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Free Body Diagrams

Learn how to construct and interpret free body diagrams, the critical first step in analyzing biomechanical events. Understand internal and external forces, static equilibrium, and more.

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Free Body Diagrams

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  1. Free Body Diagrams Chapter 1 in Text Dr. Sasho MacKenzie - HK 376

  2. Free-body diagram • An essential tool for evaluating every situation in biomechanics. • The critical first step in analyzing any biomechanical event. • Isolates the “body” (leg, arm, shoe, ball, block etc.) from all other objects. • Only shows external forces acting on an object. Dr. Sasho MacKenzie - HK 376

  3. Internal Forces • Forces that act within the object or system whose motion is being investigated. • Newton’s 3rd Law states that forces come in equal and opposite pairs. • With internal forces, the forces act on different parts of the same system. • These forces cancel each other out, and therefore don’t affect the motion of the system. • Forces at the knee if you are looking at the motion of the entire leg. Dr. Sasho MacKenzie - HK 376

  4. External Forces • Only external forces can change the motion of an object or system. • External forces are those forces that act on an object as a result of its interaction with the environment. • These include friction, air resistance, gravity, pushing or pulling… Dr. Sasho MacKenzie - HK 376

  5. Static Equilibrium • The state of a system when all the external forces on that system sum to zero and the system is not moving. • In other words, the system is at rest, and has no net force acting on it. Dr. Sasho MacKenzie - HK 376

  6. Constructing a Free Body Diagram of a Man pushing a Book on a Desk Step 1 Decide which body or combination of bodies (system) to isolate as the free body diagram Step 2 The body (or system) is isolated by a diagram that represents its complete external boundary Dr. Sasho MacKenzie - HK 376

  7. Step 3 Represent all external forces acting on the isolated body in their proper positions. Known external forces should be represented by vector arrows with their appropriate magnitude and direction indicated. Gravity acts on the CM of an object. Dr. Sasho MacKenzie - HK 376

  8. Step 4 The coordinate axis should be shown on the diagram indicating positive and negative directions. Note The acceleration of the body will always be in the direction of the net force. Friction force will always oppose the direction of motion (velocity). Dr. Sasho MacKenzie - HK 376

  9. y x Fx1 mg1 Fx3 Fx2 Fy1 Fy2 The Man Fy1 and Fy2 = upward ground reaction forces mg1 = body weight Fx2 and Fx3 = friction force Fx1 = reaction force of book on subject Dr. Sasho MacKenzie - HK 376

  10. y x Fx1 mg2 Fx4 Fy3 The Book Fy3 = upward table reaction force mg2 = book weight Fx4 = friction force Fx1 = push from instructor on book If book + accelerates Fx1 > Fx4 If book - accelerates Fx1 < Fx4 Zero acceleration Fx1 = Fx4 Dr. Sasho MacKenzie - HK 376

  11. Y X The right hand ring Static Equilibrium Gymnast Performing Iron Cross • Show the complete free body diagram for • The right hand ring • The gymnast • The cable • The cable and ring Given ax = 0 ay = 0 Dr. Sasho MacKenzie - HK 376

  12. Fy2 Fx2 mg Fx1 Fy1 a) The Right Hand Ring Given ax = 0 ay = 0 Fx = max Fx2 – Fx1 = max = 0 Fx2 = Fx1 Fy = may Fy2 – Fy1 – mg = may = 0 Fy2 = Fy1 + mg Dr. Sasho MacKenzie - HK 376

  13. Fy1 Fy2 Fx1 Fx2 mg b) The Gymnast Given ax = 0 ay = 0 Fx = max Fx1 – Fx2 = max = 0 Fx1 = Fx2 Fy = may Fy2 + Fy1 – mg = may = 0 Fy2 + Fy1 = mg Dr. Sasho MacKenzie - HK 376

  14. Fy1 Fx1 mg Fx2 Fy2 c) The Cable Given ax = 0 ay = 0 Fx = max Fx1 – Fx2 = max = 0 Fx1 = Fx2 Fy = may Fy1 – Fy2 – mg = may = 0 Fy1 = Fy2 + mg Dr. Sasho MacKenzie - HK 376

  15. Fy1 Fx1 mg Fx2 Fy2 d) Cable and Ring Given ax = 0 ay = 0 Fx = max Fx1 – Fx2 = max = 0 Fx1 = Fx2 Fy = may Fy1 – Fy2 – mg = may = 0 Fy1 = Fy2 + mg Dr. Sasho MacKenzie - HK 376

  16. Y X Down Hill Skier Show the complete free body diagram for the skier and skis system Dr. Sasho MacKenzie - HK 376

  17. Y X New Reference Frame mgy mgx Fx2 Fy1 Fx1 mgx mgy mg Given ax < 0 ay = 0 Fx = max Fx1 + Fx2 – mgx = max < 0 Fx1 + Fx2 < mgx Fy = may Fy1 – mgy = may = 0 Fy1 = mgy Dr. Sasho MacKenzie - HK 376

  18. Y X Pushing Book on Table • Draw the complete FBD of • The book • The table Given ax > 0 ay = 0 Dr. Sasho MacKenzie - HK 376

  19. Y X a) The Book Given ax > 0 ay = 0 Fx2 mg Fx1 Fy1 Fx = max Fx2 – Fx1 = max > 0 Fx2 > Fx1 Fy = may Fy1 – mg = may = 0 Fy1 = mg Dr. Sasho MacKenzie - HK 376

  20. Fy1 Fx1 mg Fx2 Fx3 Y Fy2 Fy3 X b) The Table Given ax = 0 ay = 0 Fx = max Fx1 – Fx2 – Fx3 = max = 0 Fx1 = Fx2 + Fx3 Fy = may Fy2 + Fy3 – Fy1 – mg = may = 0 Fy2 + Fy3 = Fy1 + mg Dr. Sasho MacKenzie - HK 376

  21. Y X Hammer Thrower • Draw the complete FBD of • The athlete • ax < 0 ay = 0 • The hammer • ax > 0 ay < 0 Dr. Sasho MacKenzie - HK 376

  22. Fx1 mg Y Fx2 Fy1 X a) The Athlete Given ax < 0 ay = 0 Fx = max Fx2 – Fx1 = max < 0 Fx2 < Fx1 Fy = may Fy1– mg = may = 0 Fy1 = mg Dr. Sasho MacKenzie - HK 376

  23. Fx1 mg Y X b) The Hammer Given ax >0 ay < 0 Fx = max Fx1 = max > 0 Fx1 > 0 Fy = may – mg = may < 0 0 > mg Dr. Sasho MacKenzie - HK 376

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