Transcript L09_Econs - barransclass

Group Work
1. A perfectly elastic ball of mass m collides
with velocity v directly perpendicular into
a rigid, massive wall.
a. What is the direction of the net force on the
ball as it squishes into the wall?
b. What is the direction of the net force on the
ball as it pushes away from the wall?
v
Group Work
1. A perfectly elastic ball of mass m collides
with velocity v directly perpendicular into
a rigid, massive wall.
c. What is the sign of the work done on the ball
as it squishes into the wall?
d. What is the sign of the work done on the ball
as it pushes away from the wall?
Group Work
1. A perfectly elastic ball of mass m collides
with velocity v directly perpendicular into
a rigid, massive wall.
e. If the ball’s initial and final speeds are equal,
what is the net work done on the ball?
Announcements
• Exam 2 Thursday
– impulse, momentum, Newton’s third law,
conservation of momentum, work, kinetic
energy, gravitational potential energy
– Standards 6–9
• First re-do of Standards 2–5 Thursday too
– If you do the practice problems before Wed
Work-Energy Theorem
• The work done on an object by the net
force acting on it is its change in kinetic
energy.
∑F·Dr = DK
Objective
• Calculate the average power necessary to
change an object’s energy by a given
amount in a given time.
Power
Rate of doing work
Power =
DE
Dt
w
=
Dt
DE = change in energy ( = work)
Dt = time interval
Units of Power
Power =
DE
Dt
Energy
= J/s = W = watt
time
kg m2
kg m2
W= 2
=
s s
s3
Group Work
2. The 2004 Tour de France’s Alpe d’Huez
time trial stage was a steep climb with its
finish 1200 m higher than the start. Lance
Armstrong won with a time Dt of 39:41
(2381 s). He and his gear had a combined
mass of 84 kg.
What was Lance’s average power DE/Dt
during the stage?
Hint: Use change in gravitational potential
energy for DE.
Power
A different but equivalent formula
w
Power =
Dt
F·Dd
=
Dt
Dd = change in position
v = velocity
= F·v
Example Problem
Show that (force·velocity) gives the same
units as (work/time).
force units =
velocity units =
work units =
time units =
Conservation of Energy
What’s the point?
• Nature keeps careful account of energy.
Objectives
• Track energy transfers in interactions.
Think Question
Which is greater?
A. The force F1 exerted downward on the lever arm
B. The force F2 exerted upward on the rock
C. They are the same magnitude
Think Question
Which is greater?
A. The distance d1 traveled by the lever arm
B. The distance d2 traveled by the rock
C. They are the same distance
Poll Question
Which is greater?
A. The work done on the lever arm
B. The work done on the rock
C. They are the same
Simple Machines
• Input and output forces can be different
• Trade-off is distance traveled
• Work is unchanged
– work input = work output
Simple Machines
Conservation of Energy
• Energy can be transferred between
objects or transformed into different forms,
but the total amount of energy can never
change.
Convert Potential  Kinetic
Gravity exerts force
mg as object drops
distance h.
work = mgh
PE decreases mgh
KE increases mgh
Source: Griffith, The Physics of Everyday
Phenomena
Conservation of Energy
Source: Griffith, The Physics of Everyday Phenomena
Think Question
The piglet has a choice of three frictionless
slides to descend. Which slide’s path gives
the piglet the greatest change in potential
energy?
A
B
D. Same for all.
C
Think Question
The piglet has a choice of three frictionless
slides to descend. At the end of which slide
will the piglet have the greatest kinetic
energy?
A
B
D. Same for all.
C
Poll Question
The piglet has a choice of three frictionless
slides to descend. Down which slide will the
piglet have the greatest speed at the end?
A
B
D. Same for all.
C
Poll Question
If the slides have friction, with the same m
against the piglet, along which is the force of
friction the greatest?
A
B
D. Same for all.
C
Poll Question
If the slides all have the same m > 0 against
the piglet, along which will friction do the
most (negative) work on the piglet?
A
B
D. Same for all.
C
Poll Question
All three slides have the same m > 0 against
the piglet. Down which slide will the piglet
have the greatest speed at the end?
A
B
D. Same for all.
C
Rebound and Stop
initial v
final v
initial v
final v = 0
Think Question
Which changes its momentum the most?
A. A moving object that stops when it hits a
barrier.
B. A moving object that bounces back from
a barrier.
Hint: Momentum is a vector.
Poll Question
Which changes its kinetic energy the most?
A. A moving object that stops when it hits a
barrier.
B. A moving object that bounces back from
a barrier.
Hint: kinetic energy depends on speed, not
direction.
Inelastic Collisions
• Total kinetic energy decreases.
• Work done against friction and drag:
– is not stored as potential energy
– cannot be recovered as kinetic energy
• Thermal energy increases.
• Energy is conserved!
Reading for Next Time
• Uniform circular motion
• Big ideas:
– Direction of motion changes but speed does
not.
– Acceleration and net force are well-defined,
with a specific direction.