Download Physics 1422 - Introduction

Physics 203 – College Physics I
Department of Physics – The Citadel
Physics 203
College Physics I
Fall 2012
S. A. Yost
Chapter 5
Circular Motion,
Universal Gravitation
Physics 203 – College Physics I
Department of Physics – The Citadel
Announcements
Chapter 4’s homework, HW04, was due today.
Chapter 5’s homework, HW05, is due next Tuesday.
Read Chapter 5, except the last section “Nonuniform
Circular Motion” for Thursday.
Today we will do an inclined plane problem in class,
then look at circular motion.
Physics 203 – College Physics I
Department of Physics – The Citadel
Quiz: Question 1
Which of the following is the frictional force on a
sliding object always proportional to?
(a) the contact surface area
(b) its weight
(c) the normal force
(d) the contact pressure
Physics 203 – College Physics I
Department of Physics – The Citadel
Quiz: Question 2
For a given object on a surface, which is larger?
(a) the coefficient of kinetic friction
(b) the coefficient of static friction
(c) Neither, they are equal.
(d) Either could be larger, depending on the object.
Physics 203 – College Physics I
Department of Physics – The Citadel
Quiz: Question 3
A rocket of mass m is near earth,
accelerating into space, as its
engines produce a thrust of Fth.
The rocket is propelled upward by
(a)
(b)
(c)
(d)
(e)
the force of the rocket on the earth.
the force of the earth on the rocket.
the force of the rocket on its exhaust.
the force of the exhaust on the rocket.
the force of the rocket exhaust on
empty space.
a
Physics 203 – College Physics I
Department of Physics – The Citadel
Quiz: Question 4
A rocket of mass m is near earth,
accelerating into space, as its
engines produce a thrust of Fth.
The force of the rocket on the
earth at this time is
(a) Fth downward
(b) Fth upward
(c) mg downward
(d) mg upward
(e) zero
a
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane
3m
A block slides down
the inclined plane
shown, starting at
the top. How long
does it take to reach
the bottom?
4m
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane
Fnet = ma
N
Fnet = mg sin q = 3/5 mg
a = 3/5 g = 5.88 m/s2
Time to reach bottom…
x = ½ a t2
q
Fnet
mg q
sin q = 3/5
5 m = (2.94 m/s2) t2
t = 1.3 s.
a = g/5 = 1.96 m/s2
Physics 203 – College Physics I
Department of Physics – The Citadel
Uniform Circular Motion
In uniform circular motion,
and object goes around
the circumference at
constant speed.
Which way does the
velocity vector point?
It is always tangential to the
path.
→
R
→
v
Physics 203 – College Physics I
Department of Physics – The Citadel
Uniform Circular Motion
The circle has radius R.
If the period is T, what is
the magnitude of the
velocity vector?
It is the length the radius
vector traces out divided
by the period:
v = 2pR/T.
→
v
→
R
Physics 203 – College Physics I
Department of Physics – The Citadel
Uniform Circular Motion
What is the direction of the
acceleration vector?
The speed is constant, so
the component of
acceleration in the
direction of motion must
be zero.
→
→
a is perpendicular to v.
→
→
a points inward, since v →
a is called the
turns that way.
→
v
→
R
→
a
centripetal acceleration.
Physics 203 – College Physics I
Uniform Circular Motion
What is the magnitude of
the acceleration?
Each revolution, the
velocity vector traces out
a circle of radius 2pv.
Department of Physics – The Citadel
→
v
→
v
→
R
→
a
Then a = 2pv/T.
Recall that T = 2pR/v.
Then a = v2/R.
Physics 203 – College Physics I
Department of Physics – The Citadel
Force in Uniform Circular Motion
From the fact that there is acceleration directed
toward the center of a circle in uniform circular
motion, we can infer that the net force on the
object is F = ma , also directed →
toward→the
center of the circle.
Note! This is not a new force due to the
circular motion. It is the result of all of the
forces acting on the object together.
Physics 203 – College Physics I
Department of Physics – The Citadel
Circular Motion
If you twirl an object around your head on a
string and then let go, which way does it
travel?
(a)
(b)
view from above
(c)
Physics 203 – College Physics I
Department of Physics – The Citadel
Roller Coaster
A roller coaster car goes
over a hill with radius of
curvature R at speed v.
How fast must it go for
the riders to feel
weightless at the top?
v
R
Note: it is ok that the motion isn’t uniform –
it’s the instantaneous speed and radius
that matter.
Physics 203 – College Physics I
Department of Physics – The Citadel
Roller Coaster
Feeling “weightless” means there is no
contact force between the rider and car:
FN = 0
Gravity must be responsible for the entire
centripetal acceleration:
mg = mv2/R
g = v2/R.
v = √ g/R
→
FN
→
mg
Physics 203 – College Physics I
Department of Physics – The Citadel
Conical Pendulum
A 120 g mass hanging from a
string of length 1.50 m swings in
a circle of radius 24 cm.
a) What is the direction of the net
force on the mass?
Toward the center.
b) Find the tension in the string
and the period of revolution.
→
Fnet
R = 0.24 m
Physics 203 – College Physics I
Department of Physics – The Citadel
Conical Pendulum
The net force is F = mv2/R.
What forces are responsible for
the net force?
→
→
→
Fnet = T + mg.
→
→
Use F = ma, separated into
horizontal and vertical
components.
→
FT
→
Fnet
R = 0.24 m
→
mg
Physics 203 – College Physics I
Department of Physics – The Citadel
Vertical Circular Motion
A mass is rotated at
constant speed in
a vertical circle on
the end of the rod.
Which vector(s)
could correctly
show the force of
the rod on the
mass?
A
B
C
D
Physics 203 – College Physics I
Department of Physics – The Citadel
Vertical Circular Problem
Suppose the mass is
1.5 kg and the rod is
35 cm long. If the
rod is tilted at
q = 30o with respect
to the horizontal,
and it is spinning
around at 200 rpm,
what is the force of
the rod at this
instant?
Fr
Fc
q
Fg