Transcript CSUN PHYSICS WORKSHOP SUMMER 2001 July 9

Reading Quiz
1. Which is true? The gravitational force
between two particles
___ 1. can be shielded by the presence of
an
intervening mass.
___ 2. is inversely proportional to the
distance
between the particles.
___ 3. obeys the law of superposition.
___ 4. is independent of the distance
between
the particles.
2. The gravitational constant G is
___ 1. equal to g at the surface of Earth.
___ 2. different on the Moon than on Earth.
___ 3. obtained by measuring the speed of
falling objects having different
masses.
___ 4. none of the above
3. Which is one of Kepler’s laws?
___ 1. The gravitational attraction of Earth
and the Sun provides a
centripetal
acceleration explaining Earth’s
orbit.
___ 2. The gravitational and inertial
masses of
an object are equivalent.
___ 3. The radial line segment from the
Sun to a planet sweeps out equal
areas in
equal time intervals.
4. Which term was not introduced in
today’s reading assignment?
___ 1. escape velocity
___ 2. perihelion
___ 3. gravitational mass
___ 4. Hubble’s constant
Circular Motion
• Motion with constant speed in a circle - is
the particle accelerated? Why?
• Centripetal acceleration - acceleration due
to change in direction of velocity vector:
(magnitude)
aR  vr2
• Direction - radially inward.
• Centripetal force: force needed to provide
centripetal acceleration - Newton’s 2nd Law
gives magnitude and direction of force:
FR  mvr2
radially inward
Conceptual Questions
1) The game of tetherball is played with a ball tied to
a pole with a string. When the ball is struck, it
whirls around the pole as shown. At this moment,
in what direction is the acceleration of the ball, and
what causes the acceleration?
____ a) up
____ a) gravity
____ b) down
____ b) gravity
____ c) right
____ c) string
____ d) left
____ d) string
____ e) not accelerated
____ e) not needed
2) Suppose you are in a car moving with a
constant speed along a straight road. You
have a pendulum that is hanging freely. If
the car now approaches a curve and makes a
left turn, which way will the bob move?
____ a) left
____ b) right
____ c) up
____ d) forward
____ e) backward
3) Suppose you have a stone tied to a string, and
you swing the stone around (clockwise when
viewed from above) in an almost horizontal circle.
If the string breaks just when the stone is on the
north point of the compass, how does the stone
move subsequently?
____ a) northward, projectile motion
____ b) southward, projectile motion
____ c) eastward, projectile motion
____ d) westward, projectile motion
____ e) south-east, projectile motion
____ f) north-east, projectile motion
4) Consider a particle moving with constant
speed such that its acceleration of constant
magnitude is always perpendicular to its
velocity.
____ a) It is moving in a straight line.
____ b) It is moving in a circle.
____ c) It is moving in a parabola.
____d) None of the above is definitely true all
of the time.
Quantitative Questions
1) A flat puck (mass M) is rotated in a circle on a
frictionless air hockey tabletop, and is held in
this orbit by a light cord which is connected to a
dangling mass (mass m) through the central hole
as shown in the figure below. Find the speed of
the puck in terms of the given quantities.
2) At what minimum speed must a roller coaster be
traveling when upside down at the top of a circle
if the passengers are not to fall out? Assume the
radius of curvature is 8.6 m.
3) A device for training astronauts and jet
fighter pilots is designed to rotate the trainee
in a horizontal circle of radius 10.0 m. If the
force felt by the trainee is 7.75 times her own
weight, how fast is she rotating? How many
revolutions per second is that?
Banking & Centrifuge
• Why do cars skid (in what direction) when
rounding a curve? What provides the force?
• Banking - angling of surface so normal force
provides centripetal force. Examples: banked
roads, velodromes, airplanes & birds.
• Centrifuge - effective “gravity” that can be
used to separate materials with slightly
different characteristics: washer.
• Non-uniform Circular Motion: centripetal
and tangential accelerations.
Conceptual Problems
1) If the bank of a road is designed for a speed of
50 mph, how does the car tend to slip at a speed
of 60 mph?
____ a) not at all
____ b) inwards towards the center of curvature
____ c) outwards away from the center
What (if anything) prevents this from happening?
2) Artificial gravity is produced in a toroidal
space station by having it spinning about its
axis. What direction will “up” be for the
astronauts?
____ a) radially outward
____ b) radially inward
____ c) straight towards the earth
____ d) it is impossible to produce artificial
gravity
3) Two particles of the same size and shape
but different densities are suspended in a
liquid. This is put into an ultracentrifuge.
Which particle will reach the bottom first?
____ a) the denser one
____ b) the less dense one
____ c) they both reach at the same time
____ d) they do not move
Quantitative Problems
1) For a car traveling with speed v around a
curve of radius r, determine a formula for the
angle at which a road should be banked so
that no friction is required.
2) An airplane is flying in a horizontal circle
at a speed of 480 km/h. If its wings are
tilted 40 to the horizontal, what is the
radius of the circle in which the plane is
flying? Assume that the required force is
provided entirely by an “aerodynamic lift”
that is perpendicular to the wing surface.
Newton’s Gravitation
• Every particle in the universe attracts every
other particle with a force that is proportional
to the product of their masses and inversely
proportional to the square of the distance
between them. This force acts along the line
joining the two particles:
mAmB
Fgrav  G
r2
G = universal gravitation constant
mA = mass of first particle
mB = mass of second particle
r = distance between the two particles
• Experimentally verified.
• Responsible for the motion of all the
heavenly bodies. On the cosmic scale, this
is the dominant force.
• Why is acceleration near the surface of the
earth equal to 9.8 m/s2?
Conceptual Question
Where is the gravitational attraction of the
earth greatest?
____ a) at the Poles
____ b) at the equator
____ c) same all over the earth
Quantitative Problems
1) Calculate the acceleration due to gravity on the
moon. The moon’s radius is about 1.74 x 106 m
and its mass is 7.35 x 1022 kg.
2) Determine the mass of the sun. Take the
distance from the sun to be 1.5 x 1011 m.
3) A geo-synchronous satellite is one that stays
above the same point on the equator of the earth.
Such satellites are used for purposes as cable TV
transmission, for weather forecasting, and as
communication relays. What is the height above
the earth’s surface such a satellite must orbit? Do
lower orbit satellites move faster or slower?
Kepler’s Laws of Planetary Motion
• First Law: The path of
each planet about the
sun is an ellipse with
the sun at one focus
• Second Law: Each planet moves so that an
imaginary line drawn from the sun to the
planet sweeps out equal areas in equal
periods of time.
• Third Law: The ratio of the squares of the
periods of any two planets revolving about
the sun is equal to the ratio of the cubes of
their mean distances from the sun:












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


2







TA
rA
r
TB
B
3







Kepler’s Law of Periods for the Solar System
Conceptual Problems
1) According to Kepler’s third law, the time
needed for a planet to go around the sun
____ a) depends on its mass
____ b) depends on the average radius of orbit
____ c) depends on its speed of rotation
____ d) is the same for all the planets
2) The speed of a planet in its elliptical orbit
around the sun
____ a) is constant
____ b) is highest when it is closest to the sun
____ c) is lowest when it is closest to the sun
____ d) varies, but not with respect to its
distance from the sun
3) Satellite 1 is in a certain circular orbit about
a planet, while satellite 2 is in a larger
circular orbit. Which satellite has the longer
period and greater speed?
____ a) satellite 1 and satellite 1
____ b) satellite 1 and satellite 2
____ c) satellite 2 and satellite 1
____ d) satellite 2 and satellite 2
____ e) they have the same period and speed