ch09 - CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS 1...

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CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS ___________________________________________________________________________________________ 1. REASONING AND SOLUTION The magnitude of the torque produced by a force F is given by the magnitude of the force times the lever arm. When a long pipe is slipped over a wrench handle, the length of the wrench handle is effectively increased. The same force can then be applied with a larger lever arm. Therefore, a greater torque can be used to remove the "frozen" nut. ___________________________________________________________________________________________ 2. REASONING AND SOLUTION The torque produced by a force F is given by τ = F A where is the lever arm. A a. A large force can be used to produce a small torque by choosing a small lever arm. Then the product is small even though the magnitude of the force, F , is large. If the line of action passes through the axis of rotation, = 0 m, and the torque is zero regardless of how large F is. F A A b. A small force may be used to produce a large torque by choosing a large lever arm Then, the product can be large even though the magnitude of the force F is small. A . F A ____________________________________________________________________________________________ 3. REASONING AND SOLUTION In a cassette deck, the magnetic tape applies a torque to the supply reel. The magnitude of the torque is equal to the product of the tension F T in the tape, assumed to be constant, and the lever arm . As shown below, the lever arm is the radius of the tape remaining on the supply reel. Figure A shows the reel and tape at an earlier time; figure B shows the tape and the reel at a later time. A A F T A F T Figure A Figure B As the reel becomes empty, the lever arm gets smaller, as suggested in the figures above. Therefore, the torque exerted on the reel by the tape becomes smaller. A ____________________________________________________________________________________________
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Chapter 9 Conceptual Questions 425 4. REASONING AND SOLUTION A flat rectangular sheet of plywood is fixed so that it can rotate about an axis perpendicular to the sheet through one corner, as shown in the figure. In order to produce the largest possible torque with the force F (acting in the plane of the paper), the force F must be applied with the largest possible lever arm. This can be attained by orienting the force F so that it is perpendicular to the diagonal that passes through the rotation axis as shown below. The lever arm is equal to the length of the diagonal of the plywood. Axis of rotation F A ____________________________________________________________________________________________ 5. REASONING AND SOLUTION To unscrew either cap, you apply a force tangentially to it and rotate it about an axis perpendicular to the end of the cap at its center. It is the torque created by this force that turns the cap. The greater the torque, the more easily is the cap unscrewed. For a given force, a greater torque is created when the force has a greater lever arm than when it has a smaller lever arm. In the case of the two caps, the lever arms are the radii of the caps, and the “easy-off” cap has a greater radius than the normal cap. Thus, it is the greater radius of the “easy-off” cap that makes it easier to open.
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ch09 - CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS 1...

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