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Forces and Motion
Chapter 5 and 6
Focus
 Force: a push or a pull
 Acts on objects to change its velocity
Newtonian Mechanics
 The study of the relation between a force and
the acceleration it causes as discovered by
Isaac Newton
 It does not apply to some situations
 Very fast moving bodies
 Ex: Bodies traveling near the speed of light
 Must replace with Einstein’s theory of relativity
 Interacting bodies on the scale of atomic structure
 Ex: Electrons of an atom
 Must replace with quantum mechanics
 Newtonian mechanics is a special case of the
two more comprehensive theories
Newton’s Laws
 1st Law: If no net force acts on a body, the body’s velocity cannot
change (it cant accelerate
 2nd Law: The net force on a body is equal to the product of the
body’s mass and its acceleration (Fnet = ma)
 Only forces acted on a body are included in the net force of the body
 Net force can be broken into three components (x y z)
 A component force can only cause an acceleration in that component
 If Fnet = 0, the forces are balance and the body is said to be in
equilibrium
 3rd Law: When two bodies interact, the forces on the bodies from
each other are always equal in magnitude and opposite in direction
 FBC = FCB (Equal magnitude but opposite direction)
 Third Law force pair
Force
 The unit of force must be defined in terms of the mass
and acceleration
 Vector quantity
(Newton = kg × m/s2)
 Principle of superposition for forces
 A single force that has a magnitude and direction of the net force
has the same effect on the body as all the individual forces together
 Two or more forces have a net force/resultant force
 Free body diagram
 Drawing all the external forces that act on a defined system
 Net force not included
 Centripetal force not included
 Internal forces (forces between bodies in a system) not included
Examples of Forces
 Gravitational Force (Fg)
 Attraction of two bodies towards each other
 Ground of earth is inertial reference frame
 Fg = mg (For relatively small distances of an object
from earth)
 Weight (W)
 The magnitude of the net force required to prevent a
body from falling freely
 Inertial reference frame is the ground of earth
 W – Fg = Fnet = 0 or W = Fg
Examples of Forces (cont.)
 Normal Force (FN )
 The force a surface exerts on an object
 direction is perpendicular to and away from the surface
 Friction ( f )
 The resistance force from the bonding between two objects
 Direction opposite the direction of intended motion
 Tension ( T )
 The force resulting from a cord attached to a body being pulled
taut
 The force on the object being pulled and the tension force are
equivalent
 For simplification, a cord is often said to be massless and
unstretchable
Closer Look at Friction
 Static Friction ( fs )
 Friction opposes the motion of a stationary object
 Is only present when there is another force being
exerted on the object
 Equal in magnitude of that force
 Opposite in direction of that force
 Kinetic Friction ( fk )
 Friction that opposes the motion of a moving object
 Has a set magnitude that is independent of any other
forces on the object and of the velocity of the object
Properties of friction
 If a force F tries to push a stationary body…
 If the body doesn’t move, fs and the component of F
parallel to the surface are in equilibrium
 fs = μs FN
 If the body begins to slide along the surface, the
magnitude of the frictional force rapidly decreases to
fk where fk = μk FN
 μ of the friction forces are dimensionless and
must be determined experimentally
Uniform Circular Motion
 ac = v2/r
 Fc = mv2/r
 A centripetal force accelerates a body by
changing the direction of the body’s
velocity without changing the body’s speed
 Tension and friction commonly contribute
to centripetal forces
Drag Force ( D )
 Force from a fluid that opposes the motion of an
object and points in the direction the fluid flows
relative to the body
 Terminal Speed
 When considering drag force, a falling object will
eventually achieve a constant speed (terminal
velocity)
 This happens when the net force on the object is 0
 D – Fg = Fnet = 0 or D = Fg
The sum of all forces acting
on an object is also known
as?
The net force
True of False? An applied
force always causes an
acceleration
False, only a net force
What does a net force
equal to?
 F or ma
True or False? Some forces
can cause an acceleration
opposite the direction of the
force
False, a force can only cause an
acceleration in the same direction
as the force
True of False? A static friction
force can be a net force on
an object
False, static friction is strictly a
reaction forces which balances all
other forces that oppose it
An 80 kg boy pushes a 25 kg
girl with a force of 50 N. How
much force does the tiny girl
exert back on the big boy?
50 N (Newton’s third law)
A centripetal force of 10N
acts on a 5 kg object. What is
the magnitude of the
acceleration?
