Transcript 14.02.03APWeek22CentripetalMotion

AP Physics
Monday 14.02.03
Standards: 1d2 Motion in a
vertical circle (e.g., mass
swinging on the end of a string,
cart rolling down a curved track,
rider on a Ferris wheel.
Warm Up
Find the centripetal Force, the
centripetal acceleration, and the
period of a 5kg ball (radius 0.5m)
being swung through the air by a 5
m long string, if it is traveling at 8
m/s.
Objective: SWBAT solve vertical
circle problems.
Agenda
1. Warm Up
2. Collect HW
3. Vertical Circle Problems
4. HW #C2
Homework
#C2
Lab Write Up
AP Physics
Tuesday 14.02.04
Standards:
F4b determine strength of
gravitational force outside a
mass.
Objective: SWBAT solve
gravitational force problems.
Agenda
1. Warm Up
2. Review Homework
3. Gravitation Notes
4. Gravitation Practice
5. Gravitation Guided Practice
Warm Up
An astronaut in an orbiting
space craft attaches a mass m
to a string and whirls it around
in uniform circular motion. The
radius of the circle is r, the
speed of the mass is v, and the
tension in the string is F. If the
mass, radius , and speed were
to all double, the tension
required to maintain uniform
circular motion would be...
A) F/2 B) F C) 2F D) 4F E) 8F
Homework
C#3
AP Physics
Wednesday 14.02.05
Standards: Derive Kepler’s Third Law for
the case of circular orbits.
Objective: SWBAT derive Kepler’s third
Law
Agenda
1. Warm Up
2. Review HW
3. Read Kepler’s 3rd Law
4. Circular Orbits
5. C#5
Warm Up
A person weighing 800 N on
Earth travels to another planet
with twice the mass and twice
the radius of Earth. The
person’s weight on this other
planet is most nearly.
A) 400 N B)800/√2 C)800N
D)800√2 E) 1,600N
Homework
C#5
Equations Quiz Friday
AP Physics
Thursday 14.02.06
Standards: Determine the strength of
the gravitational field at a specified point
outside a spherically symmetrical mass.
Objective: SWBAT solve problems
involving Gravitational Fields
Agenda
1. Warm Up
2. Review HW
3. Gravitational Fields
4. Gravitational Field Practice
Warm Up
29. A hypothetical planet orbits a star with
mass one-half the mass of our sun. The
planet’s orbital radius is the same as the
Earth’s. Approximately how many Earth
years does it take for the planet to
complete one orbit?
(A) 1/2 (B) 1/√2 (C) 1 (D) √2 (E) 2
Homework
C#6
Equations Quiz Friday
AP Physics
Friday 14.02.07
Standards: F2 b
Apply the expression of the
period of oscillation of a mass
on a spring.
Warm Up
Find the gravitational field that I produce
when I curl up in a ball and my mass is
68kg and my average radius is 0.5m?
Objective: SWBAT
demonstrate understanding of
the motion of an oscillating
spring through problem
solving.
Agenda
1. Warm Up
2. Review HW
3. Equations Quiz
4. Mass on a spring Notes
5. Mass on a spring guided practice.
Homework
C#7
Centripetal Motion C#1
A. Fc=?
m=20kg
r=40m
v=5m/s
1.
2.
B. Fc=40N
m=4kg
r=40m
v=?
C. Fc=40N
m=2kg
r=6m
T=?
(A6)In 1995, Cathy Marsal of France cycled 47.112 km in 1.000
hour. Calculate the magnitude of the centripetal acceleration of
Marsal with respect to Earth’s center. Neglect Earth’s rotation,
and use 6.37x103 km as Earth’s radius.
(B5) In 1992, a team of 12 athletes from Great Britain and Canada
rappelled 446 m down the CN Tower in Toronto, Canada. Suppose
an athlete with a mass of 75.0 kg, having reached the ground,
took a joyful swing on the 446 m-long rope. If the speed of the
athlete at the bottom point of the swing was 12 m/s, what was
the centripetal force? What was the tension in the rope? Neglect
the rope’s mass.
Vertical Circular Motion Guided Practice.
A roller coaster spins its riders in a circular loop of radius 12m. If
the cart full of riders is 4000 kg and the tangential velocity is 30
m/s, find the force that the tracks must put on the cart to keep it
in a circle at the top of the track and at the bottom of the track?
(Free Body Diagrams are required!)
Centripetal Motion C#3
a. Horizontal Circle
Fnet=?
Fc=?
m=2kg
v=8m/s
r=4m
ac=?
b. Vertical Circle
Fnet=?
Fc=?
FT (top)=?
FT (bottom)=?
m=2kg
v=8m/s
r=4m
ac?
• 1 (28.) A 4.0 kg mass is attached to one end of a rope 2 m long. If the
mass is swung in a vertical circle from the free end of the rope, what
is the tension in the rope when the mass is at its highest point if it is
moving with a speed of 5 m/s? (A) 5.4 N (B) 10.8 N (C) 21.6 N (D) 50
N (E) 65.4 N
• 2(29.) A ball of mass m is fastened to a string. The ball swings at
constant speed in a vertical circle of radius R with the other end of
the string held fixed. Neglecting air resistance, what is the difference
between the string’s tension at the bottom of the circle and at the
top of the circle? (A) 1·mg (B) 2·mg (C) 4·mg (D) 6·mg (E) 8·mg
Centripetal Motion Lab
Objective: Create a graph whose slope is acceleration due to gravity
and is equal to g. Compare this value to g=9.80 m/s2 using % error.
r
1. Write a procedure.
m1
2.. Fill in the table below:
Trial
mball
mclip
(kg)
(kg)
mw
(kg)
total
time
(s)
# rev
T(s)
rstr+ba
v
ll (m)
(m/s)
F(N)
v2/r
(m/s2)
1
2
3
3. Graph F vs. v2/r (the right 2 columns), find the best fit line,
the slope, and the equation of the line.
