Transcript Lecture13_AmusemenParkPhysics

You’re twirling a valuable pendant
at the end of a delicate gold chain
when a fragile link snaps off.
Viewed from above,
it snaps at the
position illustrated.
Which of the paths
shown best represents
B
the likely trajectory
of the pendant?
A
The only force acting in this
horizontal plane (gravity pulls
down, of course, but that’s vertically)
was the tension from the chain. With
that gone NO FORCE acts on the
pendant, so it should, of course, move
off in a straight line (continuing
FORWARD).
C
D
E
A force acting FORWARD on a moving object
will increase its speed.
A force acting BACKWARD on a moving object
will decrease its speed.
What will a force acting
NEITHER FORWARD NOR BACKWARD
but perpendicular to the direction of motion
do to a moving object?
Steer it in a new direction
(without changing its speed).
Crash test dummy
seated in
stationary vehicle
Car accelerates:
suddenly lurching
forward
Seat accelerates
forward, compressing
back cushion
against driver
Contents of car
settles into
the moving
frame of the car
At ignition (to), explosive
fuel combustion carries the
rocket from its stationary
position near the space
outpost by producing a
~steady thrust F over the
t seconds of the brief burn.
Select the best graphical representation
of the ship’s speed:
to
to+t
to
to+t
to
to+t
to
to+t
How do you tell when you are completely stopped?
Sitting in class, at “rest” in your seat
you are in fact moving, along with your seat,
the lecture room to which its attached, the building,
and the ground its anchored in…
The swaying of follicles within the fluid of the
chochlea give us our sensation of motion.
But like the hanging fuzzy dice, these only
respond to accelerations, not constant velocity.
The sensations of just how our internal organs
(heart, stomach) normally hang within the
connective tissue that holds it, also change
under accelerations. You DO feel acceleration
in the pit of your stomach!
v0= 8 m/sec
a=g
After the 1st 1/10th of a second
ball has moved out
x  v x t  (8m / s )(0.1 s )  0.8 m
and down
y  gt  (9.8m / s )(0.1s)
1
2
2
2
1
2
 0.049 m
but it has also built vertical speed:
2
v y  (9.8 m / s )(0.1 s )  0.98 m / sec
v0= 8 m/sec
vy = 0.98 m/sec
It has turned!
2
What is YOUR experience
as you sit in a turning car?
Its your own inertia (trying to simply move along
a straight line) that feels like it pushes you out. It’s
the walls pushing inward that hold you in a circle.
Like the car’s fuzzy dice,
hanging outward on these
swings is evidence that you’re accelerating inward!
r
R
The forces (traction between tires and
road) required to complete a turn of
large radius, R, must be ________
the forces needed for a turn of
small radius, r, at the same speed.
A. smaller than
B. greater than
C. exactly the same as
V
v
The forces (traction between tires and
road) required to complete a turn
at high a speed, V, must be
________ the forces needed for
the same turn at slower speed, v.
A. smaller than
B. greater than
C. exactly the same as
Centripetal force:
2
F=
F
Centripetal
acceleration:
2
a=
Turning right on level ground relies entirely on friction
A banked curve let’s the car’s own weight help
negotiate the turn
Center of mass/ center of balance
N
N
Fgrav
Fgrav
N
N
Fgrav
Fgrav
A tricycle provides a large base
and ordinarily a rider’s center of mass
is comfortably within its boundaries.
f
v
But a child’s inertia
can carry them too
easily outside that
bounds on a fast turn.
v
v
Note the low center-of-mass for
riders of a Big Wheel
Recall:
We’ve seen our “equations of motion”
complemented by descriptions of
spinning and rotation:
F
acceleration, a
m/sec2

angular acceleration, 
radians/sec2
or
degrees/sec2
m/sec
(linear) momentum: mv
= constant
(linear) momentum: I
= constant
radians/sec
What helps keep a bicycle steady?

This unicyle is being ridden past you to the left.
By the right-hand-rule, the angular momentum
of the wheel points
A. right. B. left.
C. down. D. up.
E. into the screen.
F. out of the screen.
rotational mass I 
somewhat large since
some body parts are held
out at large distances ri
from the center.
now all body parts
are held in at small
ri from the center.
I11 = I22
 mi ri
2
This motorcyclist is
A. falling down.
B. making a left turn.
C. making a right turn.
f
W
N
f
N
total force
from road
surface on
motorcycle
f
N
The total surface forces are not off-centered at all
so produce no net torque of their own!
But what about the torque gravity applies?
If this wheel started to tip to the left:

This would
be due to
a torque
(applied by
gravity)
By the right-hand-rule, this torque
points in what direction?
A. right. B. left.
C. down. D. up.
E. into the screen.
F. out of the screen.
A torque of course produces a change
in angular momentum:


'
This change
will be in
the direction
of the torque
(out towards
you in this
picture).
the new angular
momentum
What does this mean?
This gyroscopic precession will actually
steer the wheel naturally to the left!
SOME ANSWERS
Question 1
B
The only force acting in the horizontal plane (gravity
pulls down, of course, but that’s vertically) was the
tension from the chain. With that gone NO FORCE
acts on the pendant, so it should, of course, move off
in a straight line (continuing FORWARD).
Question 2
to
Question 3
Question 4
The rocketship will accelerate uniformly
(increasing its speed smoothly and steadily)
as long as the thrust continues. Once the
thrust has vanished, it just coasts. With
No external force, its speed must be constant
(the horizontal line!).
to+t
A. smaller than
B. greater than
A large radius means a slow, gentle turn.
In fact a turn of infinite radius, would be
indistinguishable from no turn at all!
A small radius o curvature means a tight
fast turn. That requires a much bigger
change in velocity, so involves a larger
acceleration!
F. With the fingers of your right hand curled
in the direction of the rotating wheel, your
thumb will point out of the screen.
B. He is leaning to turn to his left.
F. out of the screen.
Sure, the initial angular momentum of the spinning
wheel is to the left. But the torque that’s trying to tip
the wheel is rotating it so that the top of the wheel
falls over to the left…a counter-clockwise twist of the
top over the bottom edge which is against the ground.
The direction a torque twists
is defined by the same righthand rule. When screwing in
an ordinary (right-hand
threaded) screw, with screwdriver in right hand, your
fingers curl in the direction
you’re twisting, and your thumb
points in the direction you’re
driving the screw (the direction
of the torque).