Download 2 - UMN Physics home

Final exam info
• Wednesday, May 10
• 1:30 – 4:30 pm in Willey 125
• If there are exam conflicts, please use this link
to let the office know:
• http://goo.gl/forms/Yts4LpTxR0
Some Forms of Energy
Kinetic Energy: energy of motion
A car on the highway has kinetic energy.
Gravitational Energy: energy of gravity.
Heat Energy : Energy of heat.
Elastic Energy : Energy of elasticity.
Electrical Energy : Energy of electricity.
Chemical Energy : Energy of chemistry.
Radiant Energy : Energy of light.
Nuclear Energy : Energy of nuclei.
Mass Energy : relativistic energy of rest mass
???
dark energy
The plan
Schedule (has not changed) !
Homework on chapter 9 is due
this Thursday.
Last homework on Ch 10 is due
next week.
Last lab report is due this Friday.
Lab and discussion sections meet
as usual the last two weeks.
8.3-8.4
9.1-9.2
9.3-9.4
10-Apr
12-Apr
14-Apr
9.5-9.7
REVIEW
Quiz 4
17-Apr
19-Apr
21-Apr
10.1-10.2
10.3-10.4
10.5-10.6
24-Apr
26-Apr
28-Apr
10.7-10.8
REVIEW
REVIEW
1-May
3-May
5-May
Final
exam
10-May
Office hours:
• Since Prof. Glesener is gone, TAs will be
covering her office hours at the usual times:
• Monday 3:45-5:45
• Thursday 1:00-2:00
Chapter 10: Energy
Potential
energy
Kinetic
energy
Some symbols used in this chapter:
•
• What is “work”?
• displacement of object
Work done
Applied force
Angle between
force and
displacement
*this formula only applies in the special case of a constant force.
• ? = @ABCDE
• ; and< aremagnitudes(alwayspositive)
• à Signofworkdependsonthecosineoftheangle.
• Ifforceanddisplacementareinthesamedirection,
theworkaddedtothesystemismaximized.
• (Nowastedeffort)
• Iftheforceisatanangletothedisplacement,then
Wissmaller(someforcewaswasted).
• UnitsareFG,whichwenowdefineasJoules(J)
*this formula only applies in the special case of a constant force.
Work Done by Force at an Angle to Displacement
Ex. 10.2: A strap inclined upward at a 45
degree angle pulls a suitcase through
the airport. The tension in the strap is 20 N. How much work does the tension do
if the suitcase is pulled 100 m at a
constant speed?
Work & Energy
A box is pulled up a rough (µ > 0) incline by a
rope-pulley-weight arrangement as shown below.
How many forces are doing work on the box?
(a) 2
(b) 3
(c) 4
(d) 5
Solution
Draw FBD of box:
N
T
v
Consider direction of
motion of the box
Any force not perpendicular
to the motion will do work:
f
N does no work (perp. to displacement)
T does positive work
f does negative work
mg does negative work
3 forces
do work
mg
Kineticenergy
Kinetic energy
• Energyofanobjectinmotion
• • Relevantquantities:massandvelocity
• Whichonemattersmore?Velocity!
I
H = GKJ
J
• Unitsforenergy:-L
M )
N
à O9 à J (Joule)
Wewillskiprotationalkineticenergy.
Which object has the most kinetic energy?
Ex. 10.5:
A 2-person bobsled has a mass of 390 kg.
Starting from rest, the two racers push
the sled for the first 50 m with a net
force of 270 N.
Neglecting friction, what is the sled’s
speed at the end of the 50 m?
Gravitationalpotentialenergy
• “Stored”energyinanobjectduetoitsheight.
• Whataretheimportantfactors?
• Mass
• Gravitationalstrength
• Howhigh
; = 9LSN = 9Lℎ
Gravitationalforce
Potentialenergy
Theenergyistherebecauseagravitationalforceisbeingapplied.
