Concept explainers
You’ve inherited your great-grandmother’s mantle clock. The clock’s timekeeping is established by a pendulum consisting of a 15.0-cm-long rod and a disk 6.35 cm in diameter. The rod passes through a hole in the disk, and the disk is supported at its bottom by a decorative nut mounted on the bottom portion of the rod, which is threaded: see Fig. 13.38. As shown, the bottom of the disk is 1.92 cm above the bottom of the rod. There are 20.0 threads per cm, meaning that one full turn of the decorative nut moves the disk up or down by 1/20 cm. The clock is beautiful, but it isn’t accurate; you note that it’s losing 1.5 minutes per day. But you realize that the decorative nut is an adjustment mechanism, and you decide to adjust the clock’s timekeeping.
- (a) Should you turn the nut to move the disk up or down?
- (b) How many times should you turn the nut? Note: The disk is massive enough that you can safely neglect the mass of the rod and nut. But you can’t neglect the disk’s size compared with the rod length, so you don’t have a simple pendulum. Furthermore, note that both the effective length of the pendulum and its rotational inertia change as the disk moves up or down the shaft. You can either solve a quadratic or you can use calculus to get an approximate but nevertheless very accurate answer.
FIGURE 13.38 Problem 85
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Additional Science Textbook Solutions
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
College Physics
College Physics: A Strategic Approach (3rd Edition)
University Physics Volume 2
The Cosmic Perspective (8th Edition)
University Physics (14th Edition)
- The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.arrow_forwardWe do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.arrow_forwardIf the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?arrow_forward
- A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?arrow_forwardFor each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3arrow_forwardThe pendulum in the figure consists of a uniform disk with radius r = 15.0 cm and mass 880 g attached to a uniform rod with length L = 570 mm and mass 270 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation. L.arrow_forward
- The distance of a swinging pendulum from its resting position is given by the function d(t) = 3.5cos(5t), where the distance is in inches and the time is in seconds. Once released, how long will it take the pendulum to reach its resting position? Round your answer to the nearest hundredth.arrow_forwardYour answer is partially correct. The pendulum in the figure consists of a uniform disk with radius r = 14.0 cm and mass 860 g attached to a uniform rod with length L= 690 mm and mass 250 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation. (a) Number 0.641 Units kg-m^2 (b) Number 0.721 Units (c) Number i 0.286 Units Sarrow_forwardA pendulum's angular position is given by ?= 0.0340 cos (?t), where ? is in radians and ? = 6.23 rad/s. Find the period (in s) and length (in m) of the pendulum.arrow_forward
- The angular position of a pendulum is represented by the equation ɵ = 0.032 0 cos ꙍt, where ɵ is in radians and ꙍ = 4.43 rad/s. Determine the period and length of the pendulum.arrow_forwardThe pendulum in the figure consists of a uniform disk with radius r = 19.0 cm and mass 720 g attached to a uniform rod with length L = 750 mm and mass 230 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation. (a) Number i 0.828 Units kg-m^2 (b) Number i 0.75 ! Units m (c) Number i 2.16 Units Sarrow_forwardOrangutans can move by brachiation, swinging like a pendulum beneath successive handholds. If an orangutan has arms that are 0.90 m long and repeatedly swings to a 20° angle, taking one swing immediately after another, estimate how fast it is moving in m/s.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning