Download Dynamics Review Outline

Dynamics Review Outline
2.1 Contact Forces
2.1.1A-C Newton’s Laws of Motion
o First Law (Inertia) – objects tend to remain in their current state of motion (at rest of moving at a
constant velocity) until acted upon by a net force
 Inertia is proportional to mass and is NOT affected by speed
A 10 kilogram object at rest has more inertia than a 2 kilogram object moving at 20 meters per
second.
o
Second Law – acceleration is proportional to force and inversely proportional to mass
a
Fnet
m
A 5.0 kilogram object that is subjected to a net force of 20 newtons will accelerate at a rate of 4.0
meters per second2.
o
Third Law – for every action there is an equal and opposite reaction.
If a person pushes on an object with a force of 25 newtons then the object pushes back with a force of
25 newtons.
2.1.1D Mass and Weight g 
o
Fg
m
Mass is universal (object has the same mass independent of its location).
A 10 kilogram object has a mass of 10 kilogram on Earth, in orbit and on the Moon.
o
Weight is a gravitational force that depends on location.
A 10 kilogram object weighs about 100 newtons on Earth and about 17 newtons on the Moon.
o
Acceleration due to gravity can be determined by looking at the slope of a graph of mass vs. weight.
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2.1.2A-C Forces on Angles (Top/Down)
o The resultant to a set of vectors is determined graphically by adding the vectors using the ‘head-totail’ method.
o
Vectors can be broken into components that are perpendicular to one another.
The resultant to a set of vectors is determined algebraically by adding the components of the vectors
and using the Pythagorean Theorem on the resultant components.
o
Equilibrium is a state in which the net force on a system is zero.

An equilibrant is a vector that when added to a system produces a state equilibrium within that
system.

