the mass of the planet Saturn, physics homework help

home work
PHY 205 Home Work #2 (due 9.1.16)
1. The mass of the planet Saturn (Fig.
P1.2) is 5.64 × 1026 kg, and its radius is
6.00 × 107 m. Calculate its density.
Figure P1.2
3. Iron has molar mass 55.8 g/mol. (a)
Find the volume of 1 mol of iron. (b) Use the
value found in (a) to determine the volume of
one iron atom. (c) Calculate the cube root of the
atomic volume, to have an estimate for the
distance between atoms in the solid. (d) Repeat
the calculations for uranium, finding its molar
mass in the periodic table of the elements in
Appendix C.
4. The radius r of a circle inscribed in any
triangle whose sides are a, b, and c is given by
r = [(s – a)(s – b)(s – c)/s]1/2
where s is an abbreviation for (a + b + c)/2.
Check this formula for dimensional consistency.
5. The period T of a simple pendulum is
measured in time units and is described by
T2
g
where l is the length of the pendulum and g is
the free-fall acceleration in units of length
divided by the square of time. Show that this
equation is dimensionally correct.
6. A creature moves at a speed of 5.00
furlongs per fortnight (not a very common unit
of speed). Given that 1 furlong = 220 yards and
1 fortnight = 14 days, determine the speed of
the creature in meters per second. What kind of
creature do you think it might be?
7. A quart container of ice cream is to be
made in the form of a cube. What should be the
length of each edge in centimeters? (Use the
conversion 1 gal = 3.786 L.)
8. An astronomical unit (AU) is defined as
the average distance between the Earth and
the Sun. (a) How many astronomical units are
there in one lightyear? (b) Determine the
distance from the Earth to the Andromeda
galaxy in astronomical units.
9. The amount of water in reservoirs is
often measured in acre-feet. One acre-foot is a
volume that covers an area of 1 acre to a depth
of 1 ft. An acre is an area of 43 560 ft2. Find the
volume in SI units of a reservoir containing 25.0
acre-ft of water.
10. McDonald’s sells about 250 million
packages of French fries per year. If these fries
were placed end to end, estimate how far they
would reach.
11. Suppose that someone offers to give
you $1 billion if you can finish counting it out
using only one-dollar bills. Should you accept
this offer? Assume you can count one bill every
second, and be sure to note that you need
about 8 hours a day for sleeping and eating and
that right now you are probably at least 18
years old.
12. Determine the number of significant
figures in the following measured values: (a) 23
cm (b) 3.589 s (c) 4.67 × 103 m/s (d) 0.003 2 m.
13. When a droplet of oil spreads out on a
smooth water surface, the resulting “oil slick” is
approximately one molecule thick. An oil droplet
of mass 9.00 × 10–7 kg and density 918 kg/m3
spreads out into a circle of radius 41.8 cm on
the water surface. What is the diameter of an oil
molecule?
14. As a child, the educator and national
leader Booker T. Washington was given a
spoonful (about 12.0 cm3) of molasses as a
treat. He pretended that the quantity increased
when he spread it out to cover uniformly all of a
tin plate (with a diameter of about 23.0 cm).
How thick a layer did it make?
2. How many grams of copper are required
to make a hollow spherical shell having an inner
radius of 5.70 cm and an outer radius of 5.75
cm? The density of copper is 8.92 g/cm3.
home work #2
Chapter 2: Summary
Position is the location of an object relative to a reference point
called the origin, and is specified by the use of a coordinate system.
Displacement is a measure of the change in the position of an
object. It includes both the distance between the object’s starting
and ending points, and the direction from the starting point to the
ending point. An example of displacement would be “three meters
west” or “negative two meters”.Similarly, velocity expresses an object’s speed and direction, as in
“three meters per second west.” Velocity has a direction. In one
dimension, motion in one direction is represented by positive
numbers, and motion in the other direction is negative.An object’s velocity may change while it is moving. Its average
velocity is its displacement divided by the elapsed time. In contrast,
its instantaneous velocity is its velocity at a particular moment. This
equals the displacement divided by the elapsed time for a very small
interval of time, as the time interval gets smaller and smaller.
