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.
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
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.
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?
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?
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)
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.
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)