The equilibrant is equal in magnitude to the resultant, but opposite in direction.
o
The maximum resultant produced by two vectors is obtained by
aiming them with 0° between them. Max resultant (and equilibrant)
will be A + B.
o
The minimum resultant produced by two vectors is
obtained by aiming them with 180° between them. Min
resultant (and equilibrant)will be A - B.
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o
Any resultant (and equilibrant) between A + B and A – B can be produced!
A 10 newton vector and a 7 newton vector can be added together to produce any resultant between 3
N and 17 N (it just depends on what angle you choose to have between them). It is therefore true that
any vector between 3 N and 17 N could be added this system to produce equilibrium.
2.1.2D Forces on Angles (Side-view)
o When objects are pulled or pushed along surfaces using forces at angles to the surface then
acceleration does not depend on the force itself, but the components of it.
o
Pulling on an upward angle reduces the normal force.
o
Pushing on a downward angle increases the normal force.
A 5 kilogram mass has a weight of about -50 N, so the normal force will be +50 N if it is in
equilibrium.
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o
Pulling on an angle also changes the net force. The net force in side-view systems depends only on
the sum of horizontal forces.
2.1.3A-B Friction
o
Friction is a force that attempts to keep objects from moving. It is the result of electrical attraction
between surfaces and can be reduced by lubrication.
o
Static friction is the force that must be overcome to make an object slide. This type of friction should
be used in ALL problems where there is NO SLIDING.
o
Kinetic friction is the force that acts in opposition to the motion of a sliding object. This type of
friction should be used ONLY in problems in which objects ARE SLIDING.
o
Coefficient of friction tells about the relative “stickiness” that two surfaces have when in contact with
each other – this a dimensionless quantity (has no units.)
If a 20 newton block of wood is placed on a wooden surface then the normal force between the block
and surface is 20 newtons. It will take slightly more than 8.4 newtons of force to get the block to
begin sliding along the surface. Once the block begins to move, the force of friction will immediately
drop to 6 newtons.
A 15 newton block of rubber that is sliding along an ice-covered surface will require 2.25 newtons of
force to be constantly applied to keep it moving at a constant velocity. If a force of 10.25 newtons
were applied to the same block the result would be a net force of 8.0 newtons and an acceleration of
0.53 meters per second2.
If 40 newtons of force are required to make a 3.0 kilogram object accelerate along a surface at a rate
of 5.0 meters per second2, then the net force on the object is 15 newtons and we can conclude that
there must be a 25 newton force of kinetic friction acting on the object. The kinetic coefficient of
friction in this case must be about 0.85 (arrived at using Ff = μFN where FN = 3.0 kg * 9.81 m/s2.)
If a 20 newton force of friction is acting on a 4.0 kilogram object that is accelerating at a rate of 3.5
meters per second2 then we must conclude that there is a 34 newton force pushing on the object.
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2.1.4A-B Inclined Planes
o When an object is placed on an incline its weight will point partially ALONG the plane and partially
INTO the plane.
o
Breaking the weight into components will cause all forces to be referred to in reference to the plane –
either parallel or perpendicular to it.
o
The normal force will be equal to the perpendicular component of weight.
o
Whether or not the object slides along the plane (and its direction) depends on the sum of the forces
directed along the plane.
Since the box weighs 80 newtons, there are 69 newtons of force directed into
the plane – this means the normal force is 69 newtons.
If the surface of the plane is frictionless then the net force is 40 newtons.
If the block slides down at a constant speed, then the force of friction must be 40
newtons.
If the force of friction is 30 newtons then a net force of 10 newtons is causing the
block to accelerate down the plane.
F
Ff
If the block is being pulled up the plane at a constant speed and the force of
friction is 15 newtons, then force F must be 55 newtons.
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2.2 Auxiliary Forces
2.2.1A-B Universal Gravitation G = 6.67 x 10-11 N·m2/kg2
o Gravity is a force that attracts objects with mass to one another.
o
The force of gravity between two objects is directly proportional to the masses of each object.
The force of gravity acting between two objects with masses of 3000
kilograms that are separated by 2 x 10-2 meter is 150 newtons.
If the mass of one object were doubled, the force would become 300
newtons.
If the masses of both objects were halved, the force would become 37.5
newtons.
o
The force of gravity between two objects is inversely proportional to the distance between the
CENTERS of the objects.
The force of gravity acting between two objects with masses of 3000
kilograms that are separated by 2 x 10-2 meter is 150 newtons.
If the distance between the objects is doubled, the force becomes 37.5
newtons.
If the distance between them is cut to 1/3rd of its original value the force
becomes 1350 newtons .
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2.2.2A-C Uniform Circular Motion
o Objects in circular motion are being pulled into a circular path by centripetal force – this is an
unbalanced, net force that causes centripetal acceleration.
o Both centripetal force and centripetal acceleration must point toward the center of the object’s
circular path of travel.
o The velocity of the object will be tangent to its circular path
o
The force needed to bend the path of an object depends on:
o How massive the object is (m)
o The object’s centripetal acceleration (aC)
o
The object’s centripetal acceleration depends on:
 How much speed the object has (v)
 How tight the turn needs to be (r)
An object that makes one complete trip around a path with a circumference of 4.0 meters every
0.5 seconds has an average speed of 8.0 meters per second.
An object that moves around a circular path with a radius of 5.0 meters at a speed of 20 meters
per second will take about 1.6 seconds to make one complete trip around the circle.
An object that is moving around a circular path with a radius of 10 meters while moving at a
speed of 4.0 meters per second will have a centripetal acceleration of 1.6 meters per second2.
A 5.0 kilogram object that is moving around a circular path with a speed of 6.0 meters per
second will be subjected to a centripetal force of 60 newtons if the path has a radius of 3.0 meters
and 45 newtons if the path has a radius of 4.0 meters.
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
When a car (or other object) makes a turn on a flat surface it is STATIC friction between the object
and surface that allows the turn to occur.
The maximum turning speed on a 30 meter radius turn for a 1500 kilogram car with rubber tires
on asphalt is 15.8 meters per second.
The minimum radius with which a 70 kilogram bike could make a 12 meter per second turn with
rubber tires on asphalt is 17 meters.
The minimum coefficient of friction needed for a 1000 kilogram vehicle to make a safe turn with a
10 meter per second radius while moving at 5.0 meters per second is 0.25
2.2.3 Hooke’s Law
 Force is required to change the length (compress or elongate) of a spring.

The change in the spring’s length will be:
 Directly proportional to force applied (FS)
 Inversely proportional to the spring constant of the spring (k)
A force of 200 newtons will cause a spring with a spring constant of 5000 newtons per meter to
stretch a distance of 4 centimeters.
The slope of the graph of FS vs. x is the spring constant of the spring.
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