Question: A ball rests on the table as shown. It has a
mass of 1 kg. What is the potential energy of the ball
with respect to the floor? (g = 10 m/s2 )
A) zero joules
B) 10 Joules
C) -10 Joules
Question: A ball rests on the table as shown. It has a mass of 1 kg.
What is the potential energy of the ball with respect to the floor?
2. 10 Joules
Answer: 2 The ball is 1 meter high relative to the floor.
The potential energy is therefore mgh = (1 kg) (10 m/s^2) (1 m) = 10 Joules.
Question: The ball falls to the floor. What is the
kinetic energy of the ball just before it hits?
A)
B)
C)
D)
E)
F)
zero joules
10 Joules
-10 Joules
20 Joules
Other
Cannot tell
Question: The ball falls to the floor. What is the kinetic energy of the ball
just before it hits?
2. 10 Joules
Answer: 2 The difference between the potential energy at the table and at
the floor is 10 Joules. This is all converted entirely into Kinetic Energy.
Sign o’ the Energy
Can the
A) yes
gravitational
B) no
potential energy
of an object to
be negative?
Sign o’ the Energy
Is it possible for the
gravitational potential
1) yes
2) no
energy of an object to
be negative?
Gravitational PE is mgh, where height h is measured relative
to some arbitrary reference level where PE = 0. For
example, a book on a table has positive PE if the zero
reference level is chosen to be the floor. However, if the
ceiling is the zero level, then the book has negative PE on the
table. It is only differences (or changes) in PE that have any
physical meaning.
• It is the change in gravitational potential
energy that is important!
• You can make your height=0 anywhere. Just
make sure to always measure from that point.
• Pile Driver
Example (prob 16):
The lowest point in Death Valley is 85.0 m
below sea level. The summit of nearby
Mt. Whitney has an elevation of 4420 m.
What is the change in gravitational
potential energy of an energetic 65.0 kg
hiker who makes it from the floor of Death
Valley to the top of Mt. Whitney?
Example: The simple pendulum
l
Suppose we release a mass m from rest distance
h1 above its lowest point.
"
What is the max speed of the mass and where
does this happen?
"
What is height h2 on the other side?
m
h1
h2
v
Example: The simple pendulum
l
Kinetic+potential energy is conserved since gravity is a
conservative force (E = K + U is constant).
l
Choose y = 0 at the bottom of the swing, and U = 0 at y = 0 (arbitrary choice):
E = 1/2mv2 + mgy
y
y=0
h1
h2
v
Example: The simple pendulum
l
E = 1/2mv2 + mgy.
y
y=0
"
Initially, E = mgh1
"
Hence, E = mgh1
.
Example: The simple pendulum
/2mv2 will be maximum at the bottom of the swing.
l
1
l
At y = 0
1
/2mv2 = mgh1
y
y = h1
y=0
h1
v
Example: The simple pendulum
l
The ball returns to its original height.
y
y = h1 = h2
y=0
Stopped Pendulum
Conservation of mechanical energy
The length of a pendulum is shortened in mid swing
by the string hitting a peg placed below the support.
The bob swings to the height from which it was released.
From Galileo Galilei "Dialogues Concerning Two New Sciences" (Leyden, 1638)
Ex. 10.11: While at the county fair, you try the water
slide that starts 9.0 m above the ground. You push off
with an initial speed of 2.0 m/s. If the slide is
frictionless, how fast will you be traveling at the bottom?
Ex. 10.11: While at the county fair, you try the water
slide that starts 9.0 m above the ground. You push off
with an initial speed of 2.0 m/s. If the slide is
frictionless, how fast will you be traveling at the bottom?
Kinetic and potential energy
Three balls are thrown off a cliff with the same speed, but in
different directions. Which ball has the greatest speed just before
it hits the ground?
A. Ball A
B. Ball B
C. Ball C
D. All balls have the same speed
Use the NAA.
QuickCheck
A hockey puck sliding on smooth ice at 4 m/s comes to a 1-m-high hill. Will it make it to the top of the hill?
A.
B.
C.
D.
Yes
No
Can’t answer without knowing the mass of the puck
Can’t say without knowing the angle of the hill