0 m/s2, only the direction of the
velocity changes
Which force goes in a free
body diagram?
Centripetal Force
Net Force
Static Friction
Internal Forces
True or False? Static friction
acts opposite the direction of
the motion of a sliding object
False, this is kinetic friction
A force is a…
Push or a pull
A normal force is…
A force acted on by an object from
a surface that is perpendicular to
the surface
All forces have equal and
opposite forces is which one
of Newton’s laws?
3rd law
Terminal velocity is
achieved when..
Drag force is equal to gravitational
force
Newton’s First Law is…
An object cannot accelerate
without experiencing a force
Kinetic friction applies
when objects are…
Moving relative to their surface
Which force is greater?
Maximum static friction or
kinetic friction?
Maximum static friction
What force is an object
experience when it is being
attracted by the earth?
Gravitational force
True of False? The
magnitude of the normal
force is always equal to the
magnitude of the gravitational
force.
False
True of False? A Force is
a vector quantity.
True, force has a direction and
magnitude
If net force is zero, all forces
acting are said to be in…
Equilibrium
What is the maximum magnitude of
F before this block becomes on the
verge of slipping? µs = 0.1
F – fs,max = Fnet
F – fs,max = 0
F = fs,max
F = µsmg
F=5N
5 kg
F
Two horizontal forces, F1 = 5N and F2 = -7N,
act on a 2 kg on a frictionless surface. How
much does the block accelerate?
F1 + F2 = F net
F1 + F2 = ma
(F1 + F2)/m = a
-1 m/ss = a
7N
5N
A 8.0 kg block slides across the floor at a
constant speed. The coefficient of kinetic
friction between the floor and the block is
0.25. What is the magnitude of the force
F on the block?
F net = F - f
ma = F - f
0N=F-f
f= F
µmg = F
20 N = F
F
8 kg
A block, m = 10 kg, is placed on a ramp and θ =
30°. The coefficient of static friction between
the block and ramp is μs = 0.60. Does the block
slide down the ramp?
θ
FN = Fgcosθ
FN = mgcos 30
FN = 87 N
Fgx = Fgsinθ
Fgx = mgsin30
Fgx = 50 N
Fs,max = FNμs
Fs,max = 52 N
No, the block does not slide since the maximum static friction force is greater
than the component of the force of gravity parallel to the ramp
Two blocks are connected by a massless
rope on a frictionless surface, and then
the two blocks are pulled by another rope
with a force of T1= 30 N. m1 = 5 kg and
m2 = 10kg. What is the magnitude of T2?
F net = T1
ma = T1
a = T1/(m1 + m2)
a = 2 m/s2
F net = T2
ma = T2
m2*a = T2
20 N = T2
m2
T2
T1
m1
A 20 kg monkey swings from a vine of length L
= 10 m to save his banana in a lake. The
monkey must grab the banana at the bottom of
his swing. The maximum tension T in the vine
before it snaps is 405N. Will the monkey safe
retrieve his banana if his velocity at the bottom
of his swing is10 m/s?
Fc = mac
T – Fg = mv2/L
T = mv2/L + mg
T = 400 N
He barely does, but yes the monkey gets his
banana safely
T
Fg
A system of blocks is pushed by a force
F = 105 N on a frictionless surface.
m1 = 25kg and m2 = 10 kg. The top block
is on the verge of slipping. What is μs
between the two blocks?
F net = F
ma = F
a = F/(m1 + m2)
a = 3 m/s2
F net = fs
m2*a = μ*m2*g
μ = a/g
μ = .31
F
A block is being held on a wall by a force F
perpendicular to the wall. The coefficient of static
friction between the wall and block is 0.10. The
block has m = 20kg. What is the minimum force F
needed to keep the block on the wall without
slipping?
Fs,max = Fg
FNμ = mg
F = mg/μ
F = 20 N
F
A drag force on a given object (m= 50 kg) is given by D = 5kv2. What value of
k would give a terminal velocity of 5.0m/s for the object?
D = Fg
5kv2 = mg
k = mg/5v2
k = 4 N/m
A vertical force of 12 N and a horizontal force of 9.0 N act on an object. What is
the magnitude of the net force? What is the direction of the net force?
F net = √[(Fv)2 + (Fh)2]
F net = 15 N
tan = Fv/Fh
 = arctan(Fv/Fh)
 = 53° (north of east)