Transcript PHYS160-18S

TODAY’S OUTCOMES:
FORCE, MOTION AND ENERGY
- Review oscillations and friction
- Study several demonstrations that
review the concepts of force, motion and
energy
1. When Miriam and Harold go on trips, they put the map on the passenger-side
dashboard, in case they need to look at it. On their way out of town, the map falls off the
dashboard at every stoplight, just after the light turns green..
(A) Why does the map fall off the dashboard at the stoplights? Discuss the role played
by any of the laws of motion that are relevant.
When the car accelerates forward, the inertia of the map tends to keep it still,
unless the force of friction is strong enough to accelerate it at the same rate
as the car. If the car accelerates too quickly, the friction force isn’t strong
enough to pull the map forward with the car.
(B) Harold says that the maps wouldn’t fall off if Miriam would change her driving
style.
What change is he recommending?
If Miriam would lower the acceleration of the car (by letting up on the gas a
bit), the force of friction of the dashboard on the map would be strong
enough to match the acceleration of the car, and the map would stay put.
FORCES ON A BLOCK PULLED
ACROSS A TABLE AT CONSTANT SPEED
Force of table on block
Friction
Pull on the string
Weight
FORCES ON A BLOCK PULLED
ACROSS A TABLE AT CONSTANT SPEED
Force of table on block
Friction
Pull on the string
Weight
WEIGHT INCREASES
⇒ FORCE OF TABLE INCREASES
⇒ FRICTION INCREASES
⇒ FORCE NEEDED TO PULL
THE BLOCK INCREASES
IF SPEED IS CONSTANT, THESE FORCES ARE BALANCED
FRICTION CAUSES ENERGY
TO LEAVE YOUR SYSTEM
Energy is conserved, but
it can change from measured
potential and kinetic energy
into heat and sound.
Potential energy = Weight
× height
Kinetic energy = 0
Rolling ball not much friction
Potential energy = Weight
× height
Kinetic energy = 0
Sliding box lots of friction
Potential energy = 0
Kinetic energy = ½mv2
= weight × initial height
Potential energy = 0
Kinetic energy = ½mv2
< weight × initial height
energy lost to heat
OSCILLATIONS
Oscillations can be looked at in terms of
force and acceleration, or in terms of
energy.
OSCILLATIONS
Pendulum: Force and Acceleration
weight and tension are
NOT equal and opposite
here, so there is a
net force, and thus an
ACCELERATION
tension
net force
weight
OSCILLATIONS
Pendulum: Force and Acceleration
tension
At the bottom, tension and weight
cancel - no net force
weight
OSCILLATIONS
Pendulum: Force and Acceleration
on the swing upward,
forces become unbalanced
again, net force reappears
tension
net force
weight
Acceleration in a
pendulum is always
toward the central line,
or equilibrium
position (where it would
hang if stationary.)
OSCILLATIONS
Pendulum: Energy
Potential energy is stored
as pendulum is pulled back;
there is no motion or kinetic
energy yet
OSCILLATIONS
Pendulum: Energy
At the bottom, the potential
energy is gone - but speed and kinetic
energy are highest
OSCILLATIONS
Pendulum: Energy
on the swing upward,
the speed and kinetic energy
lower; potential energy is
again stored
OSCILLATIONS
SPRING: Force and acceleration
When the spring is “pulled
back”, the pull from your
hand and the restoring force
are balanced
equilibrium line
“restoring” force
pull from hand
OSCILLATIONS
SPRING: Force and acceleration
When you release, you
remove the force from your
hand - forces are no longer
balanced - restoring force =
the net force
“restoring” force
net force
SPRING ACCELERATES UP
OSCILLATIONS
SPRING: Force and acceleration
no net force
When the spring returns to
equilibrium position, it is
MOVING quickly, but there is
no more restoring force; NO
ACCELERATION at this
instant
OSCILLATIONS
SPRING: Force and acceleration
net force
“restoring” force
When the spring passes the
equilibrium line, the restoring
force pulls the other way
SPRING ACCELERATES DOWN
OSCILLATIONS
SPRING: Energy
When the spring is pulled
down, POTENTIAL ENERGY
is stored in the spring
OSCILLATIONS
SPRING: Energy
As the spring passes the
equilibrium, there is no more
potential energy; but the
speed is maximum, along
with kinetic energy
OSCILLATIONS
SPRING: Energy
As the spring reaches the
other side, it slows, and
kinetic energy again
becomes potential energy
MASS OF SPRING vs. PENDULUM
SPRING
Mass increases, restoring force stays
same; so acceleration decreases
PENDULUM
Mass increases, restoring force
(weight) also increases, so acceleration
stays the same
Frequency does
not depend on mass
Frequency decreases with mass
WHAT YOU ARE EXPECTED TO KNOW:
- Friction can cause energy to decrease in a
measured system.
- Energy changes back and forth between kinetic
energy and potential energy in an oscillating
system
- Increasing mass affects the period of a spring,
but not a pendulum
INSTRUCTIONS FOR TODAY:
1) Find the station assigned to your group
number in your packet. You will do this activity
first, answer questions, and present the results
at the end of class. You will be given 10 minutes
to run through the first activity.
2) You will then rotate around the room to try
out (and complete as much as possible) the
other stations in the room - we will announce a
“switch” every 5 minutes.
3) When all 11 stations are complete, return to
your table and discuss how to summarize your
results in class discussion.
4) We will then rotate the discussion from group
to group as a review.
TODAY’S OUTCOMES:
FORCE, MOTION AND ENERGY
- Review oscillations and friction✓
- Study several demonstrations that
review the concepts of force, motion and
energy
A game you can play is to give a penny a shove so that it slides across a table, trying to get it to stop on a target. You wish to find out
how far the penny will go before it stops, if you give it a certain initial speed. Assume you give the penny an initial speed of
0.5 m/sec, and that the force of friction from the table is about 0.002 N. A penny has a mass of about 4 g = 0.004 kg.
A) This example is an exact analogy to the slowing barge problem you worked on a couple classes ago, except in this case you are
given the force, and have to solve for the distance. label the analogous quantities in these 2 problems. Use a “?” for an unknown
variable.
For example (do the rest yourself!):
mass of barge (100,000 kg) ↔ mass of penny (0.004 kg)
initial speed of barge (10 m/sec) ↔ initial speed of penny (0.5 m/sec)
force on barge (?) ↔ force of friction on penny (0.002 N)
distance in which barge stops (100 m) ↔ distance in which penny stops (?)
final speed of barge (0 m/sec) ↔ final speed of penny (0 m/sec)
B) Use the Laws of Motion to find the acceleration of the penny. Use the acceleration to find how much time it takes for the penny
to stop; from there you can (and should) find the distance the penny moves.
Force = mass × acceleration ⇒ acceleration = Force/mass
acceleration = change in velocity/time ⇒ time = change in velocity/acceleration
average speed = distance/time ⇒ distance = average speed × time
(Remember average speed = ½ × initial speed)