Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 15, Problem 15.5CQ
Figure CQ15.5 shows graphs of the potential energy of four different systems versus the position of a particle
in each system. Each particle is set into motion with a push at an arbitrarily chosen location. Describe its subsequent motion in each case (a), (b). (c). and (d).
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Chapter 15 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 15 - A block on the end of a spring is pulled to...Ch. 15 - Consider a graphical representation (Fig. 15.3) of...Ch. 15 - Figure 15.4 shows two curves representing...Ch. 15 - An object of mass m is hung from a spring and set...Ch. 15 - The ball in Figure 15.13 moves in a circle of...Ch. 15 - The grandfather clock in the opening storyline...Ch. 15 - If a simple pendulum oscillates with small...Ch. 15 - You attach a block to the bottom end of a spring...Ch. 15 - A block-spring system vibrating on a frictionless,...Ch. 15 - An object-spring system moving with simple...
Ch. 15 - An object of mass 0.40 kg, hanging from a spring...Ch. 15 - A runaway railroad car, with mass 3.0 105 kg,...Ch. 15 - The position of an object moving with simple...Ch. 15 - If an object of mass m attached to a light spring...Ch. 15 - You stand on the end of a diving board and bounce...Ch. 15 - A mass-spring system moves with simple harmonic...Ch. 15 - A block with mass m = 0.1 kg oscillates with...Ch. 15 - For a simple harmonic oscillator, answer yes or no...Ch. 15 - The top end of a spring is held fixed. A block is...Ch. 15 - Which of the following statements is not true...Ch. 15 - A simple pendulum has a period of 2.5 s. (i) What...Ch. 15 - A simple pendulum is suspended from the ceiling of...Ch. 15 - A particle on a spring moves in simple harmonic...Ch. 15 - You are looking at a small, leafy tree. You do not...Ch. 15 - Prob. 15.2CQCh. 15 - If the coordinate of a particle varies as x = -A...Ch. 15 - A pendulum bob is made from a sphere filled with...Ch. 15 - Figure CQ15.5 shows graphs of the potential energy...Ch. 15 - A student thinks that any real vibration must be...Ch. 15 - The mechanical energy of an undamped block-spring...Ch. 15 - Is it possible to have damped oscillations when a...Ch. 15 - Will damped oscillations occur for any values of b...Ch. 15 - If a pendulum clock keeps perfect time al the base...Ch. 15 - Prob. 15.11CQCh. 15 - A simple pendulum can be modeled as exhibiting...Ch. 15 - Consider the simplified single-piston engine in...Ch. 15 - A 0.60-kg block attached to a spring with force...Ch. 15 - When a 4.25-kg object is placed on lop of a...Ch. 15 - A vertical spring stretches 3.9 cm when a 10-g...Ch. 15 - In an engine, a piston oscillates with simpler...Ch. 15 - The position of a particle is given by the...Ch. 15 - A piston in a gasoline engine is in simple...Ch. 15 - A 1.00-kg object is attached to a horizontal...Ch. 15 - A simple harmonic oscillator takes 12.0 s to...Ch. 15 - A 7.00-kg object is hung from the bottom end of a...Ch. 15 - At an outdoor market, a bunch of bananas attached...Ch. 15 - A vibration sensor, used in testing a washing...Ch. 15 - (a) A hanging spring stretches by 35.0 cm when an...Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - A ball dropped from a height of 4.00 m makes an...Ch. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - A particle moves in simple harmonic motion with a...Ch. 15 - A 1.00-kg glider attached to a spring with a force...Ch. 15 - A 0.500-kg object attached to a spring with a...