Download The Laws of Motion . . . or Newton`s Laws

Chapter 5: Laws of Motion
Tyler Erb
Background/Summary:
An examination of Newtonʼs Three Laws of Motion in an attempt to explain what
mechanism changes motion and what factors determine acceleration.
5.1 The Concept of Force
Force: that which causes an object to accelerate
Net Force (also known as Total Force, Resultant Force, or Unbalanced Force: the vector
sum of all forces acting on an object
Net Force=Mass x Acceleration
Equilibrium: when velocity of an object is constant (so, when acceleration/net force is
zero)
Contact Forces: involve physical contact between two objects
Force Fields: do not involve physical contact. Act through empty space. (ie gravity)
Fundamental Forces: (all are force fields)
1.
gravitational forces (between objects)
2.
electromagnetic forces (between electric charges)
3.
nuclear forces (between subatomic particles)
4.
weak forces (arise in certain radioactive decay processes)
5.2 Newtonʼs First Law
Newtonʼs First Law of Motion/Law of Inertia: “When no force acts on an object,
the acceleration of the object is zero” (an object in motion stays in motion/an
object in rest stays in rest unless acted on by an outside force)
Inertia: the tendency of an object to resist any attempt to change its velocity
5.3 Mass
Mass: the property of an object that specifies how much resistance the object exhibits to
changes in its velocity
Mass is measured in kilograms (kg)
Mass is an inherent property of an object and is independent of the objects
surroundings and of the method used to measure it
Mass is a scalar quantity
Mass is not the same thing as weight. Weight is the magnitude of gravitational force and
therefore varies depending on location (because gravitational force is different in
different places)
5.4 Newtonʼs Second Law
Newtonʼs Second Law: “The acceleration of an object is directly proportional to
the net force acting on it and inversely proportional to its mass” (AKA Fnet=ma)
Force is measured in newtons (N; 1 N=1 kgm/s^2)
5.5 Gravitational Force and Weight
Gravitational Force: the attractive force exerted by the Earth on an object
Force of gravity=mass x acceleration of gravity
g=9.8 m/s^2
5.6 Newtonʼs Third Law
Newtonʼs Third Law: “If two objects interact, the force exerted by object 1 on
object 2 is equal in magnitude and opposite in direction to the force exerted by
object 2 on object 1”
Forces always occur in pairs; a single isolated force cannot exist
Normal Force: a force that balances gravitational forces so the the net force on an
object resting on a flat, sturdy surface is zero
Free Body Diagram: a diagram that displays all forces acting on a single object
5.7 Application of Newtonʼs Laws
see problems below
5.8 Forces of Friction
Force of Friction: resistance to an objectʼs motion due to interaction with its
surroundings
Force of Static Friction: the force of friction on an object that is not moving. Force of
static friction is equal to the applied external force as long as the object is not moving.
The maximum force of static friction is equal to the maximum amount of force that can
be applied to an object without it moving.
Force of Kinetic Friction: the force of friction on a moving object. Force of kinetic friction
is less than the maximum force of static friction. Force of kinetic friction is independent
of applied external force.
Force of Static Friction is less than or equal to the coefficient of static friction multiplied
by the magnitude of the normal force exerted by one surface on the other.
Force of Kinetic Friction is equal to the coefficient of kinetic friction multiplied by the
normal force exerted by one surface on the other.
- the values of the coefficients of static and kinetic friction depend on the nature of the
surfaces, but the coefficient of kinetic friction is generally less than the coefficient of
static friction
- the direction of the friction force is parallel to the surface with which the object is in
contact and opposite to the actual or impending motion of the object relative to the
surface
- the coefficients of friction are nearly independent of the area of contact between the
surfaces
Problems
1. (easy) A water balloon is in free fall. If the water balloon has a mass of 1kg, what is
the force of gravity acting on the balloon?
2. (medium) There are two blocks of equal mass 1kg. Both begin at rest One is resting
on a table with a coefficient of kinetic friction .03, the other is dangling in frictionless
air. How fast are the blocks accelerating
53
37
T1
T2
3. (hard) A brick weighing 100 N is hung from two cables forming angles of 37 and 53
degrees with the horizontal. What is the tension in each of the cables
1. 9.8 N
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Fg=mg
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Fg=1kg*9.8m/s^2
Fg
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Fg=9.8 N
2. 4.75m/s^2
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Block on table: Fnet=T-Ff=ma -->
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T
<-Block off table: Fnet=Fg-T=ma
Ff=u*Fn
Fn=Fg
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Fg
T-(.03*Fg)=ma=Fg-T
2T=1.03*Fg
2T=1.03(mg)
2T=1.03(1kg*9.8m/s^2)=10.1N
T=5.05N
mg-T=9.8N-5.05N=4.75N=ma
a=4.75m/s^2 downward
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Fn
T"
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Fg
Ff
T2
T1
3. T1=111N, T2=83.3N
T1y
53
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T2x
37
T1x
Fg
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Fnetx=-T1x+T2x=ma=0
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*T1 is negative because it is pulling in the left
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(negative) x direction while T2 is pulling in the
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right (positive) x direction
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so T1x=T2x
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T1*cos(53)=T2*cos(37)
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.602T1=.799T2
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T1=1.33T2
Fnety=T1y+T2y-Fg=ma=0
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*Fg is negative because it is pulling down
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whereas T1 and T2 are both pulling up
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so T1y+T2y=100N
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T1*sin(53)+T2*sin(37)=100N
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.799T1+.602T2=100N
SUBSTITUTE T1:
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.799(1.33T2)+.602T2=100N
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1.60T2+.602T2=100N
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2.20T2=100N
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T2=83.3N
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T1=1.33(83.3N)=111N
T2y