A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.1a. The atoms reside at
Use information on the endpapers of this book to calculate the average density of the Earth. Where does the value fit among those listed in Tables
The standard kilogram is a platinum–iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?
A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its hundredth year in business, a
What mass of a material with density P is required to make a hollow spherical shell having inner radius r 1 and outer radius r 2?
Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.
Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u,
The paragraph preceding Example 1.1 in the text mentions that the atomic mass of aluminum is 27.0u = 27.0 x 1.66 x 10-27 kg. Example 1.1 says that
On your wedding day your lover gives you a gold ring of mass 3.80 g. Fifty years later its mass is 3.35 g. On the average, how many atoms were
A small cube of iron is observed under a microscope. The edge of the cube is 5.00 x 10-6 cm long find
(a) The mass of the cube and
(b) The number
A structural I beam is made of steel. A view of its cross-section and its dimensions are shown in Figure P1.11. The density of the steel is 7.56 x
A child at the beach digs a hole in the sand and uses a pail to fill it with water having a mass of 1.20 kg. The mass of one molecule of water is
The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = kamt
Figure P1.14 shows a frustum of a cone. Of the following mensuration (geometrical) expressions, this describes
(a) The total circumference of the
Which of the following equations are dimensionally correct?
(a) vf = vi' + ax
(b) y = (2 m) cos (kx), where k = 2 m-1.
(a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and
Newton’s law of universal gravitation is represented by F = GMm / r2 Here F is the magnitude of the gravitational force exerted by one small
A worker is to paint the walls of a square room 8.00 ft high and 12.0 ft along each side. What surface area in square meters must she cover?
Suppose your hair grows at the rate 1/32 in. per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in
The volume of a wallet is 8.50 in3 Convert this value to m3, Using the definition 1 in. = 2.54 cm
A rectangular building lot is 100 ft by 150 ft. determine the area of this lot in m2.
An auditorium measures 40.0 m X 20.0 m X 12.0 m. The density of air is 1.20 kg/m3. What are?
(a) The volume of the room in cubic feet and
Assume that it takes 7.00 minutes to fill a 30.0-gal gasoline tank.
(a) Calculate the rate at which the tank is filled in gallons per second.
Find the height or length of these natural wonders in kilometers, meters and centimeters.
(a) The longest cave system in the world is the Mammoth
A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kg/m3)
A section of land has an area of 1 square mile and contains 640 acres. Determine the number of square meters in 1 acre.
An ore loader moves 1 200 tons/h from a mine to the surface. Convert this rate to lb/s, using 1 ton = 2 000 lb.
(a) Find a conversion factor to convert from miles per hour to kilometers per hour.
(b) In the past, a federal law mandated that highway speed limits
AT the time of this book’s printing, the U.S. national debt is about $6 trillion.
(a) If payments were made at the rate of $1 000 per second, how
The mass of the Sun is 1.99 x 1030 kg, and the mass of an atom of hydrogen, of which the Sun is mostly composed, is 1.67 X 10-27 kg. How many atoms
One gallon of paint (volume =3.78 X 10-3 m3) covers an area of 25.0 m2. What is the thickness of the paint on the wall?
A pyramid has a height of 481 ft and its base covers an area of 13.0 acres (Fig. P1.32). If the volume of a pyramid is given by the expression V =
The pyramid described in Problem 32 contains approximately 2 million stone blocks that average 2.50 tons each. Find the weight of this pyramid in
Assuming that 70% of the Earth’s surface is covered with water at an average depth of 2.3 mi, estimate the mass of the water on the Earth in
A hydrogen atom has a diameter of approximately 1.06 x 10-10, as defined by the diameter of the spherical electron cloud around the nucleus. The
The nearest stars to the Sun are in the Alpha Centauri multiple-star system, about 4.0 x 1013 km away. If the Sun, with a diameter of 1.4 x 109 m,
The diameter of our disk-shaped galaxy, the Milky Way, is about 1.0 x 105 light-years (Ly). The distance to Messier 31, which is Andromeda, the
The mean radius of the Earth is 6.37 x 106 m, and that of the Moon is 1.74 x 108 cm. From these data calculate
(a) The ratio of the Earth’s
One cubic meter (1.00 m3) of aluminum has a mass of 2.70 x 103 kg, and 1.00 m3 of iron has a mass of 7.86 x 103 kg. Find the radius of a solid
Let & Al represent the density of aluminum and PFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of
Estimate the number of Ping-Pong balls that would fit into a typical-size room (without being crushed). In your solution state the quantities you
An automobile tire is rated to last for 50 000 miles. To an order of magnitude, through how many revolutions will it turn? In your solution state the
Grass grows densely everywhere on a quarter-acre plot of land. What is the order of magnitude of the number of blades of grass on this plot? Explain
Approximately how many raindrops fall on a one-acre lot during a one-inch rainfall? Explain your reasoning.
Compute the order of magnitude of the mass of a bathtub half full of water. Compute the order of magnitude of the mass of a bathtub half full of
Soft drinks are commonly sold in aluminum containers. To an order of magnitude, how many such containers are thrown away or recycled each year by
To an order of magnitude, how many piano tuners are in New York City? The physicist Enrico Fermi was famous for asking questions like this on oral
A rectangular plate has a length of (21.3 ± 0.2) cm and a width of (9.8 ± 0.1) cm. Calculate the area of the plate, including its uncertainty.
The radius of a circle is measured to be (10.5 ± 0.2) m. Calculate the
(a) Area and
(b) Circumference of the circle and give the uncertainty in
How many significant figures are in the following numbers?
(a) 78.9 ± 0.2
(d) 0.005 3.