Acceleration is a change in velocity. Like velocity, it has a direction
and in one dimension, it can be positive or negative. Average
acceleration is the change in velocity divided by the elapsed time,
and instantaneous acceleration is the acceleration of an object at a
specific moment.
There are four very useful motion equations for situations where the
acceleration is constant. They are the last four equations shown on
the right.Free-fall acceleration, represented by g, is the magnitude of the
acceleration due to the force of Earth’s gravity. Near the surface of
the Earth, falling objects have a downward acceleration due to
gravity of 9.80 m/s2.
WE DO
1. A toddler has become lost in the forest and her father is trying to
retrieve her. He is currently located to the north of a large tree and
he hears her shouts coming from the south. Do we know from this
information whether the toddler is north or south of the tree?
Yes No
Anita and Nick are playing tug-of-war near a mud puddle. They
are each holding on to an end of a taut rope that has a knot
exactly in the middle. Anita's position is 6.2 meters east of the
center of the puddle and Nick's position is 3.0 meters west of the
center of the puddle. What is the location of the knot relative to
the center of the puddle? Treat east as positive and west as
negative.
A slug has just started to move straight across a busy street in Littletown that is 8.0 meters wide, at a
constant speed of 3.3 millimeters per second. The concerned drivers on the street halt until the slug
has reached the opposite side. How many seconds elapse until the traffic can start moving again?
1
The velocity versus time graph for a pizza delivery driver who is frantically trying to deliver a pizza
is shown. (a) During what time interval is he traveling at a constant velocity? (b) During what time
interval is his acceleration 5.0 m/s2? (c) During what time is his acceleration negative?
An elevator manufacturing company is stress-testing a new elevator in an airless test shaft. The
elevator is traveling at an unknown velocity when the cable snaps. The elevator falls 1.10 meters before
hitting the bottom of the shaft. The elevator was in free fall for 0.900 seconds. Determine its velocity
when the cable snapped. As usual, up is the positive direction. (3.19 m/s)
YOU DO #2 (due 9.1.16)
1.
A space shuttle sits on the launch pad for 2.0 minutes, and then goes from rest to 4600 m/s in 8.0
minutes. Treat its motion as straight-line motion. What is the average acceleration of the shuttle (a)
during the first 2.0 minutes, (b) during the 8.0 minutes the shuttle moves, and (c) during the entire 10
minute period?
The velocity of a butterfly is shown. For the
entire time interval, is the displacement of
the butterfly positive, negative, or zero?
Explain.
homework #3 summary
Summary: Work, Energy and Power
Work is the product of the force on an object and its
displacement in the direction of that force. It is a scalar
quantity with units of joules (1 J = 1 kg·m2/s2).
Work and several other scalar quantities can be computed by
taking the dot product of two vectors. The dot product is a
scalar equal to the product of the magnitudes of the two
vectors and the cosine of the angle between them. Loosely, it
tells you how much of one vector is in the direction of
another.
Energy is a property of an object or a system. It has units of
joules and is a scalar quantity. Energy can transfer between
objects and change forms. Work on an object or system will
change its energy.
One form of energy is kinetic energy. It is the energy
possessed by objects in motion and is proportional to the
object's mass and the square of its speed.
The work-kinetic energy theorem states that the work done
on a particle or an object modeled as a particle is equal to its
change in kinetic energy. Positive work increases the energy,
while negative work decreases it.
Power is work divided by time. The unit of power is the watt
(1 W = 1 J/s), a scalar quantity. It is often expressed as a rate
of energy consumption or output. For example, a 100-watt
light bulb converts 100 joules of electrical energy per second
into light and heat.
Another form of energy is potential energy. It is the energy
related to the positions of the objects in a system and the
forces between them. Gravitational potential energy is an
object's potential energy due to its position relative to a body
such as the Earth.
Forces can be classified as conservative or non-conservative.
An object acted upon only by conservative forces, such as
gravitational and spring forces, requires no net work to return
to its original position. An object acted upon by non-
conservative forces, such as kinetic friction, will not return to
its initial position without additional work being done on it.
