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Solving Force Probmems Physics Mr. Maloney Objectives You will be able to diagram Force problems use FBDs to analyze and solve force problems. © 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. © 2002 Mike Maloney Free Body Diagrams LET’S IDENTIFY SOME 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. © 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. What does this mean mathematically? © 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. F = m ∙ a Let’s try one of these. © 2002 Mike Maloney Solving Strategy 1. 2. 3. 4. 5. 6. 7. Determine whether it is a static problem or a dynamic problem if you can. Sketch a Free Body diagram. Draw and label vectors representing all forces. 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. Break forces into components if necessary 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) Use the summation equations (F) you have created to solve for unknown values. Lets go back and try a few more. © 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. © 2002 Mike Maloney Advanced Problems FN Ff surface FAy FAx Fg What forces are acting parallel to the surfaces? block FA The horizontal (x) part of the Applied Force {FA}, and the Friction Force {Ff} What about Perpendicular? The vertical (y) part of the Applied force {FA}, the Weight {Fg} and the Normal force {FN} © 2002 Mike Maloney Advanced Problems FN Ff surface block FA FAy FAx Fg We see that an applied force can be applied at any angle. So it may act perpendicular and/or parallel to the motion. © 2002 Mike Maloney Advanced Problems FN Ff surface block FA FAy FAx Fg However FN is always perpendicular to the motion. Ff is always parallel to the motion. By the Way, what On a flat surface Fg is perpendicular, butis we saw how it can be both on an incline. wrong with this Free Each problem has to be looked at and analyzed Body Diagram? individually. So lets try some. © 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? © 2002 Mike Maloney Objectives Can you … diagram Force problems use FBDs to analyze and solve force problems. © 2002 Mike Maloney APPENDIX © 2002 Mike Maloney 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 © 2002 Mike Maloney Static problem Static problems are associated with Newton’s 1st Law. Static problems are problems in which the net force is ZERO (0). In this case the sum of the forces in the X-direction and the Y-direction are both ZERO (0). BACK © 2002 Mike Maloney dynamic problem Dynamic problems are associated with Newton’s 2nd Law. Dynamic problems are problems in which the net force is not ZERO. 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 © 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 Fx and Fy to solve for the unknowns. BACK © 2002 Mike Maloney 1. A book is at rest on a table top. FN Fg BACK TO LECTURE © 2002 Mike Maloney 2. A girl is suspended motionless in the air by two ropes attached to her. FT FT BACK TO LECTURE Fg © 2002 Mike Maloney 3. An egg is free-falling from a nest in a tree. Neglect air resistance. Fg BACK TO LECTURE © 2002 Mike Maloney 4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. FAIR BACK TO LECTURE Fg © 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. FN FA Ff BACK TO LECTURE Fg © 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. FN FA Ff BACK TO LECTURE Fg © 2002 Mike Maloney 7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. FA BACK TO LECTURE Fg © 2002 Mike Maloney 8. A skydiver is descending with a constant velocity. Consider air resistance. FAIR Fg BACK TO LECTURE © 2002 Mike Maloney 9. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. FN FA Ff BACK TO LECTURE Fg © 2002 Mike Maloney 10. A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. Fg BACK TO LECTURE © 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 © 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 © 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 © 2002 Mike Maloney 12. A car is coasting to the right and slowing down. FN Ff BACK TO LECTURE Fg © 2002 Mike Maloney 13. Mr. M is holding a book against a flat wall. Ff FA FN Fg BACK TO LECTURE © 2002 Mike Maloney