2. Solving Force Probmems Physics Mr. Maloney

3. © 2002 Mike Maloney Objectives You will be able to  diagram Force problems  use FBDs to analyze and solve force problems.

4. © 2002 Mike Maloney “Picturing Force” Free-Body Diagrams  Free Body Diagrams are vector diagrams.  We use them to graphically depict what is acting on an object.  They represent the magnitude and direction of all forces acting on an object.

5. © 2002 Mike Maloney Free Body Diagrams  The diagram at right shows all the forces acting on this object.  Here we have Gravity, a Frictional Force, an Applied Force, and a Normal Force.  Objects can have any number of forces acting on them, depending on the situation. LET’S IDENTIFY SOME

6. © 2002 Mike Maloney Balanced Forces (Statics) (N1L)  There are often situations where a number of forces are acting on something, and the object has no motion – it is STATIC or in EQUILIBRIUM.  This means the NET FORCE on the object is zero, or in other words the forces balance each other out.NET FORCE  What does this mean mathematically?mathematically

7. © 2002 Mike Maloney unBalanced Forces (Dynamics) (N2L)  There are other situations where all the forces acting on something do not cancel each other out completely.  This means the NET FORCE on the object is not zero, the object will change its motion and accelerate proportional to the object’s mass.NET FORCE   F = m ∙ a  Let’s try one of these.one of these

8. © 2002 Mike Maloney Solving Strategy 1. Determine whether it is a static problem or a dynamic problem if you can. 2. Sketch a Free Body diagram. 3. Draw and label vectors representing all forces. 4. Pick an “X” and “Y” direction. If there is any motion, you should choose either X or Y to be in the direction of motion. 5. B Break forces into components if necessary 6. Sum the forces (  F) in the X and Y directions, and set them equal to either 0 or m∙a accordingly. (If you are unsure, use m∙a) 7. Use the summation equations (  F) you have created to solve for unknown values. Lets go back and try a few more.

9. © 2002 Mike Maloney More Advanced Problems  There are usually many types of forces acting on objects where friction and motion is occurring.  They can either be parallel to the motion, or perpendicular to it.  This next example has a block on a table where there is friction and an applied force at an angle.applied force

10. © 2002 Mike Maloney Advanced Problems  What forces are acting parallel to the surfaces?  The horizontal (x) part of the Applied Force {F A }, and the Friction Force {F f }Applied Force  What about Perpendicular?  The vertical (y) part of the Applied force {F A }, the Weight {F g } and the Normal force {F N }Applied force block surface FAFA FfFf F Ax FNFN FgFg F Ay

11. © 2002 Mike Maloney  We see that an applied force can be applied at any angle. So it may act perpendicular and/or parallel to the motion. Advanced Problems block surface FAFA FfFf F Ax FNFN FgFg F Ay

12. © 2002 Mike Maloney  However F N is always perpendicular to the motion.  F f is always parallel to the motion.  On a flat surface F g is perpendicular, but we saw how it can be both on an incline.  Each problem has to be looked at and analyzed individually.  So lets try some.lets try some Advanced Problems block surface FAFA FfFf F Ax FNFN FgFg F Ay By the Way, what is wrong with this Free Body Diagram?

13. © 2002 Mike Maloney Block on hill  Let’s go back to a block just sitting on a track.  What happens when I slant the track?  The cart starts to move. I did not change any of the forces acting on the cart … so what changed? changed

14. © 2002 Mike Maloney Objectives Can you …  diagram Force problems  use FBDs to analyze and solve force problems.

15. © 2002 Mike Maloney APPENDIX

16. Net Force  NET FORCE refers to the vector sum total of all forces acting on an object. It is often expressed as  F  For example, if there were two leftward forces of 10 lb each, the NET FORCE would be 20 lb leftward.  If there were one 10 lb rightward force and one 8 lb leftward force, the NET FORCE would be 2 lb rightward.  What about if the forces were in X and Y?  BACK

17. © 2002 Mike Maloney Static problem  Static problems are associated with Newton’s 1 st Law.  Static problems are problems in which the net force is ZERO (0).net force  In this case the sum of the forces in the X-direction and the Y-direction are both ZERO (0).  BACK

18. © 2002 Mike Maloney dynamic problem  Dynamic problems are associated with Newton’s 2 nd Law.  Dynamic problems are problems in which the net force is not ZERO.net force  In this case the sum of the forces in the X-direction and/or the Y-direction are not always zero, and may result in some acceleration.  BACK

19. © 2002 Mike Maloney x/y Components  If the forces are acting in more than 2 directions (i.e. applied force at an angle) break all the forces down into vertical and horizontal components or parallel and perpendicular components using vector rules (sine and cosine).  Once they are broken up, you can  F x and  F y to solve for the unknowns.  BACK

20. © 2002 Mike Maloney 1.  A book is at rest on a table top. FNFN FgFg BACK TO LECTURE

21. © 2002 Mike Maloney 2.  A girl is suspended motionless in the air by two ropes attached to her. FTFT FgFg FTFT BACK TO LECTURE

22. © 2002 Mike Maloney 3.  An egg is free-falling from a nest in a tree. Neglect air resistance. FgFg BACK TO LECTURE

23. © 2002 Mike Maloney 4.  A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. F AIR FgFg BACK TO LECTURE

24. © 2002 Mike Maloney 5.  A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. FNFN FgFg FAFA FfFf BACK TO LECTURE

25. © 2002 Mike Maloney 6.  A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. FNFN FgFg FAFA FfFf BACK TO LECTURE

26. © 2002 Mike Maloney 7.  A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. FAFA FgFg BACK TO LECTURE

27. © 2002 Mike Maloney 8.  A skydiver is descending with a constant velocity. Consider air resistance. F AIR FgFg BACK TO LECTURE

28. © 2002 Mike Maloney 9.  A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. FNFN FgFg FAFA FfFf BACK TO LECTURE

29. © 2002 Mike Maloney 10.  A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. FgFg BACK TO LECTURE

30. © 2002 Mike Maloney 11. Three smaller kids are pulling a rope against one large kid.  A. They are at a stand still  B. The big kid is winning BACK TO LECTURE

31. © 2002 Mike Maloney 11. Three smaller kids are pulling a rope against one large kid.  A. They are at a stand still  B. The big kid is winning BACK TO LECTURE

32. © 2002 Mike Maloney 11. Three smaller kids are pulling a rope against one large kid.  A. They are at a stand still  B. The big kid is winning BACK TO LECTURE

33. © 2002 Mike Maloney 12.  A car is coasting to the right and slowing down. FfFf BACK TO LECTURE FNFN FgFg

34. © 2002 Mike Maloney 13.  Mr. M is holding a book against a flat wall. FNFN FgFg FAFA FfFf BACK TO LECTURE