Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 12, Problem 54P
To determine
The angular frequency with which the plank moves with
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Chapter 12 Solutions
Principles of Physics: A Calculus-Based Text
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 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_forwardAn object of mass m1 = 9.00 kg is in equilibrium when connected to a light spring of constant k = 100 N/m that is fastened to a wall as shown in Figure P12.67a. A second object, m2 = 7.00 kg, is slowly pushed up against m1, compressing the spring by the amount A = 0.200 m (see Fig. P12.67b). The system is then released, and both objects start moving to the right on the frictionless surface. (a) When m1 reaches the equilibrium point, m2 loses contact with m1 (see Fig. P12.67c) and moves to the right with speed v. Determine the value of v. (b) How far apart are the objects when the spring is fully stretched for the first time (the distance D in Fig. P12.67d)? Figure P12.67arrow_forwardA watch balance wheel (Fig. P15.25) has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 20.0 g is concentrated around a rim of radius 0.500 cm. What are (a) the wheels moment of inertia and (b) the torsion constant of the attached spring? Figure P15.23arrow_forward
- A 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_forwardConsider the simplified single-piston engine in Figure CQ12.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion. Figure CQ12.13arrow_forwardA block of mass m rests on a frictionless, horizontal surface and is attached to two springs with spring constants k1 and k2 (Fig. P16.22). It is displaced to the right and released. Find an expression for the angular frequency of oscillation of the resulting simple harmonic motion. FIGURE P16.22 Problems 22 and 81.arrow_forward
- A nylon siring 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. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.arrow_forwardDetermine the angular frequency of oscillation of a thin, uniform, vertical rod of mass m and length L pivoted at the point O and connected to two springs (Fig. P16.78). The combined spring constant of the springs is k(k = k1 + k2), and the masses of the springs are negligible. Use the small-angle approximation (sin ). FIGURE P16.78arrow_forwardA pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (Fig. P12.65). Find the frequency of vibration of the system for small values of the amplitude (small ). Assume the vertical suspension rod of length L is rigid, but ignore its mass. Figure P12.65arrow_forward
- A block of mass m is connected to two springs of force constants k1 and k2 in two ways as shown in Figure P12.56. In both cases, the block moves on a frictionless table after it is displaced from equilibrium and released. Show that in the two cases the block exhibits simple harmonic motion with periods (a) T=2m(k1+k2)k1k2 and (b) T=2mk1+k2 Figure P12.56arrow_forwardA block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a frictionless, horizontal track (Fig. P12.69). The force constant of the spring is k, and the equilibrium length is . Assume all portions of the spring oscillate in phase and the velocity of a segment of the spring of length dx is proportional to the distance x from the fixed end; that is, vx = (x/) v. Also, notice that the mass of a segment of the spring is dm = (m/) dx. Find (a) the kinetic energy of the system when the block has a speed v and (b) the period of oscillation. Figure P12.69arrow_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
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