1. PHYSICS 11 SOLVING F=MA PROBLEMS USING FREE BODY DIAGRAMS

2. NEWTON’S SECOND LAW The sum of all the forces is equal to the mass times the acceleration. Recall that force is a VECTOR quantity. Each force has a magnitude and a direction! Acceleration is also a vector quantity. To solve for acceleration, we first need to add up all the forces on the object. To help us add the force vectors correctly we use a free body diagram (FBD).

3. FORCES WE EXPERIENCE DAILY We experience several types of forces daily. All of these forces act in order to make things move or not move. Imagine two children playing outside with a wagon. One child pulls forward on a rope tied to the front, while the other pushes on the wagon from behind. What forces act on the wagon? Photo credit: Nelson Physics 11, copyright 2011

4. FORCES WE EXPERIENCE DAILY In order to analyze the different types of force acting in this situation, two types of force diagram – system diagrams and free-body diagrams – are useful. A system diagram (like the one below) is a sketch of all the objects involved in a situation. Photo credit: Nelson Physics 11, copyright 2011

5. FORCES WE EXPERIENCE DAILY A free-body diagram (FBD) is a simple drawing representing the object being analyzed and all the forces acting on it. The object is typically shown as a rectangle or large dot (point particle) with the forces drawn as arrows originating from the object and pointing away from the centre. Each force is labeled with the symbol F and an appropriate subscript that indicates the force. This is what we will commonly use as it summarizes the important information. Photo credit: Nelson Physics 11, copyright 2011

6. FORCES WE EXPERIENCE DAILY – APPLIED FORCE (F A ) First consider the applied force. An applied force (F a ) results when one object is in contact with another object and either pushes or pulls on it. In our example, the child behind the wagon exerts an applied force on the wagon by pushing on the back Photo credit: Nelson Physics 11, copyright 2011

7. FORCES WE EXPERIENCE DAILY – TENSION FORCE (F T ) Another force is the tension force (often called tension). Tension (F T ) is a pulling force exerted on an object by a rope or a string. In our example, the child at the front of the wagon pulls on the rope, causing tension in the rope. The rope exerts tension on the wagon, pulling it forward. It is important to mention that the tension is the same at all points along the string. There is only ever one tension in a string!

8. FORCES WE EXPERIENCE DAILY – NORMAL FORCE (F N ) Whenever an object is in contact with a surface, the surface can exert two different forces on the object. One is call the normal force. The normal force (F N ) is a perpendicular force exerted on an object by the surface with which it is in contact. In our example, the ground is pushing up on the wagon.

9. FORCES WE EXPERIENCE DAILY – FRICTION FORCE (F F ) The other force exerted by a surface on an object is friction. Friction (F f ) is a force that resists the motion or attempted motion of an object and always acts parallel to the surface and opposes the direction of motion. In our example, if the wagon is moving right, then friction acts towards the left. Even if the wagon was at rest with the children pushing and pulling on it, friction would still be present.

10. FORCES WE EXPERIENCE DAILY – DID YOU KNOW? The forces described thus far require one object to be in contact with another. For this reason, they are called contact forces. Some forces, however, do not require contact. These action-at-a-distance forces are called non-contact forces.

11. FORCES WE EXPERIENCE DAILY – FORCE OF GRAVITY (F G ) The force of gravity (F g ), also called the gravitational force, is the force of attraction that exists between any two objects. The direction of this force is towards Earth’s centre. In our example, the force of gravity pulls down on the wagon.

12. FORCES WE EXPERIENCE DAILY – FORCE OF GRAVITY (F G ) The force of gravity (F g ) is an example of a non-contact force (i.e. it is a force that acts at a distance). To calculate the force of gravity acting on an object, you can use the equation, Where m is the mass of the object (kg), and g is the acceleration due to gravity (m/s 2 ).

13. FORCES WE EXPERIENCE DAILY - SUMMARY Everyday forces: Normal Force (F N )  force perpendicular to surface upon which object rests, contact force Friction Force (F f )  force that opposes (attempted) motion of object, contact force Applied Force (F a )  force exerted on object, contact force Tension Force (F T )  force exerted by string or rope on object, contact force Force of Gravity (F g )  force of attraction between Earth and object, non-contact force Force of gravity can be calculated using the formula, where m is the mass in kilograms (kg) and g is the acceleration due to gravity (m/s 2 ).

14. EXTERNAL FORCES AND INTERNAL FORCES In this course, we will usually be concerned with external forces. External forces are those that are caused by one object pushing or pulling on another. An internal force occurs when an object exerts a force on itself. For example, when skater 1 pushes on skater 2, the force on skater 2 is external. If skater 1 pulls forward on her own arms, then it is an internal force. External Force: Occurs when on object pushes/pulls on another object Internal Force: Occurs when an object exerts a force on itself

15. FREE-BODY DIAGRAMS (FBD’S) In order to study the effects of forces acting on any object, the use of a free- body diagram (FBD) is necessary. Free-Body Diagram: Simple drawing representing the object being analyzed and all the external forces acting on it.

16. FREE-BODY DIAGRAMS (FBD’S) Free-Body Diagram Steps: 1.Draw a box or point particle that will represent the system under analysis. 2.The direction of the arrow shows the direction that the force is acting. 3.The size of the arrow shows the magnitude of the force. 4.Label each force. Note: Recall that force is related by mass and acceleration of the object. When deciding which direction the force is pointing think to yourself, “what direction would the acceleration be in order to get the object to move that way?”

17. USING A FBD TO FIND ACCELERATION 1.Look at the situation and figure out which way the object is likely to move. Call that the positive direction and draw an arrow near your FBD to remind you of which way is positive. 2.Write down all the forces that act in that direction, using + and – signs to identify forces acting in the + and – directions. 3.If the object is not accelerating, then the force vectors should add to zero. (Newton’s 1 st Law.) 4.If the object is accelerating, the sum of the vectors should produce a vector in the same direction as acceleration. Use Newton’s 2 nd Law equation to solve for acceleration in that direction. a=ΣF/m

18. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? a)A book is at rest on a table top.

19. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? a)A book is at rest on a table top. FNFN FgFg

20. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? b)A girl is suspended motionless from the ceiling by a rope.

21. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? b)A girl is suspended motionless from the ceiling by a rope. FTFT FgFg

22. PRACTICE 1.Draw a FBD for the object in bold. c)An egg is free-falling from nest in a tree. Neglect air resistance.

23. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? c)An egg is free-falling from nest in a tree. Neglect air resistance. FgFg

24. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? d)An egg is falling (not freely, do not neglect air resistance) from a nest in a tree.

25. PRACTICE 1.Draw a FBD for the object in bold. d)An egg is falling (not freely, do not neglect air resistance) from a nest in a tree. F air FgFg

26. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? e)A right forward force is applied to a book in order to move it across a desk with a right ward acceleration. Consider frictional forces. Neglect air resistance.

27. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? e)A right forward force is applied to a book in order to move it across a desk with a right ward acceleration. Consider frictional forces. Neglect air resistance. FNFN FaFa FgFg FfFf

28. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? e)A mass hangs vertically from a spring.

29. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? e)A mass hangs vertically from a spring. F elastic FgFg

30. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? f)A car is stopped at a stop light

31. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? f)A car is stopped at a stop light FNFN FgFg

32. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? g)A car is coasting to the right and slowing down.

33. PRACTICE 1.Draw a FBD for the object in bold. What is Fnet? What is a? g)A car is coasting to the right and slowing down. FNFN FgFg FfFf The force of friction is the cause of the car slowing down. There is no longer an applied force.