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physics
mechanics

Questions and Answers of Mechanics

A freight train starts from rest and travels with a constant acceleration of 0.5 ft/s2. After a time t it maintains a constant speed so that when t = 160s it has traveled 2000 ft. Determine the time
The crate, having a weight of 50 lb, is hoisted by the pulley system and motor M. if the crate starts from rest and, by constant acceleration, attains a speed of 12 ft/s after rising 10 ft, determine
An automobile is traveling with a constant speed along a horizontal circular curve that has a radius P = 750 ft. If the magnitude of acceleration is a = 8ft/s2, determine the speed at which the
Block B rests on a smooth surface. If the coefficients of friction between A and B are μs = 0.4 and μk = 0.3, determine the acceleration of each block if (a) F = 6 lb, and (b) F = 50lb
The 100-kb crate is subjected to the action of two forces, F1 = 800 N and F2 = 1.5 kN, as shown. If it is originally at rest, determine the distance it slides in order to attain a speed of 6m/s. The
A 20-kg block is originally at rest on a horizontal surface for which the coefficient of static friction is μs = 0.6 and the coefficient of kinetic friction is μk = 0.5. If a horizontal force F
Two smooth billiard balls A and B have an equal mass of m = 200g. If A strikes B with a velocity of (vA)1 = 2 m/s as shown, determine their final velocities just after collision. Ball B is originally
If a 150-lb crate is released from rest at A, determine its speed after it slides 30 ft down the plane. The coefficient of kinetic friction between the crate and plane is μ* = 0.3,
Determine the tension developed in the two cords and the acceleration of each block. Neglect the mass of the pulleys and cords. Hint: Since the system consists of two cords, relate the motion of
The bottle rests at a distance of 3 ft from the center of the horizontal platform. If the coefficient of static friction between the bottle and the platform is μs = 0.3m determine the maximum
Work Prob. R1-51 assuming that the platform starts rotating from rest so that the speed of the bottle is increased at 2 ft/s2.
According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions I L = 1000 cm3 and I in. = 2.54 cm, express this volume in cubic inches.
How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)
The density of lead is 11.3 g/cm3. What is this value in kilograms per cubic meter?
The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by
A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ff. If a country lot has an area of 120 acres, what is the area in hectares?
How many years older will you be 1.00 billion seconds from now? (Assume a 365-day year.)
While driving in an exotic foreign land you see a speed limit sign on a highway that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1/8 mile, and a fortnight
A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If you are driving this car in Europe and want to compare its mileage with that of other European cars,
The following conversions occur frequently in physics and are very useful. (a) Use I mi = 5280 ft and I h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling
Neptunium In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the critical mass of neptuniwn-237 is about 60 kg. The critical mass of a fissionable material
A useful and easy-to-remember approximate value for the number of seconds in a year is π X 107 • Determine the percent error in this approximate value. (There are 365.24 days in one year.)
Figure 1.7 shows the result of unacceptable error in the stopping position of a train. (a) If a train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10 m, what is
With a wooden ruler you measure the length of a rectangular piece of sheet metal to be 12 mm. You use micrometer calipers to measure the with of the rectangle and obtain the value 5.98 mm. Give your
Estimate the percent error in measuring (a) A distance of about 75 cm with a meter stick; (b) A mass of about 12 g with a chemical balance; (c) A time interval of about 6 min with a stopwatch.
A rectangular piece of aluminum is 5.10 ± 0.01 cm long and 1.90 ± 0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm.(a) Find the
How many gallons of gasoline are used in the United States in one day? Assume two cars for every 1hree people, that each car is driven an average of 10,000 mi per year, and that the average car gets
A rather ordinary middle-aged man is in the hospital for a routine check-up. The nurse writes 1he quantity 200 on his medical chart but forgets to include 1he units. Which of the following quantities
How many kernels of corn does it take to fill a 2-L soft drink bottle?
How many words are there in this book?
Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these
How many times does a typical person blink her eyes in a lifetime?
How many times does a human bear! beat during a lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm' of blood with each beat.)
In Wagner's opera Vas Rheingold, the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of
You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0 L bottle? (Hint: Start by estimating the diameter of a drop of water.)
How many pizzas are consumed each academic year by students at your school?
How many dollar bills would you have to stack to reach the moon? Would that be cheaper than building and launching a space spacecraft? (Hint: Start by folding a dollar hill to see how many
How much would it cost to paper the entire United States (including Alaska and Hawaii) with dollar hills? What would be the cost to each person in the United States?
