Contributed by:
Elevators, Apparent weight, Friction, Pulleys, Free fall, Air drag
1.
Today: (Ch. 3)
Apparent weight
Friction
Free Fall
Air Drag and Terminal Velocity
Tomorrow: (Ch. 4)
Forces and Motion in Two and
Three Dimensions
2.
Elevators
Why do you feel heavier or lighter sometimes
when you are riding in an elevator?
3.
Elevators
There are 5 basic cases in the elevator:
moving up and speeding up
moving up and slowing down
moving down and speeding up
moving down and slowing down
moving up or down at a constant
speed
4.
Apparent Weight
• The normal force is not
always equal to the weight
e.g. in elevator
• Letting upward be positive:
• ΣF = m a = N – mg
N=ma+mg
• If the elevator moved
downward, N = m g – m a
• The normal force is called
the object’s apparent weight
6.
Example
A passenger weighing 598 N rides in an elevator.
The gravitational field strength is 9.8 N/kg. What is
the apparent weight of the passenger in each of the
following situations? In each case the magnitude of
elevator’s acceleration is 0.5 m/s2.
(a)The passenger is on the 1st floor and has pushed
the button for the 15th floor i. e. the elevator is
beginning to move upward.
(b)The elevator is slowing down as it nears the 15 th
floor.
7.
Friction
• Friction can be
– Kinetic
• Related to moving
– Static
• When objects are at rest
• The force of friction opposes the motion
& the magnitude of the frictional force is
related to the magnitude of the normal
force
• Force of kinetic friction
– Ffriction = μk N
– μk is called the coefficient of kinetic
friction
8.
Static Friction
• |Ffriction | ≤ μs N
μs Coefficient of static
– Static indicates that the two
friction
surfaces are not moving
relative to each other
• If the push is increased, the
force of static friction also
increases and again cancels
the force of the push
• The magnitude of the static
friction has an upper limit of
μs N
– The magnitude of the force
of static friction cannot be
greater than this upper limit
9.
Kinetic Friction Vs Static Friction
• Only difference is coefficients of friction
• The force of kinetic friction is just Ffriction = μk N
• Force of static friction given by |Ffriction | ≤ μs N
• For a given combination of surfaces, generally μs
> μk
– It is more difficult to start something moving than
it is to keep it moving once started
10.
Example: Friction and Walking
• The person “pushes” off during each step
• Force exerted by the shoe on the ground : Fon ground
• If the shoes do not slip, the force is due to static friction
– The shoes do not move relative to the ground
• By Newton’s third law Reaction force : Fon shoe
• If the surface was so slippery
that there was no frictional
force, the person would slip
11.
Friction and Rolling
• The car’s tire does not slip
• There
is a frictional force between the tire and road
– Fon ground
• There
is a reaction force on the tire
– Fon tire
12.
Free Fall
• A specific type of motion
• Only gravity acts on the
object
– Some air drag, but it is
generally considered
negligible
• Analyze the motion in
terms of acceleration,
velocity, and position
13.
Free Fall – Acceleration
• t = 0 be the instant after the object is released
• Choose a coordinate system that measures
position as the height y above the ground
• Using Newton’s Second Law:
Fgrav
mg
a g
m m
– The negative sign comes from gravity acting
downward
14.
Free Fall – Velocity and Position
• Velocity and position as functions
of time:
v v o a t v o g t
1 2
y y o v o t a t
2
1
y o v ot g t 2
2
• The motion can be expressed
graphically as well. Note the
constant acceleration
• The velocity and acceleration are
not always in the same direction
15.
Free Fall – Final Notes
• The ball’s speed just before it hits the ground = initial
speed
– The velocities are in opposite directions
• The time spent on the way up is equal to the time
spent falling back down
vo 2v o
tup and t ground
g g
16.
Tension Example – Elevator Cable
• Two forces: Upward
Acceleration
– Gravity acting downward
– Tension in cable acting
upward, T
• Newton’s Second Law gives
T = mg + ma
• Assume massless cable
• Applying Newton’s Second
Law gives: TC = T
• Tension has force units
17.
Cables with Mass
• Newton’s Second Law
• The upper tension, T1 must
be larger than the tension
from the box, T2
• T1 = T2 + mcable g
• If no acceleration
• Can assume a massless
cable if the mass of the
cable is small compared to
the other tensions present
18.
Single & Multiple Pulleys
19.
Air Drag
• Air drag depends on speed & Area, so at higher
speeds and area it becomes more of an effect
• An estimate of air drag can be found by using
– Fdrag = ½ ρ A v2
• A more complete equation is
– Fdrag = ½ CD ρ A v2
– CD is the drag coefficient and depends on the
aerodynamic shape
– CD is 1 for boxy shapes and less than 1 for many
streamlined shapes
20.
Skydiving & Terminal Velocity
• The skydiver will reach
a constant velocity
when Fdrag = Fgrav
– Called the terminal
velocity
2m g
v term
A
21.
Tomorrow: (Ch. 4)
Forces and Motion in Two and Three
Dimensions
22.
Some Problem solving tips
23.
Reasoning and Relationships-Problem
Notes
• We may need to identify important information that is
“missing” from the initial description of the problem
– We need to recognize that additional information
is needed
– Then make reasonable estimates of the “missing”
quantities
• An approximate mathematical solution and an
approximate numerical answer are generally
sufficient
– The estimates of the “missing” values will vary
from case to case
24.
Reasoning and Relationships –
Problem Solving Strategy
• Recognize the principle
– Determine the key physics ideas central to the problem
– What principles connect the quantity you want to calculate
with the quantities you know
• Sketch the problem
– Show all the given information
– Draw a free body diagram, if needed
• Include all the forces, velocities, etc.
• Identify the relationships
– Motion equations are an example of a set of relationships
– If some values are unknown, make estimates for these
values
25.
Reasoning and Relationships –
Problem Solving Strategy, cont.
• Solve
– An exact mathematical solution typically is not
needed
– Cast the problem into one that is easy to
solve mathematically
• Check
– Consider what your answer means
– Check to be sure the answer makes sense
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