### Physics Problem: Acceleration of a SpoolA spool of thread consists of a cylinder with the following specifications:- **Inner Radius, \( R_1 \):** 4.3 cm- **Outer Radius, \( R_2 \):** 9.9 cm- **Mass, \( m \):** 190 gThe illustration displays an end view of the spool on a rough, horizontal surface, ensuring the spool rolls without slipping. A force \( \vec{T} = 0.500 \, \text{N} \) is applied to the right on the thread's free end.**Moment of Inertia Consideration:**- The spool is treated as a solid cylinder with radius \( R_1 \), assuming the extended edges are thin and light.**Diagram Explanation:**- The diagram shows a spool with two concentric circles: - The smaller circle represents the cylinder of radius \( R_1 = 4.3 \) cm. - The larger circle illustrates the end caps with radius \( R_2 = 9.9 \) cm.- A horizontal arrow pointing right indicates the direction of the applied force \( \vec{T} \).- The ground is illustrated as a rough surface for rolling without slipping.**Problem Statement:**(a) Calculate the acceleration of the spool. Assume the positive direction is to the right.

Answered: Image /qna-images/answer/7124918f-7e94-4039-a86d-562d60dc08b5.jpg

A spool of thread consists of a cylinder of radius R1 = 4.3 cm with end caps of radius R2 = 9.9 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 190 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T = 0.500 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. \R2 R (a) What is the acceleration of the spool? Take positive to be to the right.

A spool of thread consists of a cylinder of radius R1 = 4.3 cm with end caps of radius R2 = 9.9 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 190 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T = 0.500 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. \R2 R (a) What is the acceleration of the spool? Take positive to be to the right.

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

In the figure, the block has mass m=0.45 kg and the pulley is on a frictionless horizontal axle with radius R=5.35 cm. When released from rest, the cylindrical pulley makes 10 full turns in 4.57 seconds as the block goes down. Find the rotational inertia of the pulley.
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 metal ball with 0.27 kg of mass and 0.050 m of radius rolled without slipping on a horizontal floor. A ramp was placed on the floor. The ball rolled up the incline without slipping to a vertical height of 0.47 m before stopping. The ramp has a length of 1.7 m along the incline. Find the speed of the ball before it reached the ramp. Hint: the ball has rotational kinetic energy. The rotational inertia of a solid sphere is (2/5)mr^2.
Two wheels have the same mass and radius of 4.9kg and 0.45 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 13 rad in 8.4 s. Find the net external torque that acts on each wheel.
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 ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.7 kg and radius R = 0.25 m. The rods each have mass m, = 1.2 kg and length L = 0.86 m.
Question 16 my m, Two blocks are joined by a pulley system (see Figure). The pulley is a solid disk of mass 0.5 kg and radius 179 mm. Assume that the pulley rotates smoothly. If mass 1 is 4.4 kg and mass 2 is 15 kg, what is the angular acceleration of the disk? HINT: the tensions in the horizontal and vertical portions of the rope are not equal. (PUHQ1629)
A uniform disk of radius 0.507 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.243 N applied at the rim causes an angular acceleration of 0.117 rad/s^2. Find the mass of the disk.
A cylindrical metal drum, with a radius of 0.25 m, has an inertia of 11.0.kg. The drum is hollow and you may neglect the inertia of the top and bottom of the drum. The drum is free to rotate about an axle that runs through its centre and along its long axis. A cord is wrapped around the drum. The cord is pulled straight from the drum with a constant force of 60 N. As the cord unwinds, the drum rotates, with no slippage between the cord and the drum. (a) Calculate the work done by person pulling the cord as the drum rotates through 100 radians. Give your answer in Joules (b) Assuming the drum starts from rest, what is the rotational speed of the tyre after it has rotated through 100 radians? Give your answer in rad.s
A uniform disc of mass 3.0 kg and radius 25 cm is mounted on a fixed horizontal axle. A block with mass 1.8 kg hangs from a light cord that is wrapped around the rim of the disc. What is the angular acceleration of the disc?
A metal disc with 0.18 kg of mass and 0.070 m of radius rolled without slipping on a horizontal floor. A ramp was placed on the floor. The disc rolled up the incline without slipping to a vertical height of 0.43 m before stopping. The ramp has a length of 1.7 m along the incline. Find the speed of the disc before it reached the ramp. Hint: the disc has rotational kinetic energy. The rotational inertia of a disc is (1/2)mr^2.