Hearing rattles from a snake you make two rapid displacements of magnitude 1.8 m and 2.4 m. In sketches (roughly to scale), show how your two displacements might add up to give a resultant of
A postal employee drives a delivery truck along the route shown in Fig. 1.33. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.38
For the vectors A and B if Fig. 1.34, use a scale drawing to find the magnitude and direction of(a) The vector sum A + B and(b) The vector difference A €“ B. Use your answers to find the
A spelunker is surveying a cave. She follows a passage 180m straight west, 210 m in a direction 45o east of south, and then 280 m at 30o east of north. After a fourth unmeasured displacement, she
Use a scale drawing to find the x- and y-components of the following vectors. For each vector the numbers given are 1he magnitude of the vector and the angle, measured in the sense from the + x-axis
Compute the x- and y-components of the vectors A, B, C, and D in Fig. 1.34.
Let the angle θ be the angle θ hat the vector 1 makes with the + x-axis, measured counterclockwise from hat axis. Find the angle θ for a vector that has the following compooel8: (a)
A rocket fires two engines simultaneously. One produces a thrust of 725 N directly forward, while the other gives a 513-N thrust at 3240 above the forward direction. Find the magnitude and direction
A postal employee drives a delivery truck over the route shown in Fig. 133. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-.addition
For the vectors 1 and B in Fig. 1.34, use the method of components to find the magnitude and direction of (a) The vector sum A + B; (b) The vector sum B + 1; (c) The vector difference 1 - B;
Find the magnitude and direction of the vector represented by the following pairs of components: (a) A. = -8.60 cm, Ay= 5.20cm; (b) A = -9.70m, Ay = -2.45m; (c) A = 7.75krn, Ay = -2.70krn.
A disoriented physics professor drives 3.25 km north, then 4.75 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components in a
Vector A has components Ax = 1.30 cm, Ay = 225 cm; vector B has components Bx = 4.lOcm, by= -3.75cm. Find (a) The components of the vector sum A + B; (b) The magnitude and direction of A + B;
Vector A is 2.0 cm long and is 60.0o above the x-BXIS in the first quadrani. Vector B is 1.90 cm long and is 60.0o below the x-axis in the fourth quadrant (Fig. 1.35). Use components to find the
A river flows from south to north at 5.0 km/h. On this river, a boat is heading east to west perpendicular to the current at 7.0 km/h. As viewed by an eagle hovering at rest over the shore, how fast
Use vector components to find the magnitude and direction of the vector needed to balance the two vectors shown in Figure 136. Let the 625-N vector be along the -y-axis and let the + x-axis be
Two ropes in a vertical plane exert equal magnitude forces on a hanging weight but pull with an angle of 86.00 between them. What pull does each one exert if their resultant pull is 372 N directly
Write each vector in Fig. 1.34 in terms of the unit vectors i and j.
In each case, find the x• and y-components of vector 1 : (a) A = 5.Oi - 63j; (b) A = 11.2j - 9.91i; (c) A = -15.Oi +22.4j; (d) A = 5.0B, where B = 4i - 6j.
(a) Write each vector in Fig. 1.37 in terms of the unit vectors I and j.(b) Use unit vectors to express the vector C, where C = 3.0M - 4.00B.(c) Find the magnitude and direction of C.
Given two vectors 1 = 4.00i + 3.00j and B = 5.00i - 2.00j, (a) Find the magnitude of each vector; (b) Write an expression for the vector difference A - B using unit vectors; (c) Find the
(a) Is the vector (i + j + i) a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case
(a) Use vector components to prove that two vectors commute for both addition and the scalar product. (b) Prove that two vectors anticommute for the vector product; that is, prove that A x B= -B x
(a) Find the scalar product of the two vectors 1 and B given in Exercise 1.50. (b) Find the angle between these two vectors.
For the vectors 1, B, and C in Fig 1.34 find the scalar products (a) A • B; (b) B • C; (c) A • c.
Find the angle between each of the following pairs of vectors: (a) A = -200i + 6.00j and B = 2.00i - 3.00j (b) A = 3.00i + 5.00j and B = 1O.00i + 6.00j (c) A = -4.00i + 2.00j and B =
By making simple sketches of the appropriate vector products, show that(a) A • B can be interpreted as the product of the magnitude of A times the component of B along A, or the magnitude of B
For the vectors A and b in Fig 1.3,(a) Find the magnitude and direction of the vector product A X D;(b) Find the magnitude and direction of D X A.
