Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 15, Problem 35AP
A 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. P15.55). Find the frequency of vibration of the system for small values of the amplitude (small θ). Assume the vertical suspension rod of length L is rigid, but ignore its mass.
Figure P15.35
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Physics for Scientists and Engineers with Modern Physics
Ch. 15.1 - A block on the end of a spring is pulled to...Ch. 15.2 - Consider a graphical representation (Fig. 15.3) of...Ch. 15.2 - shows two curves representing particles undergoing...Ch. 15.2 - An object of mass m is hung from a spring and set...Ch. 15.4 - The ball in Figure 15.13 moves in a circle of...Ch. 15.5 - The grandfather clock in the opening storyline...Ch. 15 - A 0.60-kg block attached to a spring with force...Ch. 15 - A piston in a gasoline engine is in simple...Ch. 15 - The position of a particle is given by the...Ch. 15 - Prob. 4P
Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - Prob. 6PCh. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12PCh. 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 - While driving behind a car traveling at 3.00 m/s,...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 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...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 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Prob. 32APCh. 15 - An object attached to a spring vibrates with...Ch. 15 - Prob. 34APCh. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - Prob. 36APCh. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - Prob. 38APCh. 15 - Prob. 39APCh. 15 - Prob. 40APCh. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Prob. 42APCh. 15 - Prob. 43APCh. 15 - Prob. 44APCh. 15 - A block of mass m is connected to two springs of...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - Prob. 49CPCh. 15 - Prob. 50CPCh. 15 - A light, cubical container of volume a3 is...
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- A 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 very light rigid rod of length 0.500 m extends straight out from one end of a meter-stick. The combination is suspended from a pivot at the upper end of the rod as shown in Figure P12.31. The combination is then pulled out by a small angle and released. (a) Determine the period of oscillation of the system. (b) By what percentage does the period differ from the period of a simple pendulum 1.00 m long? Figure P12.31arrow_forwardA 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_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_forwardWhich of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.arrow_forwardWhen a block of mass M, connected to the end of a spring of mass ms = 7.40 g and force constant k, is set into simple harmonic motion, the period of its motion is T=2M+(ms/3)k A two-part experiment is conducted with the use of blocks of various masses suspended vertically from the spring as shown in Figure P15.76. (a) Static extensions of 17.0, 29.3, 35.3, 41.3, 47.1, and 49.3 cm are measured for M values of 20.0, 40.0, 50.0, 60.0, 70.0, and 80.0 g, respectively. Construct a graph of Mg versus x and perform a linear least-squares fit to the data. (b) From the slope of your graph, determine a value for k for this spring. (c) The system is now set into simple harmonic motion, and periods are measured with a stopwatch. With M = 80.0 g, the total time interval required for ten oscillations is measured to be 13.41 s. The experiment is repeated with M values of 70.0, 60.0, 50.0, 40.0, and 20.0 g, with corresponding time intervals for ten oscillations of 12.52, 11.67, 10.67, 9.62, and 7.03 s. Make a table of these masses and times. (d) Compute the experimental value for T from each of these measurements. (e) Plot a graph of T2 versus M and (f) determine a value for k from the slope of the linear least-squares fit through the data points. (g) Compare this value of k with that obtained in part (b). (h) Obtain a value for ms from your graph and compare it with the given value of 7.40 g.arrow_forward
- Consider the system shown in Figure P16.68 as viewed from above. A block of mass m rests on a frictionless, horizontal surface and is attached to two elastic cords, each of length L. At the equilibrium configuration, shown by the dashed line, the cords both have tension FT. The mass is displaced a small amount as shown in the figure and released. Show that the net force on the mass is similar to the spring-restoring force and find the angular frequency of oscillation, assuming the mass behaves as a simple harmonic oscillator. You can assume the displacement is small enough to produce negligible change in the tension and length of the cords. FIGURE P16.68arrow_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
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