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Homework Solutions for Translational and Rotational Dynamics Problems

This document provides comprehensive solutions to a series of physics problems focused on translational and rotational dynamics. It details the application of torque and force analysis with specific reference to angles, distances, and applied forces. Each problem is systematically solved, illustrating the necessary calculations and concepts for understanding the balance of forces and torques in various scenarios. Key results, such as tension forces and net torques, are highlighted to reinforce learning outcomes.

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Homework Solutions for Translational and Rotational Dynamics Problems

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  1. Translational & Rotational Homework

  2. 1. ANSWER: 48.7 N @ 70 1.91 m to right of pivot pt GOT IT! Show me

  3. 30N Where to put it: ROTATIONAL: 42 50 10N 10N 1. 48.7 N 20.1 22.3 38.6 46.0 70° TRANSLATIONAL: Need : 45.9 up 16.3 right  = F d 10(7) = 70 CCW 20.1(5) = 101 CW 10(3.5) = 35 CCW 46(2) = 92 CW NET = 88 Nm CW 88 = 45.9 d Only the  part causes torque! 1.91 m = d 48.7 N @ 70° 45.9 16.3 You need CCW….so think if it should be 1.91 meters to left or right! Need : 88 Nm CCW

  4. 2. ANSWER: 1230 N GOT IT! Show me

  5. All angles of a triangle add to 180 78 55 700 N 2. T? 47 55 55 800 CW  = CCW  sin55(800)(2.5)+ sin55(700)(5) = sin47(T)(5) 1638 + 2867 = 3.657 T 1230 N = T

  6. 3. ANSWER: 16.6 N @ 80 3.29 m to right of pivot pt GOT IT! Show me

  7. ROTATIONAL: Where to put it: 3. Break the forces into components 18.1 9.19 19.1 65 50 30 7.71 8.45 11 TRANSLATIONAL:  = F d Need : 16.3 down 2.94 left 11(2) = 22.0 CCW 9.19(.5) = 4.6 CW 18.1(2) = 36.2 CCW NET = 53.6 Nm CCW 53.6 = 16.3 d 2.94 Only the  part causes torque! 3.29 m = d 16.3 You need CW….so think if it should be 3.29 meters to left or right! 16.6 N @ 80 Need: 53.6 Nm CW

  8. 20. ANSWER: 553 N & 327 N GOT IT! Show me

  9. ROTATIONAL: 20. TA TB  Put pivot pt on one of the forces you don’t know (either one) You could move pivot pt to other end to get TB ..or use TRANS like I did 205 675 TRANSLATIONAL: CW = CCW UP = DOWN 205(1.5) + 675(2) = TB(3) TA + 553 = 205 + 675 307.5 + 1350 = 3TB TA = 327 N 553 N = TB

  10. 21. ANSWER: T = 392 N 0 vertical & 339 N horizontal to right GOT IT! Show me

  11. T 196 21. 30° ROTATIONAL: TRANSLATIONAL: CW = CCW Up & Down already cancel 196 L = sin30 T L Need: cos30(392) to right T = 392 N 339 N to right

  12. 22. ANSWER: T = 1465 n “Reaction Force” 2902 N @ 63 GOT IT! Show me

  13. 22. 619 T Tension is a right angle Break tension into Components to look at forces UP, DOWN, LEFT, & RIGHT 25 25 1327 2000 25 1200 TRANSLATIONAL: ROTATIONAL: CW = CCW Need: 1327 right 2581 up 2581 sin25(2000)L + sin25(1200)(½ L) = T(¾ L) 845 + 254 = .75T 2000 + 1200 - 619 1327 1465 N = T 2902 N @ 63

  14. THE END

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