Find the vector product A X B (expressed in unit vectors) of the two vectors given in Exercise 1.50. What is the magnitude of the vector product?
For the two vectors in Fig. 1.35, (a) Find the magnitude and direction of the vector product A X B; (b) Find the magnitude and direction of B X A.
An acre, a unit of land measurement still in wide use, has a length of one furlong (1 mi) and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square
An Earthlike Planet In January 2006, astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass of about 5.5 times the earth's mass. It is
The Hydrogen Maser You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another nanre for one
Estimate the number of atoms in your body. Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix D
Biological tissues are typically made up of 98% water. Given that the density of water is 1.0 X 10' kg/m', estimate the mass of (a) The heart of an adult human; (b) A cell with a diameter of 0.5
Iron has a property such that a 1.00-m' volume has a mass of 7.86 X 10' kg (density equals 7.86 X 10' kg/m'). You want to manufacture iron into cubes and spheres. Find (a) The length of the side of
Stars in the Universe Astronomers frequently say that there are more stars in the universe than there are grains of sand on all the beaches on the earth. (a) Given that a typical grain of sand is
Physicists, mathematicians, and others often deal with large numbers. The number 10100 has been given the whimsical name googol by mathematicians. Let us compare some large numbers in physics with
Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A, B, and C shown in Fig. 1.38. Find the magnitude and direction of a fourth force on the stone that will
Two workers poll horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0° west of north, and the resultant of these two pulls is 350.0 N directly
Emergency landing a plane leaves the airport in Galis-teo and flies 170 Ian at 68° east of north and then changes direction to fly 230 Ian at 48° south of east, after which it makes an immediate
You are to program a robotic arm on an assembly line to move in the x, r-plane. Its first displacement is A; its second displacement is B, of magnitude 6.40 cm and direction 63.0° measured in the
(a) Find the magnitude and direction of the vector R that is the sum of the three vectors A, B, and C in Fig. 1.34. In a diagram, show how R is formed from these three vectors. (b) Find the
As noted in Exercise 1.33, a spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45° east of south, and then 280 m at 30° east of north. After a
A sailor in a small sailboat encounters shifting winds. She sails 2.00 Ian east, then 3.50 Ian southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km
Equilibrium we say an object is in equilibrium if all the forces on it balance (add up to zero). Figure 1.40 shows a beam weighing 124 N that is supported in equilibrium by a l00.0-N pull and a force
On a training flight, a student pilot flies form Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig 1.41). The directions are shown relative to
A graphic artist is creating a new logo for her company's website. In the graphics program she is using, each pixel in an image file has coordinates (x, y), where the origin (0, 0) is at the upper
Getting back an explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60° north of west, then 50 steps due south. Assume his steps all have
A ship leaves the island of Guam and sails 285 Ian at 40.0° north of west. In which direction must it now head and how far must it sail so that its resultant displacement will be 115 Ian directly
A boulder of weight w rests on a hillside that rises at a constant angle a above the horizontal, as shown in Fig. 1.42. Its weight is a force on the boulder that has direction vertically downward.
Bones and muscles a patient in therapy has a forearm that weighs 20.5 N and that lifts a 112.0-N weight. These two forces have direction vertically downward. The only other significant forces on his
You are hungry and decide to go to your favorite neighborhood fast-food restaurant. You leave your apartment and take the elevator 10 flights down (each flight is 3.0 m) and then go 15 m south to the
While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 Ian at 30.00 west of north, and finally walk 1.00 Ian at 40.00 north of
You are camping with two friends, tow and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 21.0 m from yours, in the direction 23.0° south of
Vectors A and B are drawn from a common point. Vector A has magnitude A and angle B A measured in the sense from the + x-axis to the +y-axis. The corresponding quantities for vector B are B and
For the two vectors A and B in Fig. 1.37, (a) Find the scalar product A • B, and (b) Find the magnitude and direction of the vector product A X B.
Figure 1.11 c shows a parallelogram based on the two vectors A and B.(a) Show that the magnitude of the cross product of these two vectors is equal to the area of the parallelogram. (b) What is
The vector A is 3.50 cm long and is directed into this page. Vector B points from the lower right comer of this page to the upper left comer of this page, define an appropriate right-handed
Given two vectors A = -2.00i + 3.00J + 4.0ok and B= 3.00i + 1.00J - 3.0ok, do the following. (a) Find the magnitude of each vector. (b) Write an expression for the vector difference 1 - B, using unit
Bond Angle in Methane In the methane molecule CH4, each hydrogen atom is at a comer of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C – H bonds is in

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