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1. Connecting Rotational and Translational Motion: In nuclear reactors, control rods are made of materials that absorb neutrons. Emergency control rods are "dropped" into the reactor core At the Chernobyl reactor, the control rods were attached by cables to pulleys. The mass of the pulley is 4M, and its radius is R. It is mounted on frictionless bearings. The mass of the control rod is M Treat the pulley as solid disk. a Draw the free body diagram for the rod. b. Draw an extended free body diagram for the pulley showing both the forces and where they act 4M, R • Gravity acts at the center of mass . Don't forget the pivot force that holds the pulley up. M c. Using the forces in your free body diagram, write Newton's 2nd law in the vertical direction for the control rod. Choose your coordinate system so that the acceleration is in the positive direction. s↓ g. Determine the tension. O 0 _Mg-T=__Ma_ d. Using the forces in your free body diagram, write the rotational second law for the pulley. Choose your coordinate system so that the angular acceleration is in a positive direction. e. What is the relation between the angular acceleration and the acceleration : f. You should have three equations and three unknowns. Solve for the acceleration in terms of M, R. and/org.

1. Connecting Rotational and Translational Motion: In nuclear reactors, control rods are made of materials that absorb neutrons. Emergency control rods are "dropped" into the reactor core At the Chernobyl reactor, the control rods were attached by cables to pulleys. The mass of the pulley is 4M, and its radius is R. It is mounted on frictionless bearings. The mass of the control rod is M Treat the pulley as solid disk. a Draw the free body diagram for the rod. b. Draw an extended free body diagram for the pulley showing both the forces and where they act 4M, R • Gravity acts at the center of mass . Don't forget the pivot force that holds the pulley up. M c. Using the forces in your free body diagram, write Newton's 2nd law in the vertical direction for the control rod. Choose your coordinate system so that the acceleration is in the positive direction. s↓ g. Determine the tension. O 0 _Mg-T=__Ma_ d. Using the forces in your free body diagram, write the rotational second law for the pulley. Choose your coordinate system so that the angular acceleration is in a positive direction. e. What is the relation between the angular acceleration and the acceleration : f. You should have three equations and three unknowns. Solve for the acceleration in terms of M, R. and/org.

Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotation Of A Rigid Object About A Fixed Axis
Section: Chapter Questions
Problem 13P
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Activity 4.7 - Rolling and Rotational Dynamics 1. Connecting Rotational and Translational Motion: In nuclear reactors, control rods are made of materials that absorb neutrons. Emergency control rods are "dropped" into the reactor core At the Chernobyl reactor, the control rods were attached by cables to pulleys. The mass of the pulley is 4M, and its radius is R. It is mounted on frictionless bearings. The mass of the control rod is M. Treat the pulley as solid disk. a. Draw the free body diagram for the rod. b. Draw an extended free body diagram for the pulley showing both the forces and where they act. 4M, R Gravity acts at the center of mass Don't forget the pivot force that holds the pulley up. M c. Using the forces in your free body diagram, write Newton's 2nd law in the vertical direction for the control rad. Choose your coordinate system so that the acceleration is in the positive direction. of g. Determine the tension. O 0 _Mg-T=__Ma_ d. Using the forces in your free body diagram, write the rotational second law for the pulley. Choose your coordinate system so that the angular acceleration is in a positive direction. e. What is the relation between the angular acceleration a and the acceleration : f. You should have three equations and three unknowns. Solve for the acceleration in terms of M, R, and/or g. 2. A billiard ball of mass M and radius R rolls without slipping down an incline of angle & We want to determine the acceleration of the ball. Suggestion: consider the axis of rotation to be through the center of mass of the object. a. Draw an extended free body showing the forces acting on the object and where they act. b. Write Newton's 24 law for the object in terms of the forces on your FBD and the magnitude of the acceleration a. Choose +x to be down the ramp. Q c. Use your extended FBD to write the rotational second law in terms of forces, R, and a. Look up the moment of inertia if needed. Hint: it will be simpler if you choose the + rotation to be the same direction as the angular acceleration. d. Use the relation between a anda and the Newton's 2 Law and rotational 2 Law relations from (b) and (c) to solve for the acceleration. e. What is the static friction force between the ball and the ramp? f. The experiment is repeated with a thin hoop of the same mass and radius. Will the acceleration of the hoop be larger, smaller or the same as the billiard ball?
Transcribed Image Text:Activity 4.7 - Rolling and Rotational Dynamics 1. Connecting Rotational and Translational Motion: In nuclear reactors, control rods are made of materials that absorb neutrons. Emergency control rods are "dropped" into the reactor core At the Chernobyl reactor, the control rods were attached by cables to pulleys. The mass of the pulley is 4M, and its radius is R. It is mounted on frictionless bearings. The mass of the control rod is M. Treat the pulley as solid disk. a. Draw the free body diagram for the rod. b. Draw an extended free body diagram for the pulley showing both the forces and where they act. 4M, R Gravity acts at the center of mass Don't forget the pivot force that holds the pulley up. M c. Using the forces in your free body diagram, write Newton's 2nd law in the vertical direction for the control rad. Choose your coordinate system so that the acceleration is in the positive direction. of g. Determine the tension. O 0 _Mg-T=__Ma_ d. Using the forces in your free body diagram, write the rotational second law for the pulley. Choose your coordinate system so that the angular acceleration is in a positive direction. e. What is the relation between the angular acceleration a and the acceleration : f. You should have three equations and three unknowns. Solve for the acceleration in terms of M, R, and/or g. 2. A billiard ball of mass M and radius R rolls without slipping down an incline of angle & We want to determine the acceleration of the ball. Suggestion: consider the axis of rotation to be through the center of mass of the object. a. Draw an extended free body showing the forces acting on the object and where they act. b. Write Newton's 24 law for the object in terms of the forces on your FBD and the magnitude of the acceleration a. Choose +x to be down the ramp. Q c. Use your extended FBD to write the rotational second law in terms of forces, R, and a. Look up the moment of inertia if needed. Hint: it will be simpler if you choose the + rotation to be the same direction as the angular acceleration. d. Use the relation between a anda and the Newton's 2 Law and rotational 2 Law relations from (b) and (c) to solve for the acceleration. e. What is the static friction force between the ball and the ramp? f. The experiment is repeated with a thin hoop of the same mass and radius. Will the acceleration of the hoop be larger, smaller or the same as the billiard ball?
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