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Chapter 11 Solutions
Physics for Scientists and Engineers
- A uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35arrow_forwardA child works on a project in art class and uses an outline of her hand on a sheet of construction paper to draw a turkey (Fig. P16.36). The teacher pins the turkey to the bulletin board in the front of the classroom by using a thumbtack. The student notices that if she flicks her finger on the end of the turkey, it oscillates back and forth with a frequency of about 1.65 Hz. If the rotational inertia of the paper turkey is 1.25 105 kgm2 and its mass is 0.005 kg, what is the distance between the thumbtack and the center of mass of the turkey? FIGURE P16.36arrow_forwardA particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.arrow_forward
- A Two particles A and B move at a constant speed in circular paths at the same angular speed . Particle As circle has a radius that is twice the length of particle Bs circle. What is the ratio TA/TB of their periods?arrow_forwardMarianne puts her favorite Bon Jovi disc in her CD player. If it spins with a frequency of 1800 revolutions per minute, what is the period of spin of the compact disc? *Use g=9.8 a. 30.0 s b. 18.7 s c. 0.033 s d. 0.435 s e. 0.187 sarrow_forwardA solid cylinder has length L = 14 cm and radius R = 2 cm. The center of one face of the cylinder is located at the origin and the cylinder’s axis lies along the positive x-axis. The mass density of the cylinder varies along its length and is given by the function: ρ(x) = Ax2 + Bx + C, where A = 13.5 kg/m5, B = 5.2 kg/m4, and C = 14.2 kg/m3. Consider a thin slice of the cylinder that is a disk located at distance x from the origin and having thickness dx. Enter an expression for the mass of this disk in terms of the defined quantities and dx. Integrate the expression you entered in part (a) and enter an expression for the mass of the whole cylinder in terms of the defined quantities. Calculate the mass of the cylinder, in grams. Enter an expression for the location of the cylinder’s center of mass along the x-axis, in terms of the defined quantities. Calculate the location of the cylinder’s center of mass along the x-axis, in centimeters.arrow_forward
- A 0.500 kg particle moves in a circle of radius 0.150 m at constant speed. The time for 20 complete revolutions is 31.7 s. What is the period T of the motion? What is the speed of the particle?arrow_forwardCalculate the weight of the solid generated by the line segment bounded by points A (1, 4) m and B (5, 2) m when it rotates around the X axis, considering that the density is ρ = x in kg / m3. A) 2646.583 NB) 269.784 NC) 1150.517 ND) 117.286 Narrow_forwardAn object undergoing purely oscillatory motion in one dimension has an acceleration given by: ax(t)=−amaxsin(2pi t / T+ delta) with amax = 2.97 m/s2, T = 8.9 s, and delta= 1.03 rad. What is the maximum speed of the object? What is the amplitude of the object's position? What is the change in x-component velocity of the object from t = 0 s to t = 4.70 s? (your calculator must be in radians for this problem)arrow_forward
- A 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for small-angle oscillations is 0.940 s. (a) What is the moment of inertia of the wrench about an axis through the pivot? (b) If the wrench is initially displaced 0.400 rad from its equilibrium position, what is the angular speed of the wrench as it passes through the equilibrium position?arrow_forwardConsider a person along with a frame of reference in each of the following situations. In which one or more of the following situations is the frameof reference an inertial frame of reference? (a) The person is oscillating insimple harmonic motion at the end of a bungee cord. (b) The person is in acar going around a circular curve at a constant speed. (c) The person is ina plane that is landing on an aircraft carrier. (d) The person is in the spaceshuttle during lift-off . (e) None of the above.arrow_forwardA solid sphere has a uniformly distributed mass of 1.0 * 104 kg and a radius of 1.0 m.What is the magnitude of the gravitational force due to the sphere on a particle of mass m when the particle is located at a distance of (a) 1.5 m and (b) 0.50 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r < 1.0 m from the center of the sphere.arrow_forward
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