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - To test the resiliency of its bumper during...Ch. 15 - A 200-g block is attached to a horizontal spring...Ch. 15 - A block of unknown mass is attached to a spring...Ch. 15 - A block-spring system oscillates with an amplitude...Ch. 15 - A particle executes simple harmonic motion with an...Ch. 15 - The amplitude of a system moving in simple...Ch. 15 - A 50.0-g object connected to a spring with a force...Ch. 15 - A 2.00-kg object is attached to a spring and...Ch. 15 - A simple harmonic oscillator of amplitude A has a...Ch. 15 - Review. A 65.0-kg bungee jumper steps off a bridge...Ch. 15 - Review. A 0.250-kg block resting on a...Ch. 15 - Prob. 15.32PCh. 15 - While driving behind a car traveling at 3.00 m/s,...Ch. 15 - A seconds pendulum is one that moves through its...Ch. 15 - A simple pendulum makes 120 complete oscillations...Ch. 15 - A particle of mass m slides without friction...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - The angular position of a pendulum is represented...Ch. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - Prob. 15.41PCh. 15 - A very light rigid rod of length 0.500 m extends...Ch. 15 - Review. A simple pendulum is 5.00 m long. What is...Ch. 15 - A small object is attached to the end of a string...Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...Ch. 15 - A pendulum with a length of 1.00 m is released...Ch. 15 - A 10.6-kg object oscillates at the end of a...Ch. 15 - Show that the time rate of change of mechanical...Ch. 15 - Show that Equation 15.32 is a solution of Equation...Ch. 15 - A baby bounces up and down in her crib. Her mass...Ch. 15 - As you enter a fine restaurant, you realize that...Ch. 15 - A block weighing 40.0 N is suspended from a spring...Ch. 15 - A 2.00-kg object attached to a spring moves...Ch. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - Damping is negligible for a 0.150-kg object...Ch. 15 - The mass of the deuterium molecule (D2) is twice...Ch. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Review. This problem extends the reasoning of...Ch. 15 - A small ball of mass M is attached to the end of a...Ch. 15 - Review. A rock rests on a concrete sidewalk. An...Ch. 15 - Four people, each with a mass of 72.4 kg, are in a...Ch. 15 - To account for the walking speed of a bipedal or...Ch. 15 - Prob. 15.63APCh. 15 - An object attached to a spring vibrates with...Ch. 15 - Review. A large block P attached to a light spring...Ch. 15 - Review. A large block P attached to a light spring...Ch. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - A block of mass m is connected to two springs of...Ch. 15 - A horizontal plank of mass 5.00 kg and length 2.00...Ch. 15 - A horizontal plank of mass m and length L is...Ch. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - A ball of mass m is connected to two rubber bands...Ch. 15 - Review. One end of a light spring with force...Ch. 15 - People who ride motorcycles and bicycles learn to...Ch. 15 - A simple pendulum with a length of 2.23 m and a...Ch. 15 - When a block of mass M, connected to the end of a...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - Consider the damped oscillator illustrated in...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - Your thumb squeaks on a plate you have just...Ch. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Prob. 15.82APCh. 15 - Two identical steel balls, each of mass 67.4 g,...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - An object of mass m1 = 9.00 kg is in equilibrium...Ch. 15 - Review. Why is the following situation impassible?...Ch. 15 - A block of mass M is connected to a spring of mass...Ch. 15 - Review. A system consists of a spring with force...Ch. 15 - A light, cubical container of volume a3 is...