When only conservative forces are present, the work to move
an object between two points does not depend on the path
taken. The work is path independent. When non-conservative
forces are acting, the work does depend on the path taken,
and the work is path dependent.
When work is being done by a conservative force within a system, the force can be calculated as the
negative of the derivative of the potential energy curve with respect to displacement.
The law of conservation of energy states that the total energy in an isolated system remains constant,
though energy may change form or be transferred from object to object within the system.
Mechanical energy is conserved only when there are no non-conservative forces acting in the system.
When a non-conservative force such as friction is present, the mechanical energy of the system
decreases. The law of conservation of energy still holds, but we have not yet learned to account for the
other forms into which the mechanical energy might be transformed, such as thermal (heat) energy.
We Do
An airline pilot pulls her 12.0 kg rollaboard suitcase along the ground with a force of 25.0 N for 10.0
meters. The handle she pulls on makes an angle of 36.5 degrees with the horizontal. How much work
does she do over the ten-meter distance? (210J)
Vector v has a magnitude of 44 m and vector u has a magnitude of 77 m. The angle between v and u
is 150°. What is v·u? ( -2.9e+3 m2)
The magnitude of u is 5.0, the magnitude of v is 7.0 and u·v is 28. What is the angle between u and
v? Choose the positive solution between 0 and 180 degrees. (37°)
You are about shoot two identical cannonballs straight up into the air. The first cannonball has 7.0
times as much initial velocity as the second. How many times higher will the first cannonball go
compared to the second? ( 49 times higher)
You Do (Due 9.29.16)
The graph shown describes a certain force
that is exerted on an object, as a function of
the position of the object. How much work
is done by this force as the object moves
from the position 0.0 m to 6.0 m? (5.0 J)
Let the Sun, with mass M = 2.0×1030 kg, be
fixed at the origin. For a comet with mass m = 8.0×1013 kg that lies on the positive x axis, the
attractive force of gravity felt by the comet is F = −GMm/x 2. G is a constant with the value
6.67×10−11 N·m2/kg2. How much work does the Sun do on this comet as it moves from a
distance of 7.8×1010 m to 1.5×1010 m? (5.7e+23 J)
A horizontal net force of 75.5 N is exerted on a 47.2 kg sofa, causing it to slide 2.40 meters
along the ground. How much work does the force do? (181 J)
Fritz Strobl thrilled the world when he won the gold medal in the Salt Lake City games of
2002 in a daring run down an alpine skiing course. The course had a vertical drop of 880
meters. Assume his highest speed was 140 km/h, and that he was moving at that speed at the
end. (a) How fast would he have been moving if he could have "ignored" forces like air
resistance and friction? (b) How much energy did he lose to forces like air resistance,
friction, and so forth (assume his mass is 80 kg, and express the answer as a positive
number)? ((a) 131 m/s(b) 6.3e+5 J)
The diagram shows a map of a local cross country ski
area. You are starting at the lodge, marked as point A
on the map, and want to go to point B. How much work
is required to get to point B given the following
information:
1) To go from D to E requires −300 J of work.
2) To go from D to G requires 200J of work.
3) To go from A to G requires 400J of work.
4) To go from B to E requires −200 J of work. (100 J)
A motor lifts a 70.0 kg box off the ground, starting from rest. In 8.00 seconds it lifts the box
to a height of 20.0 m. At that time, the box is moving upward with a velocity of 5.00 m/s.
What is the average power of the motor during this time interval? (1820 W)
The Queen Mary 2, whose maiden voyage was in January 2004, is a cruise ship that has a
mass of 150,000 gross tons (which equals 1.52×108 kg, about three times that of the Titanic).
Her electrically driven pod motors have a maximum power rating of 1.57×105 hp, or
117MW. (a) What is the kinetic energy of the QM2 when she is moving at
15.0 meters/second? (b) Find the absolute minimum time in which the ship's engines could
accelerate her from rest up to 15.0 m/s. Ignore the drag resistance of the water, air, and so on.
(c) What is the force that the ship's propellers exert on the water when the Queen Mary 2 is
moving at 15.0 m/s (assume that the maximum power is used)? ((a) 1.71e+10 J (b) 146 s (c)
7.80E+6 N)