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Contact forces
- Involve physical contact between
objects.
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Field forces:
- No physical contact between
objects
- Forces act through empty space
gravity
electric
magnetic
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Measuring forces
- Forces are often measured by determining the elongation of a calibratedspring.
- Forces are vectors !emember vector addition.
- "o calculate net force on an object you must use vector addition.
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Newton’s first law:
In the absence of e#ternal forces:
$ an object at rest remains at rest
$ an object in motion continues in motion with
constant velocity %constant speed& straight line'
%assume no friction'.
(r: )hen no force acts on an object& the acceleration ofthe object is *ero.
Inertia: (bject resists any attempt to change is velocity
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Inertial frame of reference:
- + frame %system' that is not accelerating.
- Newton,s laws hold only true in non-accelerating %inertial'frames of reference
+re the following inertial frames of reference:
- + cruising car
- + braing car
- "he earth
- +ccelerating car
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Mass
- Mass of an object specifies how much inertia the
object has.
- /nit of mass is g.
- "he greater the mass of an object& the less it
accelerates under the action of an applied force.
- 0on,t confuse mass and weight %see: bit later'.
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Newton,s second law%very important'
"he acceleration of an object is directly proportional tothe net force acting on it and inversely proportional to itsmass.
am F ⋅=
x x am F ⋅= y y am F ⋅=
z z
am F ⋅=
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/nit of force:
$ "he unit of force is the Newton %1N'
$ (ne Newton: "he force re2uired to accelerate a 1 g
mass to 1m3s4.
$ 1N 5 1g6m3s4
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"wo forces act on a hocey puc%mass m 5 7.8 g' as shown
in the figure.
%a' 0etermine the magnitude and direction of the net force actingon the puc
%b' 0etermine the magnitude and the direction of the pucs
acceleration.
9lac board e#ample .1
%related to ;) problem' F4 5 <.7 N
θ4 5 =7>
F1 5 .7 N
θ1 5 47>
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"he force of gravity and weight
$ (bjects are attracted to the ?arth.$ "his attractive force is the force of gravity Fg.
$ "he magnitude of this force is called the weight of the
object.$ "he weight of an object is& thus m6g.
g m F g ⋅=
"he weight of an object can very with location %less weight on the moon thanon earth& since g is smaller'.
"he mass of an object does not vary.
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Newton,s third law
If two objects interact& the force F14 e#erted by object 1 on object 4
is e2ual in magnitude and opposite in direction to the force F41
e#erted by object 4 on object 1:
@For every action there is an
e2ual and opposite reaction.A
4114 F F −=
+ction and reaction forces always act on different objects.
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)here is the action and reaction force
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Conceptual example:
+ large man and a small boy stand facing each other on
frictionless ice. "hey put their hands together and push
against each other so that they move apart.
%a' )ho e#periences the larger force
%b' )ho e#periences the larger acceleration
%c' )ho moves away with the higher speed
%d' )ho moves farther while their hands are in contact
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$ +naly*ing forces
$ Free body diagram
$ "ension in a rope 5 magnitude of the force that the rope
e#erts on object.
9lac board: Free body diagram
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+pplying Newton,s laws
$ Mae a diagram %conceptuali*e'
$ Categori*e: no acceleration:
accelerating object:
$ Isolate each object and draw a free body
diagram for each object. 0raw in all forces that
act on the object.
$ ?stablish a convenient coordinate system.$ )rite Newton,s law for each body and each
coordinate component. set of e2uations.
$ Finali*e by checing answers.
∑ = 7 F
∑ = ma F
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+ traffic light weighing 14 N hangs from a cable tied to twoother cables fastened to a support as shown in the figure.
Find the tension in the three cables.
9lac board e#ample .4 %on ;)'
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9lac board e#ample .8 %on ;)'
+ crate of mass m is placed on a frictionless plane of incline θ 5 87°.
%a' 0etermine the acceleration of the crate.
%b' Btarting from rest& the crate travels a distance d 5 17.4 m to the
bottom of the incline. ;ow long does it tae to reach the bottom&
and what is its speed at the bottom
α
α
α
α
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9lac board e#ample .
%on ;)'
+ttwood,s machine.
"wo objects of mass m1 5 4.77 g and m4 5 .77 g are hung overa pulley.
%a' 0etermine the magnitude of the acceleration of the two objects andthe tension in the cord.
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Forces of Friction
$ Btatic friction& f s
$ Dinetic friction& f
Friction is due to the
surfaces interacting with
each other on the
microscopic level.
$ sliding over bumps
$ chemical bonds
time
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"he following empirical laws hold true about friction:
- Friction force& f& is proportional to normal force& n.
- µs and µ : coefficients of static and inetic friction& respectively
- 0irection of frictional force is opposite to direction of relative
motion
- Ealues of µs and µ depend on nature of surface.
- µs and µ don’t depend on the area of contact.
- µs and µ don’t depend on speed.
- µs& ma# is usually a bit larger than µ .
- !ange from about 7.778 %µ for synovial joints in humans' to 1 %µs for rubber on concrete . Bee table .4 in boo.
n f s s µ ≤ n f k k µ =
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9lac board e#ample .
%related to ;)'
Measuring the coefficient of staticfriction
+ bric is placed on an inclined
board as shown in the figure.
"he angle of incline is
increased until the bloc starts
to move.
0etermine the static friction coefficient from the critical angle& αc& at
which the bloc starts to move. Calculate for αc 5 4=.>.
α
α
α
α
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+ppro#imate friction coefficients
µs µ
!ubber onconcrete
1.7 7.<
)ood on wood 7.4-7. 7.4
)a#ed wood onwet snow
7.1 7.1
Bynovial jointsin humans
7.71 7.778
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9lac board e#ample .=%on ;)'
+ car is traveling at 7.7 mi3h on a hori*ontal highway.
%a' If the coefficient of inetic friction and static friction betweenroad and tires on an icy day are 7.7<7 and 7.1& respectively&
what is the minimum distance in which the car can stop
%b' )hat are the advantages of antiloc braes
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