Transcript sp211_lecturedemo1x

SP211 Lecture Demo 1 (Fall 2016)
Demo #1: Ring Dance
Most of the topics
in this course
require fluency
with vectors.
It is worth your
while to master the
basics!
Demo #2: Falling Sinkers
  
 2
1
r  r0  v0t  2 at
y
For an object dropped from rest from a
height h, we have for the y-component,
0  h  0  gt
1
2
x
g t  2
hn 
n
2
2
2
hang
For equal time intervals,
t hang  nt
where n = 1, 2, 3, 4, 5…
Demo #3: Drafting Coffee Filter
y
If air drag can be eliminated as a significant
contributing force,
Fnet y  ma y
(mg )  ma y
x
Olympic cyclist
John Howard hits
152.2 MPH
July 20, 1985
Bonneville Salt Flats, UT
Demo #4: Coffee Filter Races
When it reaches terminal velocity …
Fdrag
Fnet y  ma y
Linear model of air drag,
mg  bvterminal  0
x
Quadratic model of air drag,
mg  CAv
1
2
mg
2
terminal
0
y
In each case, how do we need to change the mass
to double the terminal speed?
Demo #5: Cannon barrel points up,
cannon moves right.
Keep x and y component analyses separate!
These equations describe the
x-component of both the
cannon and the cannonball.
y
ax  0
vx  constant
x
Demo #6: Shoot the Bear
y
ybear  h  gt
1
2
The line of sight
intersects the y
axis at y = h.
h
vi
2
Distance fallen
below the line
of sight.
ybullet  v0 sin(  )t  gt
1
2

x
Straight line trajectory
along line of sight
2
Demo #7: Carts exert forces on one
another that are equal in size, opposite in
direction (Newton’s 3rd Law).
FAB  mAaA
FBA  mB aB
(Newton’s 2nd Law)
Constant velocity with
zero net force
(Newton’s 1st Law).
m A aB vB d B



Result:
mB a A v A d A
Demo #8a: Slowly Increasing Tension
Newton’s 2nd Law,


Fnet  ma
FT1
Statics:

Fnet  0
mg
FT 2
• As we slowly increase
the tension in the
lower string, the
tension in the upper
string slowly grows as
well.
• The tension in the
upper string will reach
breaking point first!
Demo #8b: A very quick snap.
FT1
Mg
• What happens to the upper string for it
to exert a tension force?
• Can we quickly create breaking-point
tension in the lower string before the
upper string has a chance to stretch to
breaking point?
• Maybe! If M is large then a is small,


Fnet  Ma
FT2
Thinking Carefully about
Newton’s 2nd Law
Demo #9: With 5N on each of the end
scales, what will the middle scale read?
Hint: How can the end scales read ‘5N’
yet not be accelerating?
(Visualize force diagrams for each scale.)
Thinking Carefully about
Newton’s 2nd Law
Demo #10: When I release the slinky
from the top, describe the motion of
the bottom few turns of the slinky.
Hint: Visualize a force diagram for
the last link of the slinky. Just think
about that last link, keep your focus a
local one!
Demo #11: Free-Body Diagrams
FN
Newton’s
2nd
Fpeg
Fpeg
Law,


Fnet  ma

Statics: a  0

Fnet  0
FN
mg
mg
Demo #12: Bucket of water.
Isolate the water as an object,
v
Fnet x  ma x
2
where a x   a  v / R
a
FN  mg  m(v / R)
mg
2
The normal force here is
the downward force
exerted on the water by the
floor of the bucket.
FN
x
Demo #13: Model of kinetic friction.
f k  k FN
•Proportional to the normal force.
•Independent of sliding speed.
•Independent of the macroscopic
area of contact.
Demo #14: No normal force when
the books are in free fall!
Tip: Let Newton’s 2nd Law tell you
what the normal force has to be.
How hard a surface pushes depends
on the situation!
Demo #15: Table cloth and dishes.
Only kinetic friction in the
horizontal direction, and
not for long!