Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
5th Edition
ISBN: 9781305586871
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 12, Problem 15OQ
To determine
The frequency of oscillation for the system in terms of
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A vibrator, pulley, and hanging object are arranged as in Figure P18.219(attachment) with a compound string, consisting of two strings of different masses and lengths fastened together end-to-end. The first string, which has a mass of 1.56 g and a length of 61.0 cm, runs from the vibrator to the junction of the two strings. The second string runs from the junction over the pulley to the suspended 7.02 kg object. The mass and length of the string from the junction to the pulley are, respectively, 6.75 g and 100.3 cm.
a) Find the lowest frequency for which standing waves are observed in both strings, with a node at the junction. The standing wave patterns in the two strings may have different numbers of nodes.
b) What is the total number of nodes observed along the compound string at this frequency, excluding the nodes at the vibrator and the pulley?
Problem 19: While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.5 seconds.Randomized VariablesT = 6.5 seconds
Part (a) Calculate the frequency of oscillation (in Hertz) of the chandelier.
Part (b) Calculate the angular frequency ω of the chandelier in radians/second. Part (c) Determine the length L in meters of the chandelier. Part (d) That evening, while hanging out in J.J. Thompson’s House O’ Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 seconds. Determine the acceleration due to gravity in m/s2 at the club.
The tail board of a lorry is 1.5 m long and 0.75 m high. It is hinged along the bottom edge to the
floor of the lorry. Chains are attached to the top corners of the board and to the sides of the lorry
so that when the board is in a horizontal position the chains are parallel and inclined at 45° to the
horizontal. A tension spring is inserted in each chain so as to reduce the shock and these are adjusted
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Find the greatest force in each spring and the resultant force at the hinges when the board falls
freely from the vertical position. Assume that the tail board is a uniform body of mass 30 kg.
[Ans. 3636 N ; 9327 N]
Chapter 12 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
Ch. 12.1 - A block on the end of a spring is pulled to...Ch. 12.2 - Consider a graphical representation (Fig. 12.3) of...Ch. 12.2 - Figure 12.4 shows two curves representing...Ch. 12.2 - An object of mass m is hung from a spring and set...Ch. 12.4 - A grandfather clock depends on the period of a...Ch. 12.5 - Prob. 12.6QQCh. 12 - Which of the following statements is not true...Ch. 12 - Prob. 2OQCh. 12 - Prob. 3OQCh. 12 - Prob. 4OQ
Ch. 12 - Prob. 5OQCh. 12 - Prob. 6OQCh. 12 - If a simple pendulum oscillates with small...Ch. 12 - Prob. 8OQCh. 12 - Prob. 9OQCh. 12 - Prob. 10OQCh. 12 - Prob. 11OQCh. 12 - Prob. 12OQCh. 12 - Prob. 13OQCh. 12 - You attach a block to the bottom end of a spring...Ch. 12 - Prob. 15OQCh. 12 - Prob. 1CQCh. 12 - The equations listed in Table 2.2 give position as...Ch. 12 - Prob. 3CQCh. 12 - Prob. 4CQCh. 12 - Prob. 5CQCh. 12 - Prob. 6CQCh. 12 - The mechanical energy of an undamped blockspring...Ch. 12 - Prob. 8CQCh. 12 - Prob. 9CQCh. 12 - Prob. 10CQCh. 12 - Prob. 11CQCh. 12 - Prob. 12CQCh. 12 - Consider the simplified single-piston engine in...Ch. 12 - A 0.60-kg block attached to a spring with force...Ch. 12 - When a 4.25-kg object is placed on top of a...Ch. 12 - The position of a particle is given by the...Ch. 12 - You attach an object to the bottom end of a...Ch. 12 - A 7.00-kg object is hung from the bottom end of a...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - A 1.00-kg glider attached to a spring with a force...Ch. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - A 500-kg object attached to a spring with a force...Ch. 12 - In an engine, a piston oscillates with simple...Ch. 12 - A vibration sensor, used in testing a washing...Ch. 12 - A blockspring system oscillates with an amplitude...Ch. 12 - A block of unknown mass is attached to a spring...Ch. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - A 200-g block is attached to a horizontal spring...Ch. 12 - A 50.0-g object connected to a spring with a force...Ch. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - The angular position of a pendulum is represented...Ch. 12 - A small object is attached to the end of a string...Ch. 12 - A very light rigid rod of length 0.500 m extends...Ch. 12 - A particle of mass m slides without friction...Ch. 12 - Review. A simple pendulum is 5.00 m long. What is...Ch. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Show that the time rate of change of mechanical...Ch. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - Four people, each with a mass of 72.4 kg, are in a...Ch. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - A block of mass m is connected to two springs of...Ch. 12 - Review. One end of a light spring with force...Ch. 12 - Prob. 58PCh. 12 - A small ball of mass M is attached to the end of a...Ch. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - A smaller disk of radius r and mass m is attached...Ch. 12 - A pendulum of length L and mass M has a spring of...Ch. 12 - Consider the damped oscillator illustrated in...Ch. 12 - An object of mass m1 = 9.00 kg is in equilibrium...Ch. 12 - Prob. 68PCh. 12 - A block of mass M is connected to a spring of mass...
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- A 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_forwardA small ball of mass M is attached to the end of a uniform rod of equal mass M and length L that is pivoted at the top (Fig. P12.59). Determine the tensions in the rod (a) at the pivot and (b) at the point P when the system is stationary. (c) Calculate the period of oscillation for small displacements from equilibrium and (d) determine this period for L = 2.00 m. Figure P12.59arrow_forwardReview. A system consists of a spring with force constant k = 1 250 N/m, length L = 1.50 m, and an object of mass m = 5.00 kg attached to the end (Fig. P15.49). The object is placed at the level of the point of attachment with the spring unstretched, at position yi = L, and then it is released so that it swings like a pendulum. (a) Find the y position of the object at the lowest point. (b) Will the pendulums period be greater or less than the period of a simple pendulum with the same mass m and length L? Explain. Figure PI 5.49arrow_forward
- A spherical bob of mass m and radius R is suspended from a fixed point by a rigid rod of negligible mass whose length from the point of support to the center of the bob is L (Fig. P16.75). Find the period of small oscillation. N The frequency of a physical pendulum comprising a nonuniform rod of mass 1.25 kg pivoted at one end is observed to be 0.667 Hz. The center of mass of the rod is 40.0 cm below the pivot point. What is the rotational inertia of the pendulum around its pivot point?arrow_forwardA smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P12.64. The center of the small disk is located at the edge of the large disk. The large disk is mounted at its center on a frictionless axle. The assembly is rotated through a small angle from its equilibrium position and released. (a) Show that the speed of the center of the small disk as it passes through the equilibrium position is v=2[Rg(1cos)(M/m)+(r/R)2+2]1/2 (b) Show that the period of the motion is T=2[(M+2m)R2+mr22mgR]1/2 Figure P12.64arrow_forwardA nylon string has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P14.56). The wheels have a mass that is negligible compared with that of the string, and they roll without friction on the track so that the upper end of the string is essentially free. At equilibrium, the string is vertical and motionless. When it is carrying a small-amplitude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the string. (b) The strings vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an anti-node at the free top end. Find the nodeantinode distances for each of the three simplest states. (c) Find the frequency of each of these states. Figure P14.56arrow_forward
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