F(N)
binder clip
m2
mtotal (kg)
4. slope = acceleration due to gravity of the ball, so we will compare the acceleration due to
gravity with our measured value to find its accuracy
g
-g
%error =|
actual
measured
gactual
| x100%
Gravitational Force Guided Practice.
The sun has a mass of 2.0x1030kg and a radius of
7.0x105km. What mass must be located at the sun’s
surface for a gravitational force of 470N to exist between
the mass and the sun?
Gravitational Force
Practice C#4
A. Fg=?
m1=40kg
m2=20kg
r=3x105m
B.
Fg=4x1040N
m1=8x1035 kg
m2=4x1030kg
r=?
1.Deimos, a satellite of Mars, has an average radius of 6.3 km. If the
gravitational force between Deimos and a 3.0 kg rock at its surface is
2.5x10-2N, what is the mass of Deimos?
2. A 3.08x104kg meteorite is on exhibit in New York City. Suppose this
meteorite and another meteorite are separated by 1.27x107m (a
distance equal to the Earth’s average diameter). If the gravitational
force between them is 2.88x10-16N, what is the mass of the second
meteorite?
3. Jupiter, the largest planet in the solar system, has a mass 318 times
that of Earth and a volume that is 1323 times greater than Earth’s.
Calculate the magnitude of the gravitational force exerted on a 50.0 kg
mass on Jupiter’s surface. Volume=4/3πr3
Guided Practice: Kepler’s 3rd Law
• A satellite in geostationary orbit rotates at exactly the
same rate as Earth, so the satellite always remains in the
same position relative to Earth’s surface. the period of
Earth’s rotation is 23 hours, 56 miutes, and 4 seconds.
What is the altitude of a satellite in geostationary orbit.
Kepler’s 3rd Law C#5
1. m2=4x1021
r=4x106m
T=?
1.
2.
3.
1. m2=?
r=4x1020m
T=5 years
2. Derive Kepler’s 3rd Law
from the concepts of
Gravitational Force &
CentripetalForce
(1) The period of Mars’ rotation is 24 hours, 37 minutes, and 23
seconds. At what altitude above Mars would a “Mars-stationary”
satellite orbit?
(4,5) Earth’s moon orbits the Earth at a mean distance of
3.84x108m. What is the moon’s orbital speed? What is the
moon’s orbital period. Use your book to find the mass of the
earth and moon if required.
The asteroid (45) Eugenia has a small moon named S/1998(45)1.
The moon orbits Eugenia once every 4.7 days at a distance of
1.19x103km. What is the mass of (45) Eugenia?
C#6 Gravitational Fields
a. g=ag=?
m=3x1019kg
r=1.5x105m
b. Fg=400 N
mplanet=3x1019kg
mshuttle=4x104kg
g=ag=?
c. g=ag=4 m/s2
m=?
r=6x1011 m
1 (5.) Mars has a mass 1/10 that of Earth and a diameter 1/2 that of
Earth. The acceleration of a falling body near the surface of Mars is
most nearly (A) 0.25 m/s2 (B) 0.5 m/s2 (C) 2 m/s2 (D) 4 m/s2 (E) 25 m/s2
2. (9.) The planet Mars has mass 6.4 x1023 kilograms and radius 3.4 x
106 meters. The acceleration of an object in free-fall near the surface
of Mars is most nearly (A) zero (B) 1.0 m/s2 (C) 1.9 m/s2 (D) 3.7 m/s2 (E)
9.8 m/s2
3. (30.) A hypothetical planet has seven times the mass of Earth and
twice the radius of Earth. The magnitude of the gravitational
acceleration at the surface of this planet is most nearly (A) 2.9 m/s2 (B)
5.7 m/s2 (C) 17.5 m/s2 (D) 35 m/s2 (E) 122 m/s2
Force & Energy in Springs Guided Practice
The pygmy shrew has an average mass of 2.0 g. If 49 of these
shrews are placed on a spring scale with a spring constant of 24
N/m, what is the springs displacement? How much energy is
stored in the spring?
C#7 Force & Energy in Springs.
a. Object hanging on spring
Fsp=?
Fnet=?
ms=20 kg
k=10 N/m
x=?
Usp=?
1.
2.
b. Object hanging from elastic band
Fnet=?
Fsp=?
ms=5 kg
k=?
x=2 m
Usp=?
(1) The largest meteorite of lunar origin reportedly has a mass of
19 g. If the meteorite is placed on a sale whose spring constant is
83 N/m, what is the compression of the spring? How much
energy is stored in the spring through its compression?
(3) The largest tigers, and therefore the largest members of the
cat family, are the Siberian tigers. Male Siberian tigers are
reported to have an average mass of about 389 kg. By contrast, a
variety of very small cat that is native to India has an average adult
mass of only 1.5 kg. Suppose this small cat is placed on a spring
scale, causing the spring to be extended from its equilibrium
position by 1.2 mm. How far would the spring be extended if a
typical male Siberian tiger were placed on the same scale? How
much more energy will be stored in the spring with the Tiger than
with the cat?
AP Weekly Equations Quiz 1
1. List correctly two equations used to describe the motion
objects in elastic and inelastic collisions.
2. List correctly two equations used to find the motion of a
satellite around a star.
3. List correctly two equations used to find the period of an
object spinning in circles on a massless string.