4. A homogeneous, rigid cylinder of mass M and radius R is placed on a small rectangular plate of mass m. There is sufficient static friction between the cylinder and the plate. The plate itself is placed on a flat, frictionless table. A constant force of magnitude F is applied to the plate in direction parallel to the table as shown on the diagram. Once the force F is applied, the cylinder goes immediately into pure rolling (no slipping or skidding). Find: a. The translational (linear) acceleration of the block, a,. b. The angular acceleration of the cylinder, a. c. The translational (linear) acceleration of the cylinder a̟. М,R F m

4. A homogeneous, rigid cylinder of mass M and radius R is placed on a small rectangular plate of mass m. There is sufficient static friction between the cylinder and the plate. The plate itself is placed on a flat, frictionless table. A constant force of magnitude F is applied to the plate in direction parallel to the table as shown on the diagram. Once the force F is applied, the cylinder goes immediately into pure rolling (no slipping or skidding). Find: a. The translational (linear) acceleration of the block, a,. b. The angular acceleration of the cylinder, a. c. The translational (linear) acceleration of the cylinder a̟. М,R F m

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

Consider the setup shown below. The blocks have masses 3.6 kg and 24 kg. The pulley has mass 7.4 kg, and is a uniform disc with radius 0.23 m. Assume the pulley to be frictionless, but the coefficient of friction between the block and the surface is 0.36. What is the acceleration of the blocks? Assume the 24 kg mass is descending with acceleration a. The moment of inertia of the disk is 1/2MR2 and the acceleration of gravity is 9.8 m/s2.
A solid wood door 0.900 m wide and 2.20 m high is hinged along one side and has a total mass of 20.0 kg. Initially open and at rest, the door is struck at it center by a blob of mud with a mass 4.00 kg, traveling perpendicular to the door at 12.0 m/s just before impact. The mud sticks to the door after the impact. a. What is the rotational inertia of the door? (Give your answer in kg m2.) I for a plane rotating about its end is: Iplane = 1/3 MR2. b. What is the rotational inertia of the blob of mud about an axis along the door's hinge just before the impact? (Give your answer in kg m2.) The rotational inertia for a point mass is given by: I = mR2. c. What is the total angular momentum of the system about an axis along the door's hinge just before the mud hits the door? (Give your answer in N m s.) d. What is the angular velocity of the door after the impact? (Give your answer in rad/s.) e. What is the speed of the doorknob located 0.85 m from the hinge? (Give your answer in m/s.)
A uniform hollow spherical ball of mass 2.14 kg and radius 0.56 m rolls without slipping up a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is 3.42 m.s1. While the ball is moving up the ramp, find (a) the magnitude of the acceleration of its center of mass. m.s2 (b) the magnitude of the friction force acting on it due to the surface of the ramp. N
A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in the image. The pulley can be considered as a uniform solid cylindrical disk. Draw a free body diagram and explain if the tensions in the two strings equal? Why? Why not? To solve the problem, why can’t I use the system approach and write the equation for M and m at the same time? Please write the equations that will help solve for T1 and T2
A pulley is bolted to a wall as shown. The pulley is a flat disk of mass mp, radius R and moment of inertia I = mpR². A mass MH hangs from it by a rope that is wound about the pulley and does not slip. a. Give an appropriate force diagram for each of the two masses. b. Write ALL equations necessary to solve for the linear acceleration of MH. B мн
A. A light, rigid rod of length L = 1.00 m joins two particles, with masses m_1 = 4.00 kg and m_2 = 3.00 kg, at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below). Determine the angular momentum of the system about the origin when the speed of each particle is 7.40 m/s. B. What would be the new angular momentum of the system (in kg · m2/s) if each of the masses were instead a solid sphere 13.5 cm in diameter?
A solid cylinder with mass m, radius R, and rotational inertia I (about its center) is released from rest and rolls down a ramp. Friction between the bottom of the cylinder and the ramp causes the cylinder to roll without slipping. The linear acceleration of the cylinder is a. Which TWO of the equations below are correct for this scenario? The equations are in terms of m, I, R, and a, as well as f (the force of static friction between the cylinder and the ramp) and g. (You must pick BOTH of them to get this question correct!) f = ma mg sin θ = ma mg sin θ - f = ma f R = I (a/R) mg sin θ - f = I (a/R) R mg sin θ = IaR
A bug is on the surface of a small wheel, which is a solid disk.
How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a radius of 29.0 mm from the center of the disk. Ignore the small circular hole at the CD’s center. in J
A uniform hoop of radius R and mass m rotates freely (without friction) about a perpendicular axis through its rim, as shown. It is released from a position, labeled "Initial", with the hoop's center directly above with the axis. It swings past position "A" where the center is level with the axis and continues swinging through "B" where the center is below the axis. What are the angular accelerations at positions A and B?
A uniform solid sphere of mass 6.0 kg and radius 10 cm is rolling without slipping along a horizontal surface with a speed of 4.9 m/s (this is the speed of the center of mass) when it starts up a ramp that makes an angle of 30° with the horizontal. 1st а) b) While the ball is moving up the ramp, find What is the maximum distance it can go up the ramp, measured along the surface of the ramp? 2nd? the acceleration (magnitude and direction) of its center of mass and i) ii) | 3rd 3] the friction force (magnitude and direction) acting on it due to the surface of the ramp. Moment of inertia of a solid sphere is I em =MR². ст
Baby Huey rolls a hollow sphere of mass M and radius R up a hillside, giving it an initial kinetic energy of Ki. It rolls over the top of the hill of height h and keeps going. The ball rolls without slipping the whole way, but it loses Wnc due to non-conservative forces between the foot of the hill and the top. a. If M = 6.82 kg and R = 10.9 cm, find its rotational inertia. b. Find the translational velocity at the top of the hill.