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Kinematics and Force Problem Solving

Kinematics and Force Problem Solving. 8.01 W02D3. Next Reading Assignment: W03D1. Young and Freedman: 4.1-4.6, 5.1-5.3. Today’s Reading Assignment: W02D3. Young and Freedman: University Physics (Review) 5.1-5.3. Newton’s Second Law Detailed Problem Solving Strategy.

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Kinematics and Force Problem Solving

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  1. Kinematics and Force Problem Solving 8.01 W02D3

  2. Next Reading Assignment: W03D1 Young and Freedman: 4.1-4.6, 5.1-5.3

  3. Today’s Reading Assignment: W02D3 Young and Freedman: University Physics (Review)5.1-5.3

  4. Newton’s Second Law Detailed Problem Solving Strategy

  5. Methodology for Newton’s 2nd Law • Understand – get a conceptual grasp of the problem Sketch the system at some time when the system is in motion. Draw free body diagrams for each body or composite bodies: Each force is represented by an arrow indicating the direction of the force Choose an appropriate symbol for the force

  6. II. Devise a Plan Choose a coordinate system: • Identify the position function of all objects and unit vectors. • Include the set of unit vectors on free body force diagram. Apply vector decomposition to each force in the free body diagram: Apply superposition principle to find total force in each direction:

  7. II. Devise a Plan: Equations of Motion • Application of Newton’s Second Law • This is a vector equality; the two sides are equal in magnitude and direction.

  8. II. Devise a Plan (cont’d) Analyze whether you can solve the system of equations • Common problems and missing conditions. • Constraint conditions between the components of the acceleration. • Action-reaction pairs. • Different bodies are not distinguished. Design a strategy for solving the system of equations.

  9. III. Carry Out your Plan Hints: Use all your equations. Avoid thinking that one equation alone will contain your answer! Solve your equations for the components of the individual forces.

  10. IV. Look Back • Check your algebra • Substitute in numbers • Check your result • Think about the result: Solved problems become models for thinking about new problems.

  11. Group Problem: Non-Uniform Acceleration An object has an acceleration given by   At t = 0 the object is located at x(t = 0)= x0 with a x-component of velocity v(t = 0) = v0. Find x(t).

  12. Group Problem: Building 24 Elevator A person of given mass m is standing on a scale in an elevator in Building 24. Initially the elevator is at rest. The elevator then begins to ascend to the sixth floor, which is a given distance h above the starting point. The elevator undergoes an unknown constant acceleration of magnitude a for a known time interval t1. Then the elevator moves at a constant velocity for a time interval 4t1 . Finally the elevator brakes with a deceleration of the same magnitude as the initial acceleration for a time interval t1 until stopping at the sixth floor. Assume the gravitational constant is given as g. Find the magnitude of the acceleration.

  13. Group Problem: Blocks and Pulleys on Table Two blocks rest on a frictionless horizontal surface. They are connected by 3 massless strings and 2 frictionless, massless pulleys as shown above. A force F is applied to block 1. What is the resulting acceleration of block 1?

  14. Next Reading Assignment: W03D1 Young and Freedman: University Physics (Review) 5.1-5.3 Experiment 1: Force and Motion

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