(c) 2.46 X 10-6
(b) 3.788 X 109
The radius of a solid sphere is measured to be (6.50 ± 0.20) cm, and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the
Carry out the following arithmetic operations:
(a) The sum of the measured values 756, 37.2, 0.83, and 2.5;
(b) The product 0.003 2 X 356.3;
The tropical year, the time from vernal equinox to the next vernal equinox, is the basis for our calendar. It contains 365.242199 days. Find the
A farmer measures the distance around a rectangular field. The length of the long sides of the rectangle is found to be 38.44 m, and the length of
A sidewalk is to be constructed around a swimming pool that measures (10.0 ± 0.1) m by (17.0 ± 0.1) m. If the sidewalk is to measure (1.00 ± 0.01)
In a situation where data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 m = 6.37m. When a number ends in 5, we
For many electronic applications, such as in computer chips, it is desirable to make components as small as possible to keep the temperature of the
The basic function of the carburetor of an automobile is to “atomize” the gasoline and mix it with air to promote rapid combustion. As an
The consumption of natural gas by a company satisfies the empirical equation V = 1.50t + 0.008 00t 2, where V is the volume in millions of cubic feet
In physics it is important to use mathematical approximations. Demonstrate that for small angles (
A high fountain of water is located at the center of a circular pool as in Figure P1.61. Not wishing to get his feet wet, a student walks around the
Collectible coins are sometimes plated with gold to enhance their beauty and value. Consider a commemorative quarter-dollar advertised for sale at
There are nearly π X 107 s in one year. Find the percentage error in this approximation, where “percentage error’’ is defined
Assume that an object covers an area A and has a uniform height h. If its cross-sectional area is uniform over its height, then its volume is given
A child loves to watch as you fill a transparent plastic bottle with shampoo. Every horizontal cross-section is a circle, but the diameters of the
One cubic centimeter of water has a mass of 1.00 x 10-3 kg.
(a) Determine the mass of 1.00 m3 of water.
(b) Biological substances are 98% water.
Assume there are 100 million passenger cars in the United States and that the average fuel consumption is 20 mi/gal of Gasoline. If the average
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
The distance from the Sun to the nearest star is about 4 x 1016 m. The Milky Way galaxy is roughly a disk of diameter ~1021 m and thickness ~1019.
The position of a pine wood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of
(a) Sand dunes in a desert move over time as sand is swept up the windward side to settle in the lee side. Such “walking” dunes have been known
The position versus time for a certain particle moving along the x axis is shown in Figure P2.3. Find the average velocity in the time
A particle moves according to the equation x = 10 t 2 where x is in meters and t is in seconds
(a) Find the average velocity for the time interval
A person walks first at a constant speed of 5.00 m/s along a straight line from point A to point B and then back along the line from B to A at a
The position of a particle moving along the x axis varies in time according to the expression x = 3t2, where x is in meters and t is in seconds.
A position-time graph for a particle moving along the x axis is shown in Figure P2.7.
(a) Find the average velocity in the time interval t = 1.50 s
(a) Use the data in Problem 1 to construct a smooth graph of position versus time.
(b) By constructing tangents to the x (t) curve, find the
Find the instantaneous velocity of the particle described in Figure P2.3 at the following times:
(a) t = 1.0 s,
(b) t = 3.0 s
(c) t = 4.5 s,
A hare and a tortoise compete in a race over a course 1.00 km long. The tortoise crawls straight and steadily at its maximum speed of 0.200 m/s
The data in the following table represent measurements of the masses and dimensions of solid cylinders of aluminum, copper, brass, tin, and iron. Use
A 50.0-g superb all traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is
A particle starts from rest and accelerates as shown in Figure P2.12. Determine
(a) The particle’s speed at t = 10.0 s and at t = 20.0 s, and
Secretariat won the Kentucky Derby with times for successive quarter-mile segments of 25.2 s, 24.0 s, 23.8, and 23.0 s.
(a) Find his average speed
A velocity–time graph for an object moving along the x axis is shown in Figure P2.14. ]
(a) Plot a graph of the acceleration versus time.
A particle moves along the x axis according to the equation x = 2.00 + 3.00t - 1.00t 2, where x is in meters and t is in seconds. At t = 3.00 s, find
An object moves along the x axis according to the equation x (t) = (3.00t2 - 2.00t + 3.00) m. Determine
(a) The average speed between t = 2.00 s
Figure P2.17 shows a graph of vx versus t for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line.
Draw motion diagrams for
(a) An object moving to the right at constant speed,
(b) An object moving to the right and speeding up at a constant
Jules Verne in 1865 suggested sending people to the Moon by firing a space capsule from 220-m-long cannon with a launch speed of 10.97 km/s. What
A truck covers 40.0 m in 8.50 s while smoothly slowing down to a final speed of 2.80 m/s.
(a) Find its original speed.
(b) Find its acceleration.
An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x direction when its x coordinate is 3.00 cm. If its x
A 745i BMW car can brake to a stop in a distance of 121 ft. from a speed of 60.0 mi/h. To brake to a stop from a speed of 80.0 mi/h requires a
A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 100m ahead. The pilot slows the boat with a constant acceleration of - 3.50 m/s2 by
Figure P2.24 represents part of the performance data of a car owned by a proud physics student.
(a) Calculate from the graph the total distance
A particle moves along the x axis. Its position is given by the equation x = 2 x 3t - 4t2 with x in meters and t in seconds. Determine
In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 71.5 m/s. The driver of the
A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of - 5.00 m/s2 as it comes to rest.
(a) From the instant the plane
A car is approaching a hill at 30.0 m/s when its engine suddenly fails just at the bottom of the hill. The car moves with a constant acceleration of
Help! One of our equations is missing! We describe constant acceleration motion with the variables and parameters vxi, vxf, ax, t, and xf - xi. Of
Get In Touch