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Lecture 9

Lecture 9. Newton’s Laws applied to systems with two or more accelerated bodies. Serway and Jewett : 5.7, 5.8. Problems with several accelerated objects:. Free-body diagram for each object. Relate forces by finding action-reaction pairs, etc.

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Lecture 9

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  1. Lecture 9 • Newton’s Laws applied to systems with two or more accelerated bodies. Serway and Jewett : 5.7, 5.8 Physics 1D03 - Lecture 9

  2. Problems with several accelerated objects: • Free-body diagram for each object. • Relate forces by finding action-reaction pairs, etc. • Look for constraints on the motion to relate accelerations. • “F=ma” for each diagram, break into components. • Count unknowns: do you have enough equations? • Use algebra to solve. Physics 1D03 - Lecture 9

  3. Two blocks connected by a rope are being pulled by a horizontal force FA. Given that F=60 N, m1=12kg and m2=18kg, and that μk=0.1, find the tension in the rope between them and the acceleration of the system. T m2 FA m1 Physics 1D03 - Lecture 9

  4. Atwood’s Machine Calculate the acceleration of the blocks. Assume : - no friction - massless rope and pulley - rope doesn’t stretch Plan:• free-body diagram for each mass • relate tensions, accelerations • use Newton’s second Law m2 m1 Physics 1D03 - Lecture 9

  5. Constraints on the motion: Why are the accelerations equal (in magnitude)? • Because the cord doesn’t stretch! Any downward motion of m1 requires an equal upward motion of m2. This is a constraint on the motion, which comes from the geometry of the apparatus. • Label directions of aconsistently on both diagrams: if m1 accelerates up, m2 accelerates down. Physics 1D03 - Lecture 9

  6. Forces on m2 Forces on m1 T1 T2 a2 a1 m2g m1g • Tensions are equal (“ideal” pulley, light rope) • Accelerations are equal in magnitude (why?), opposite in direction Physics 1D03 - Lecture 9

  7. a1 m1 m2 Concept Quiz Consider the more elaborate Atwood’s machine shown. Assuming the rope and pulleys are ideal, the relation between the accelerations will be: a2 Physics 1D03 - Lecture 9

  8. A block of mass m1 on a rough horizontal surface is pulled with a force FA at an angle θ to the horizontal. A ball of mass m2 is connected to the other side, hanging over a lightweight frictionless pulley. The coefficient of friction is given by μk. Determine the acceleration of the system. FA θ m1 m2 Physics 1D03 - Lecture 9

  9. m2 m3 m1 Eg: Given no friction, determine the acceleration of the system and the tension in the strings. Physics 1D03 - Lecture 9

  10. Example: How do you calculate the acceleration of each block: • if the upper block doesn’t slide? • if the upper block does slide? m = 1.0 kg M = 2.0 kg ms = 0.6 mk = 0.4 FP = 15 N m FP M Physics 1D03 - Lecture 9

  11. Suggested Problems Chapter 5: Problems 17, 25, 29, 43, 44, 62, Questions 19, 21 Physics 1D03 - Lecture 9

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