- 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 (b) The
- 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. (b)
- 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; (c)
- 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 (
- 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. (b)
- 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. (a)
- 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 (a) Its
- 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
- 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