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- Review. A 0.250-kg block resting on a frictionless, horizontal surface is attached to a spring whose force constant is 83.8 N/m as in Figure P15.15. A horizontal force F causes the spring to stretch a distance of 5.46 cm from its equilibrium position. (a) Find the magnitude of F. (b) What is the total energy stored in the system when the spring is stretched? (c) Find the magnitude of the acceleration of the block just after the applied force is removed. (d) Find the speed of the block when it first reaches the equilibrium position. (e) If the surface is not frictionless but the block still reaches the equilibrium position, would your answer to part (d) be larger or smaller? (f) What other information would you need to know to find the actual answer to part (d) in this case? (g) What is the largest value of the coefficient of friction that would allow the block to reach the equilibrium position? Figure P15.15arrow_forwardConsider the data for a block of mass m = 0.250 kg given in Table P16.59. Friction is negligible. a. What is the mechanical energy of the blockspring system? b. Write expressions for the kinetic and potential energies as functions of time. c. Plot the kinetic energy, potential energy, and mechanical energy as functions of time on the same set of axes. Problems 5965 are grouped. 59. G Table P16.59 gives the position of a block connected to a horizontal spring at several times. Sketch a motion diagram for the block. Table P16.59arrow_forwardA horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m. (a) What is the spring constant? (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? (d) What is the speed of the block when its displacement is 0.160 m? (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.240 m on a rough surface so that it loses 14.0 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?arrow_forward
- A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m. (a) What is the spring constant? (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? (d) What is the speed of the block when its displacement is 0.160 m? (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.240 m on a rough surface so that it loses 14.0 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?arrow_forwardUse the data in Table P16.59 for a block of mass m = 0.250 kg and assume friction is negligible. a. Write an expression for the force FH exerted by the spring on the block. b. Sketch FH versus t.arrow_forwardA lightweight spring with spring constant k = 225 N/m is attached to a block of mass m1 = 4.50 kg on a frictionless, horizontal table. The blockspring system is initially in the equilibrium configuration. A second block of mass m2 = 3.00 kg is then pushed against the first block, compressing the spring by x = 15.0 cm as in Figure P16.77A. When the force on the second block is removed, the spring pushes both blocks to the right. The block m2 loses contact with the springblock 1 system when the blocks reach the equilibrium configuration of the spring (Fig. P16.77B). a. What is the subsequent speed of block 2? b. Compare the speed of block 1 when it again passes through the equilibrium position with the speed of block 2 found in part (a). 77. (a) The energy of the system initially is entirely potential energy. E0=U0=12kymax2=12(225N/m)(0.150m)2=2.53J At the equilibrium position, the total energy is the total kinetic energy of both blocks: 12(m1+m2)v2=12(4.50kg+3.00kg)v2=(3.75kg)v2=2.53J Therefore, the speed of each block is v=2.53J3.75kg=0.822m/s (b) Once the second block loses contact, the first block is moving at the speed found in part (a) at the equilibrium position. The energy 01 this spring-block 1 system is conserved, so when it returns to the equilibrium position, it will be traveling at the same speed in the opposite direction, or v=0.822m/s. FIGURE P16.77arrow_forward
- The position of a particle attached to a vertical spring is given by y=(y0cost)j. The y axis points upward, y0 = 14.5 cm. and = 18.85 rad/s. Find the position of the particle at a. t = 0 and b. t = 9.0 s. Give your answers in centimeters.arrow_forwardA horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Figure 5.22. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 6.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. Substitute to obtain a numerical value. (e) What is the speed at the halfway point? Why isnt it half the speed at equilibrium?arrow_forwardA spring with spring constant 25 N/m is compressed a distance of 7.0 cm by a ball with a mass of 202.5 g (Fig. P13.33). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 7.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. a. What is the speed of the ball at point B? b. What is the speed of the block at point B? FIGURE P13.33 Problems 33 and 34.arrow_forward
- Review. A light spring has unstressed length 15.5 cm. It is described by Hookes law with spring constant 4.30 N/m. One end of the horizontal spring is held on a fixed vertical axle, and the other end is attached to a puck of mass m that can mow without friction over a horizontal surface. The puck is set into motion in a circle with a period of 1.30 s. (a) Find the extension of the spring x as it depends on m. Evaluate x for (b) m = 0.070 0 kg. (c) m = 0.140 kg, (d) m = 0.180 kg, and (e) m = 0.190 kg. (f) Describe the pattern of variation of x as it depends on m.arrow_forwardA block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15arrow_forwardA restaurant manager has decorated his retro diner by hanging (scratched) vinyl LP records from thin wires. The records have a mass of 180 g, a diameter of 12 in., and negligible thickness. The records oscillate as torsion pendulums. a. Records hung from a small hole near their rims have a period of roughly 3.5 s (Fig. P16.41A). What is the torsion spring constant of the wire? b. If a record is hung from its center hole using a wire of the same torsion spring constant (Fig. P16.41B), what is its period of oscillation? FIGURE P16.41arrow_forward
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