A torsion pendulum consists of a metal disk with a wire

Chapter , Problem 97

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A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure 15-58a gives the magnitude t of the torque SSM Figure 15-55 81. F (N) x (m) 0.30 0.30 Fs Fs Figure 15-56 92. Rotation axis L r as as t a (m/s2) Figure 15-57 94. (103 N ! m) 0 0.10 (rad) (a) (b) 0.20 (rad) 0.2 0 0.2 0 ts t (s) s Figure 15-58 97. face is attached to a horizontal spring with k $ 480 N/m. Let x be the displacement of the block from the position at which the spring is unstretched. At t $ 0 the block passes through x $ 0 with a speed of 5.2 m/s in the positive x direction. What are the (a) frequency and (b) amplitude of the blocks motion? (c) Write an expression for x as a function of time. 102 A simple harmonic oscillator consists of an 0.80 kg block attached to a spring (k $ 200 N/m). The block slides on a horizontal frictionless surface about the equilibrium point x $ 0 with a total mechanical energy of 4.0 J. (a) What is the amplitude of the oscillation? (b) How many oscillations does the block complete in 10 s? (c) What is the maximum kinetic energy attained by the block? (d) What is the speed of the block at x $ 0.15 m? 103 A block sliding on a horizontal frictionless surface is attached to a horizontal spring with a spring constant of 600 N/m. The block executes SHM about its equilibrium position with a period of 0.40 s and an amplitude of 0.20 m. As the block slides through its equilibrium position, a 0.50 kg putty wad is dropped needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle u. The vertical axis scale is set by ts $ 4.0 ( 10!3 N*m. The disk is rotated to u $ 0.200 rad and then released. Figure 15-58b shows the resulting oscillation in terms of angular position u versus time t. The horizontal axis scale is set by ts $ 0.40 s. (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speed du/dt of the disk? (Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol v. Hint: The potential energy U of a torsion pendulum is equal to ku2 , analogous to U $ kx2 for a spring.)