Physics 2111
Unit 8
Today's Concepts:
a) Potential Energy
b) Mechanical Energy
Mechanics Lecture 8, Slide 1
Stuff you asked about:
A bit more conceptual analysis with the ball problem would be nice
Dang...I'm really not sure. The Box and Spring problem and the Earth's Gravity problem
kind of left me going "...what?“
The relationships between forces and energy seems to be a little hazy to me.
We got this guy
Go over the earth's gravity problem.
The last checkpoint about 2 balls and Earth's Gravity.
Well i wasn't sure about the earths gravity problem!
I would like more examples of problems changing the U sub naut for potential
The concepts were nice and simple. No Sweat.
Can we go over the problem where a ball is dropped from far away from Earth? Also,
can you write out the meaning of the subscripts of your equations. Thank You.
the spring part of the lecture i found most difficult to understand
Too many equations. id like to go over them
Cover the examples from the pre lecture so we have a change to ask clarifying
questions.
Not sure where negative signs belong when talking about work/energy and
Mechanics Lecture 8, Slide 2
Potential Energy – NOTHING NEW!
Wtot = DKE
WNC + WCON = DKE
WCON = -DPE
WNC -DPE = DKE
WNC =DPE +DKE = DME
Mechanics Lecture 8, Slide 3
Conservative Forces
Force conservative if
𝐹 ∙ 𝑑𝑥 = 0
Examples:
Gravity, Springs
Not Friction!
Mechanics Lecture 7, Slide 4
Example 8.1 (Box on Spring)
10cm
40cm
A 20kg box is placed gently on a
vertical spring which compresses it
10cm. I then compress the spring an
additional 40cm with my hand.
When I release the box and spring,
how high will the box fly?
WNC = 0
 DME = 0
 DPE +DKE = 0
Mechanics Lecture 7, Slide 5
Example 8.2 (Skier)
A skier starts from rest and
goes
down
a
10.4m
long
25
25o slope. The coefficient
of kinetic friction
3.5m
between the skis and the
snow is mk=0.2.
At the end of the slope, he flies off a 3.5m high
cliff.
What is his velocity just before he connects with
the snow at the bottom of the cliff and skis
coolly off for a hot chocolate?
o
Mechanics Lecture 8, Slide 6
CheckPoint
Three balls of equal mass are fired simultaneously with
equal speeds from the same height h above the ground.
Ball 1 is fired straight up, ball 2 is fired straight down,
and ball 3 is fired horizontally. Rank in order from
largest to smallest their speeds v1, v2, and v3 just before
each ball hits the ground.
A) v1 > v2 > v3
B) v3 > v2 > v1
C) v2 > v3 > v1
D) v1 = v2 = v3
2
1
3
h
Mechanics Lecture 8, Slide 7
Example 8.3 (Pendulum)
30o
3m
A pendulum consists of a mass at
the end of a 3 meter long string.
It is held at rest 30o from the
vertical. If it is released, what is
its velocity when the string is
completely vertical?
Mechanics Lecture 7, Slide 8
ACT
A block attached to a spring is oscillating between point x (fully
compressed) and point y (fully stretched). The spring is un-stretched at
point o. At which point is the acceleration of the block zero?
x
o
y
A) At x
B) At o
C) At y
Mechanics Lecture 8, Slide 9
CheckPoint
A box sliding on a horizontal frictionless surface runs into a fixed spring,
compressing it a distance x1 from its relaxed position while momentarily
coming to rest.
If the initial speed of the box were doubled, how far x2 would the spring
compress?
A) x2
 2 x1
B)
x2  2 x1
C)
x2  4 x1
x
Mechanics Lecture 8, Slide 10
Spring Summary
M
kx2
x
Mechanics Lecture 8, Slide 11