Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 13, Problem 64PQ
To determine
Reason for the usage of rubber on ends of twirling baton.
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A solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0 cm.5.0 cm. A very small "eyelet" is screwed into the surface of the sphere and a horizontal support rod is passed through the eyelet, allowing the sphere to pivot around this fixed axis, as shown in the figure. If the sphere is displaced slightly from equilibrium on the surface of Earth, determine the period ?T of its harmonic motion when it is released.
A uniform plank 6.0 m long rests on two supports,2.5 m apart (Fig.P12.44).The gravitational force on the plank is 100 N.The left end of the plank is 1.5 m to the left of the left support,so the plank is not centered on the supports.A persom is standing on the plank half a meter to the right of the right support.The gravitational force on this person is 80.0 N.How far to right can the person walk before the plank begins to tip?
53. In Figure P10.53, the hanging object has a mass of m, =
0.420 kg; the sliding block has a mass of m, = 0.850 kg;
R2 R
m2
and the pulley is a hollow cylinder with a mass of M =
0.350 kg, an inner radius of R, = 0.020 0 m, and an
outer radius of R, = 0.030 0 m. Assume the mass of the
spokes is negligible. The coefficient of kinetic friction
between the block and the horizontal surface is µz
0.250. The pulley turns without friction on its axle. The
light cord does not stretch and does not slip on the pul-
ley. The block has a velocity of v; = 0.820 m/s toward
the pulley when it passes a reference point on the table.
(a) Use energy methods to predict its speed after it has
moved to a second point, 0.700 m away. (b) Find the
angular speed of the pulley at the same moment.
Chapter 13 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 13.1 - CASE STUDY When Is Energy Conserved? Under what...Ch. 13.6 - Figure 13.24 shows a particle with momentum p....Ch. 13.7 - Prob. 13.3CECh. 13.7 - Prob. 13.4CECh. 13.7 - Prob. 13.5CECh. 13 - Prob. 1PQCh. 13 - Prob. 2PQCh. 13 - A Frisbee flies across a field. Determine if the...Ch. 13 - Prob. 4PQCh. 13 - Prob. 5PQ
Ch. 13 - Rotational Inertia Problems 5 and 6 are paired. 5....Ch. 13 - A 12.0-kg solid sphere of radius 1.50 m is being...Ch. 13 - A figure skater clasps her hands above her head as...Ch. 13 - A solid sphere of mass M and radius Ris rotating...Ch. 13 - Suppose a disk having massMtot and radius R is...Ch. 13 - Problems 11 and 12 are paired. A thin disk of...Ch. 13 - Given the disk and density in Problem 11, derive...Ch. 13 - A large stone disk is viewed from above and is...Ch. 13 - Prob. 14PQCh. 13 - A uniform disk of mass M = 3.00 kg and radius r =...Ch. 13 - Prob. 16PQCh. 13 - Prob. 17PQCh. 13 - The system shown in Figure P13.18 consisting of...Ch. 13 - A 10.0-kg disk of radius 2.0 m rotates from rest...Ch. 13 - Prob. 20PQCh. 13 - Prob. 21PQCh. 13 - In Problem 21, what fraction of the kinetic energy...Ch. 13 - Prob. 23PQCh. 13 - Prob. 24PQCh. 13 - Prob. 25PQCh. 13 - A student amuses herself byspinning her pen around...Ch. 13 - The motion of spinning a hula hoop around one's...Ch. 13 - Prob. 28PQCh. 13 - Prob. 29PQCh. 13 - Prob. 30PQCh. 13 - Sophia is playing with a set of wooden toys,...Ch. 13 - Prob. 32PQCh. 13 - A spring with spring constant 25 N/m is compressed...Ch. 13 - Prob. 34PQCh. 13 - Prob. 35PQCh. 13 - Prob. 36PQCh. 13 - Prob. 37PQCh. 13 - Prob. 38PQCh. 13 - A parent exerts a torque on a merry-go-round at a...Ch. 13 - Prob. 40PQCh. 13 - Today, waterwheels are not often used to grind...Ch. 13 - Prob. 42PQCh. 13 - A buzzard (m = 9.29 kg) is flying in circular...Ch. 13 - An object of mass M isthrown with a velocity v0 at...Ch. 13 - A thin rod of length 2.65 m and mass 13.7 kg is...Ch. 13 - A thin rod of length 2.65 m and mass 13.7 kg is...Ch. 13 - Prob. 47PQCh. 13 - Two particles of mass m1 = 2.00 kgand m2 = 5.00 kg...Ch. 13 - A turntable (disk) of radius r = 26.0 cm and...Ch. 13 - CHECK and THINK Our results give us a way to think...Ch. 13 - Prob. 51PQCh. 13 - Prob. 52PQCh. 13 - Two children (m = 30.0 kg each) stand opposite...Ch. 13 - A disk of mass m1 is rotating freely with constant...Ch. 13 - Prob. 55PQCh. 13 - Prob. 56PQCh. 13 - The angular momentum of a sphere is given by...Ch. 13 - Prob. 58PQCh. 13 - Prob. 59PQCh. 13 - Prob. 60PQCh. 13 - Prob. 61PQCh. 13 - Prob. 62PQCh. 13 - A uniform cylinder of radius r = 10.0 cm and mass...Ch. 13 - Prob. 64PQCh. 13 - A thin, spherical shell of mass m and radius R...Ch. 13 - To give a pet hamster exercise, some people put...Ch. 13 - Prob. 67PQCh. 13 - Prob. 68PQCh. 13 - The velocity of a particle of mass m = 2.00 kg is...Ch. 13 - A ball of mass M = 5.00 kg and radius r = 5.00 cm...Ch. 13 - A long, thin rod of mass m = 5.00 kg and length =...Ch. 13 - A solid sphere and a hollow cylinder of the same...Ch. 13 - A uniform disk of mass m = 10.0 kg and radius r =...Ch. 13 - When a person jumps off a diving platform, she...Ch. 13 - One end of a massless rigid rod of length is...Ch. 13 - A uniform solid sphere of mass m and radius r is...Ch. 13 - Prob. 77PQCh. 13 - A cam of mass M is in the shape of a circular disk...Ch. 13 - Prob. 79PQCh. 13 - Consider the downhill race in Example 13.9 (page...Ch. 13 - Prob. 81PQ
