A spool of thread consists of a cylinder of radius R, with end caps of radius R, as depicted in the end view shown in Figure P10.45. The mass of the spool, including the thread, is m, its moment of inertia about an axis through its center is I. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T acting to the right is applied to the free end of the thread. (a) Show that the magnitude of the friction force exerted by the surface on the spool is given by and (I+ mR,Rq T I+ mR,2 f = (b) Determine the direction of the force of friction. \R2 R1 Figure P10.45

A spool of thread consists of a cylinder of radius R, with end caps of radius R, as depicted in the end view shown in Figure P10.45. The mass of the spool, including the thread, is m, its moment of inertia about an axis through its center is I. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T acting to the right is applied to the free end of the thread. (a) Show that the magnitude of the friction force exerted by the surface on the spool is given by and (I+ mR,Rq T I+ mR,2 f = (b) Determine the direction of the force of friction. \R2 R1 Figure P10.45

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

The wheel and axle have forces applies tangentially as shown in the figure. There is also a frictional torque of 0.02 Nxm on the wheel, once the wheel starts moving. The radius of the axel is 20 cm and the radius of the wheelis 60 cm and F1 = 2.4 N, F2 = 3.0 N and F3 = 1.2 N. a. Calculate the net torque on the moving wheel due to the applied forces F1 F2 and F3. b. What direction of rotation would the applied forces cause? Explain. c. What is the direction of frictional torque? Explain. d. Calculate the net torque on the wheel and axle.
A 1.00 kg solid, uniform disk rolls without slipping across a level surface, translating at 3.00 m/s. If the disk's radius is 0.150 m, find the following. HINT (a) the disk's translational kinetic energy (in J) (b) the disk's rotational kinetic energy (in J)
a 7kg solid sphere rolls without slipping on a horizontal surface with its center of mass moving at 5m/s. what is the ratio between the translational and the rotational kinetic energies?
A merry-go-round accelerates from rest to 0.74 rad/s in 33 s. Assuming the merry-go-round is a uniform disk of radius 6.0 m and mass 3.10×104 kg, calculate the net torque required to accelerate it. Express your answer to two significant figures and include the appropriate units.
A spool of thread consists of a cylinder of radius R₁ = 4.5 cm with end caps of radius R₂ = 9.0 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 280 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T= 0.620 N acting to the right is applied to the free end of the thread. For the moment of inertia treat the spool as being a solid cylinder of radius R₁, as the extended edges are thin and therefore light. (a) What is the acceleration of the spool? Take positive to be to the right. .739 m/s² (b) Determine the direction of the force of friction. to the left to the right straight up straight down
Two Thin rectangular sheets (0.28m x 0.47 m) are identical. In the first sheet the axis of rotation lies along the 0.28 inside, and in the second it lies along 0.47m side. The same torque is applied to each sheet. The first sheet starting from rest reaches its final angular velocity in 5.2 s. How long does it take for the second seat starting from rest to reach the same Angularer velocity?
A counterweight of mass m = 3.60 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 3.00 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? V N.m to the right along the axis of rotation v magnitude 2.4695 direction (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (3.705 Note that your numerical answer is multiplied by the symbol v in the answer box. kg • m)v (c) Using your result from (b) and 7 = L/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) 6.925 The expression for the angular momentum in part (b) has a factor of v. How do you determine dL/dt, from this expression? m/s2
A 250-g mass hangs from a string that is wrapped around a pulley, as shown in the figure. The pulley is suspended in such a way that it can rotate freely. When the mass is released, it accelerates toward the floor as the string unwinds. Model the pulley as a uniform solid cylinder of mass 1.00 kg and radius 9.00 cm. Assume that the thread has negligible mass and does not slip or stretch as it unwinds. Determine the magnitude a of the pulley's angular acceleration. rad/s? a = Determine the magnitude of the acceleration a of the descending weight. a = m/s? Calculate the magnitude of the tension T' in the string. T =
A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.85). Assuming the spool is a uniform solid cylinder that doesn’t slip, show that (a) The acceleration of the center of mass is 4F/3M and (b) The force of friction is to the right and equal in magnitude to F/3. (c) If the cylinder starts from rest and rolls without slipping, what is the speed of its center of mass after it has rolled through a distance d?