Transcript Announcements! - Classroom Geeks

Announcements!
• Extra credit posted this coming Sunday--get
your team together!
• Mon/Tue-Circular applications of Newton’s
Laws
•Good examples in the book!
• Fuddrucker’s tomorrow (Tuesday) night
•Test this Thursday/Friday--practice test
posted now!
Centripetal Acceleration
An object moving in a circle of
radius r w/ constant speed v has
an acceleration directed toward
the middle of the circle, with a
magnitude
2
ac 

v
r
Centripetal Force!
“Kinematics” = how things move
“Dynamics” = why things move
Objects moving in circles are
accelerating (centripetally), so the
next question is: “What causes
centripetal acceleration?
The answer: centripetal force.
Fcentripetal
Centripetal Force
Centripetal Force = the “center-seeking” force
necessary to keep an object moving in a circle.
It’s important to understand that centripetal force is a
general name used to describe any force(s) that keep
an object moving in a circle, just like we use Fnet
generally to describe the forces that accelerate an
object linearly. The actual forces that make an object
move centripetally are due to things that we’ve already
discussed: FTension for ropes, cords, strings, etc., Fgravity
for graviational force, Ffriction for... friction, and (in
some odd cases) Fnormal, etc.
Centripetal Force
Centripetal Force = the “center-seeking” force
necessary to keep an object moving in a circle.
F
 ma
v
ac 
F
2
r
c
 ma c 
mv
r
2
Example
At the beginning of a hammer throw, a 5 kg mass is
swung in a horizontal circle of 2.0 m radius, at 1.5
revolutions per second. What is the centripetal force
required to keep this object moving in a horizontal
circle? (Ignore the vertical effect of gravity.)
Cool problem
Example: A 1000 kg car on a flat road is traveling at 14
m/s.
a. On a curve of radius 50m, what centripetal force will
be necessary to keep the car on the road?
b. If the µ static for this road is 0.60, will the car make the
turn?
c. If the µ static for the road is 0.20, will the car make the
turn?
d. What is the maximum speed the car can have and still
make the turn?
Advanced Cool Problem
Example: A 1000 kg car on a flat road is traveling at 14
m/s.
d. How high should we bank the turn if we want the car
to be able to stay on with no friction?
How the heck...? Problem
Example: A small body of mass m is suspended from a
string of length L which makes an angle  with the
vertical. The body revolves in a horizontal circle.
Find the speed of the body and the period (time) of
one revolution in terms of L, , and fundamental
constants.
Vertical Circles
Objects that are traveling in
vertical circles are treated
exactly the same as objects
traveling in horizontal
circles: the sum of the
centripetal forces adds up to
allow the object to accelerate
centripetally, and thus, travel
in a circle. (∑Fc=mac)
Vertical Circle
Vertical Circles
One obvious challenge is
that the Tension in the rope
(in this example) is no
longer the only force that is
a factor in the ball’s circular
motion--the force of gravity
now has to be taken into
account.
Vertical Circle
Vertical Circles
Example: A 1.8-kg ball is being
swung in a vertical circle, at
the end of a 1.2-m long rope.
a. What is the minimum velocity
the ball can have at the top of
its circular path?
b. What is the Tension in the
rope as the ball swings past
the bottom of the path at 5.0
m/s?
Vertical Circle
Vertical Circles
a. What is the minimum velocity
the ball can have at the top of
its circular path?
Vertical Circle
Fg
F Tension
Vertical Circles
a. What is the minimum velocity
the ball can have at the top of
its circular path?
Fg
 F c  ma c
F g  FTension  m (
v
mg  0  m (
v
2
)
r
2
)
r
v 
rg 
Vertical Circle
2
(1 .2 m )( 9 .8 m / s )
v  3 .43 m / s
F Tension
Vertical Circles
b. What is the Tension in the
rope as the ball swings past
the bottom of the path at 5.0
m/s?
Vertical Circle
F Tension
Fg
Vertical Circles
b. What is the Tension in the
rope as the ball swings past
the bottom of the path at 5.0
m/s?
Vertical Circle
 F c  ma c
 F g  FTension  m (
v
 mg  FTension  m (
FTension  m (
v
2
)
r
v
F Tension
2
)
r
2
Fg
)  mg
r
FTension  (1.8 kg )(
(5 m / s)
1.2 m
2
2
)  (1.8 kg )( 9.8 m / s )  55 .1N
So... what is centrifugal force?
Centrifugal Force
Centrifugal force is an “apparent”
force--a fake force!--that we
mistakenly think pulls an object
away from the center of the circle.
There is no force pulling the
ball outward!!!
If you’re holding on to the string
attached to the ball while it goes in a
circle, it’s true that your hand feels an
outward pull: this is due to Newton’s
3rd Law (your hand pulls on the ball to
keep it moving in a circle, the ball pulls
back on your hand).
Centrifugal Force
It may help to think about what
happens when we let go of the
string: does the ball go flying
away from the center of the circle,
due to the mysterious, fake,
centrifugal force?
No! It continues to travel in a
straight line from the point where
it was let go.
The fake centrifugal force is due
to ball’s inertia.
Non-Uniform Circular Motion
Earlier, we said that an object moving in a
circle can have radial and tangential
accelerations.
a  at  ar
These obviously result from radial and
tangential forces.

F  Ft  Fr
Calculate the radial and tangential forces
acting on the billiard ball, in terms of m, v, r,
and Ø (angle from vertical).