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- In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. (b) Find the angular speed of the pulley at the same moment. Figure P10.40arrow_forwardA square plate with sides 2.0 m in length can rotatearound an axle passingthrough its center of mass(CM) and perpendicular toits surface (Fig. P12.53). There are four forces acting on the plate at differentpoints. The rotational inertia of the plate is 24 kg m2. Use the values given in the figure to answer the following questions. a. Whatis the net torque acting onthe plate? b. What is theangular acceleration of the plate? FIGURE P12.53 Problems 53 and 54.arrow_forwardA square plate with sides of length 4.0 m can rotate about an axle passing through its center of mass and perpendicular to the plate as shown in Figure P14.36. There are four forces acting on the plate at different points. The rotational inertia of the plate is 24 kgm2. Is the plate in equilibrium? FIGURE P14.36arrow_forward
- A uniform solid sphere of mass m and radius r is releasedfrom rest and rolls without slipping on a semicircular ramp ofradius R r (Fig. P13.76). Ifthe initial position of the sphereis at an angle to the vertical,what is its speed at the bottomof the ramp? FIGURE P13.76arrow_forwardA uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28arrow_forwardFind the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23arrow_forward
- A disk with a radius of 4.5 m has a 100-N force applied to its outer edge at two different angles (Fig. P12.55). The disk has arotational inertia of 165 kg m2. a. What is the magnitude of the torque applied to the disk incase 1? b. What is the magnitude of the torque applied to the disk incase 2? c. Assuming the force on the disk is constant in each case,what is the magnitude of the angular acceleration applied tothe disk in each case? d. Which case is a more effective way of spinning the disk?Describe which quantity you are using to determine effectiveness and why you chose that quantity. FIGURE P12.55arrow_forwardConsider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75arrow_forwardThe angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure P11.31. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by p=/I, where is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earths axis of rotation processes about the perpendicular to its orbital plane with a period of 2.58 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. Figure P11.31 A precessing angular momentum vector sweeps out a cone in space.arrow_forward
- A wheel of inner radius r1 = 15.0 cm and outer radius r2 = 35.0 cm shown in Figure P12.43 is free to rotate about the axle through the origin O. What is the magnitude of the net torque on the wheel due to the three forces shown? FIGURE P12.43arrow_forwardA ball of mass M = 5.00 kg and radius r = 5.00 cm isattached to one end of a thin,cylindrical rod of length L = 15.0 cm and mass m = 0.600 kg.The ball and rod, initially at restin a vertical position and freeto rotate around the axis shownin Figure P13.70, are nudgedinto motion. a. What is therotational kinetic energy of thesystem when the ball and rodreach a horizontal position? b. What is the angular speed of the ball and rod when they reach a horizontal position? c. What is the linear speed of the centerof mass of the ball when the ball and rod reach a horizontalposition? d. What is the ratio of the speed found in part (c) tothe speed of a ball that falls freely through the same distance? FIGURE P13.70arrow_forwardThree forces are exerted on the disk shown in Figure P12.71,and their magnitudes are F3 = 2F2 = 2F1. The disks outer rimhas radius R, and the inner rim has radius R/2. As shown in thefigure, F1 and F3 are tangent to the outer rim of the disk, and F2 is tangent to the inner rim. F3 is parallel to the x axis, F2 is parallel to the y axis, and F1 makes a 45 angle with the negative x axis. Find expressions for the magnitude of each torque exertedaround the center of the disk in terms of R and F1. FIGURE P12.71 Problems 71-75arrow_forward
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