Scalars and Vectors
• Magnitude
– Size or amount (number and unit)
Chapter 5 – Forces in Equilibrium
• What can we say about forces when nothing is
moving?
• How do we account for friction?
• Scalar
– Quantity without direction, only magnitude
• Vector
– Quantity with direction and magnitude
– Useful in giving directions
Vectors
• Force Vectors
Vectors
• Resultant
– Show magnitude and
direction of a force
– Have a Head and a
Tail
– Must use a scale to
show magnitude
• Like making a map
Vectors
• Head to Tail Method
– Used to find resultant
– Line up all vectors so
that the head of one
vector touches the tail
of the other
– Draw from the tail of
the first to the head of
the final vector
– Total of all vectors
– Overall direction and
magnitude of all
forces
Vectors
• Magnitudes of
resultants can be
calculated using the
Pythagorean theorem
a 2 + b2 = c2
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Friction
Friction
• Kinetic Friction
• Friction (Ff)
– Force that resists
motion of objects or
surfaces
– Caused by grinding
between two surfaces
– Depends on both
surfaces in contact
• Ex: puck on ice, puck
on street
– Objects in motion
– Can be rolling, sliding or air
friction
– Can cause objects to stop
motion
– To keep object at constant
speed, applied force must
equal kinetic friction
Friction
• Static Friction
Friction
• Friction
– Keeps objects stationary
– Typically more than kinetic friction
– If force is applied, but object doesn’t move
• Static friction is equal to applied force
– Eventually, motion occurs
• Static friction is less than applied force
Friction
• Normal Force (Fn)
– Force that opposes
weight of an object
– Pushes up on object
– Floors must be able
to provide at least as
much Fn as an
object’s Fg
– Changes with the
surfaces involved
– Also changes with
mass of object
– Heavier object more
friction
Friction
• Coefficient of Friction (μ)
– Unit-less number used to indicate amount of
friction
Ff = μ(Fn)
• Ff – force of friction
• μ – coefficient of friction
• Fn – normal force
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Friction
• Events/Objects that require friction:
– Tires
• Friction to move vehicles
• Tread to remove water and increase
friction
– Brakes
• Friction to slow vehicles
– Walking
– Nails
Free-Body Diagrams
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•
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•
Fa – Applied force
Fg – Gravity (weight)
Fn – Normal Force
Fair – Air resistance
FF –Friction
– Fk – Kinetic, Fs – Static
• FT – String tension
• Fspring – force from a spring
Free-Body Diagrams
• Free-Body Diagram (FBD)
– Shows ALL forces acting on
an object
– Indicates direction and
magnitude of forces
– Usually include weight and
Normal Force
Free-Body Diagrams
• Net Force
– Overall force acting on an object
– Includes magnitude and direction
– Find resultant vector of FBD
Free-Body Diagrams
• Net Force
– To find mass or acceleration from FBD
• Use F = ma
– Ex: A 45 kg skydiver encounters 18 N of air
resistance. What is the diver’s acceleration?
• 9.4 m/s2
Equilibrium
• Equilibrium
– All forces on an object are balanced
• Net force is zero
– No acceleration
• Constant or no speed
– Normal force is equal to weight
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Equilibrium
• Equilibrium
Springs
• Springs
– To solve problems:
1. Draw FBD
2. Find resultant force to balance others
– Coils of metal or
plastic that creates a
force when stretched
or compressed
– Stretching or
compressing
Increases Potential
Energy
Springs
• Spring Constant (k)
– Stiffness of spring
– Measured in N/m
– Higher k
• Harder to
compress/stretch
Springs
• Hooke’s Law
– Ratio between a spring’s
force and the change in
length is constant
F = kx
• F – force applied (N)
• k – spring constant (N/m)
• x – distance stretched (m)
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