1. Free-Body Diagrams PHYSICS SEMESTER ONE NANSLO Physics Core Units and Laboratory Experiments by the North American Network of Science Labs Online,North American Network of Science Labs Online a collaboration between WICHE, CCCS, and BCcampusWICHECCCSBCcampus is licensed under a Creative Commons Attribution 3.0 Unported License;Unported License based on a work at rwsl.nic.bc.ca.rwsl.nic.bc.ca Funded by a grant from EDUCAUSE through the Next Generation Learning Challenges. EDUCAUSENext Generation Learning Challenges

2. Introduction Physical objects can be subjected to several different forces at one time Force magnitudes and directions vary Forces can be related to each other Finding unknown forces may be complicated Creative Commons Attribution 3.0 Unported License

3. Free-Body Diagrams Free-body diagrams (FBDs) are sketches showing the relative magnitude and direction of all forces acting on an object They help us see the relationships between the forces They assist in organizing our solutions. Creative Commons Attribution 3.0 Unported License

4. Creating a FBD Case: Find the net force on a 1.0 kg object (rock, animal, crate, computer …) on a horizontal surface with an applied force of 5.0 N to the right, and a coefficient of kinetic friction of 0.20. Creative Commons Attribution 3.0 Unported License

5. Creating a FBD 1.Represent the object with a square. 2.Add and label an arrow with the approximate magnitude and direction of one force acting on the object. 3.Repeat step 2 for all forces. 4.Choose a convenient set of axes. FgFg n FFkFk FBD showing the forces on the object. y x Creative Commons Attribution 3.0 Unported License

6. Other Notes on FBDs It is usually easiest to set one axis in the expected direction of motion. FBDs only show all forces on a single object. If you need to consider forces on two objects, draw two FBDs. Assume that all forces apply to the same point. Otherwise, the question is a torque and rotational equilibrium problem. Creative Commons Attribution 3.0 Unported License

7. Back to Case: Define Terms m = 1.0 kg, F = 5.0 N i, μ k = 0.20, ΣF =? We can assume that the acceleration due to gravity is g = 9.8 m/s 2 (this doesn’t need to be stated). You can often define most variables within the FBD itself. Creative Commons Attribution 3.0 Unported License

8. Net Force We are looking the net force ΣF = F N + F g + F + F f Express the forces in components ΣF x i + ΣF y j= F N j – F g j + F i – F f i ΣF x = F – F f ΣF y = F N – F g Creative Commons Attribution 3.0 Unported License

9. Using the FBD There is no motion in the y-direction so, according to Newton’s First Law, the normal force must balance force of gravity. ΣF y = F N – F g = 0 Creative Commons Attribution 3.0 Unported License

10. Using the FBD The magnitudes of the normal force and friction are related by the equation Evaluating, Creative Commons Attribution 3.0 Unported License

11. Using the FBD Using the definitions of the directions, we can write the forces as vectors. F g = -9.8 N j, F N = 9.8 N j, F = 5.0 N i and F f = -2.0 N i The net force on the object is then F net = n + F g + F + F f = 3.0 N i The net force is 3.0 N to the right. Creative Commons Attribution 3.0 Unported License

12. Sample FBDs A book at rest on a table top. A satellite orbiting earth. FgFg FNFN FgFg Creative Commons Attribution 3.0 Unported License

13. More Sample FBDs An apple suspended from a branch. A crate being pushed up a ramp. FgFg T FAFA FfFf FNFN FgFg coordinates x y Creative Commons Attribution 3.0 Unported License

14. Summary Free-Body Diagrams are useful tools in organizing the relationships between the forces on a single object. –The object in a FBD is represented by a box. –The forces are represented by arrows with appropriate directions and relative magnitudes. A suitable coordinate system can be selected to simplify calculations. Unknown forces can be found using Newton’s Laws of Motion and other physics relationships. Creative Commons Attribution 3.0 Unported License