are three cables
Cable 1
Cable 2
Cable 3
There is on object
Traffic light
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Application of Newtons Laws
Forces on the light
Forces on the cables
T2
T1
T3
W
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Application of Newtons Laws
For the light T3 W 0
Therefore W T3
T3
W
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Application of Newtons Laws
For the cable
In the y direction
T2
T1
T2sin53 T1sin 37 W 0
T3
In the x direction
T2cos53 - T1cos37 0
The two equations can be solved simultaneously to
find T1 and T2.
Answer T1 51.8 N, T2 68.8 N, T3 100 N
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Application of Newtons Laws

• Example Block, mass m, sliding down a smooth
  plane

Forces are on the block are
Normal force
In the x direction
Gravity
mgsinq max
In the y direction
N-mgcosq 0
q
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Friction

• Consider a block on mass, m, weight, W, sitting
  on a rough surface subject to a horizontal force
  Fa.

Forces are on the block are
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Friction

• There are two types of frictional force.
• 1. Static friction ms
• 2. Kinetic friction mk

As Fa increases a static force Ffr opposes the
motion. Ffr increases until it is not able to
match the increasing force and the body starts to
move (maximum static force). The kinetic
frictional force then acts.
Frictional force is proportional to the normal
force acting on the block
Ffr mFN where m is the coefficient of friction
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Frictions

• Example A block, mass m, on a rough surface at
  an angle q to the horizontal. Increase the angle
  until the block just starts to slip. Find the
  kinetic coefficient of friction as a function of
  angle.

Then In the x direction
FN - mgsinq 0
In the y direction
mgsinq Ffr 0
Solving for Ffr gives
Ffr FNtanq
But Ffr mkFN
mk tanq
q
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Friction

• Example Block m1, on a rough surface is
  connected to m2 by a light cord over a
  frictionless pulley and is pulled at an angle q
  to the horizontal. Determine the acceleration and
  tension of the cord.

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Friction

• Force diagrams are as follows

For m1
For m2
Fcosq Ffr - T m1a
In the x direction
T m2g m2a
N Fsinq - m1g 0
In the y direction
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Newtons Law of Circular Motion

• Consider a ball, m, tied to a string of length r
  moving with a linear speed v.

Forces
Force on ball exerted by string
Force on hand exerted by string
Fr mar
mv2/r
mrw2
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Newtons Law of Circular Motion

• Example A 1500 kg car moves on a flat road with
  a speed of v. It enters a 35 m radius curve. If
  the coefficient of static friction is m 0.5
  what is the maximum value for v before the car
  starts to slide?

and Ffr mFN mmg
F Ffr mv2/r
Therefore mv2/r mmg
Or v2 mrg
Answer v 13.1 m/s
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Newtons Law of Circular Motion

• Example A VicRoads engineer is designing an exit
  from a freeway which, because of nearby buildings
  needs to be in the form of a curved circular road
  of radius no greater than 100 m. What advisory
  speed should be posted for there to be no
  sideways for on the tyres (no skidding) if the
  curve cannot be banked at greater than 15o.

Answer 16 m/s or 58 km/hr
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Newtons Law of Circular Motion

• Example What is the force between the 70 kg
  driver and the seat of the car is driving at 80
  km/hr when
• She its the bottom of the depression of radius
  100 m?
• She hits the top of a small bridge of radius 100
  m?

Answer a 1032 N (ie. 50 heavier)
Answer b 340 N (ie. 50 lighter)