Forces

1. Forces

2. Things to recall • A force is usually simply defined as a push or pull. • Alt: An influence which causes motion. • A force acting on a body can cause the object to accelerate. • When multiple forces act on a body, the resultant (or net) force is a superposition of the forces.

3. We start this discussion by recalling Newton’s 2nd law. • Definition: The net force on a body is equal to the product of its mass and acceleration. (As an equation)

4. We start this discussion by recalling Newton’s 2nd law. • Definition: The net force on a body is equal to the product of its mass and acceleration. • Note that we can write this law in component form for each axis. (As an equation)

5. Application of Newton’s laws Example

6. Example • A jumbotron weighing 48000N is suspended above the 3Ws field by cables shown in the diagram. Find the tension in the cables if there is equilibrium.

7. We start by drawing a free body diagram.

8. We start by drawing a free body diagram. • A free body diagram is one where all of the forces acting on a body are shown while all other forces and bodies are removed. • Using a free body diagram helps you to visualise the problem!

9. Identify the system of interest . • In this case the jumbotron is the object of interest. • Identify and draw of the external forces acting on the body.

10. Identify the system of interest . • In this case the jumbotron is the object of interest. • Identify and draw of the external forces acting on the body. • The forces on the jumbotron are its weight and the tension due to the cables. • Write the equations for each axis.

11. Example • Free body diagram: T1 T2 W=48000N

12. Sol: writing Newton’s 2nd law: T1 T2 (1) (2) Fnet = 0 in each case as there is no acceleration in equilibrium W

13. Sol: writing Newton’s 2nd law: • Resolving components, T1 T2 (1) (2) Fnet = 0 in each case as there is no acceleration in equilibrium W +ve dir (3) (4)

14. From equation 3,

15. Special types of Forces

16. Some special forces • Normal force • Friction • Tension • Gravitational force

17. Friction • A simple explanation of friction (or formally the frictional force) is the resistance to motion. • The friction is attributed to a single force. • The friction acts in the direction opposing the intended motion. a T fr

18. The friction force is usually: • Proportional to the force pressing to surfaces together (the normal force) • Depends on the “roughness” of the surfaces.

19. Normal force • The normal force is the force which occurs when an object is in contact with a stable object. • It is an example of an applied force. • It can be considered the “supporting” force. • The normal force acts perpendicular to the surface to which the applied the force acts.

20. From Newton’s third law, a book placed on a table pushes down on the table and the table pushes up on the book. N Halliday/ Resnick/ Walker Fundamentals of Physics The forces acting on the book: The weight of the book and the normal force N. The normal force acts perpendicular to the surface of table. W

21. Tension • The tension is a force which is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. • The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire.

22. Tension (T) Tension (T) Pull Rope attached to a wall

23. Newton’s 3rd law Applications of Action-Reaction

24. When an object interacts with another object they exert a force on each other. • These forces are equal in magnitude and are called action-reaction forces. • Definition: when two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

25. Consider the given situation: The table-book interaction FBT (The force that the table exerts on the book) Halliday/ Resnick/ Walker Fundamentals of Physics FTB (The force that the book exerts on the table)

26. Example • Two blocks attached by a “massless” cord which slides over a frictionless pulley as shown below. The hanging block falls causing the large block to slide. Find the (a) acceleration of the blocks and (b) tension in the cord. a M Frictionless surface m

27. Solution • Show the forces acting on the blocks. N T a a Mg M N mg T T m (The free body diagrams for each block) mg Mg

28. Sliding block • Consider the sliding block: • Newton’s 2nd law for the x and y direction: a (x-direction) (y-direction) N T Mg

29. Sliding block • Consider the sliding block: • Newton’s 2nd law for the x and y direction: a (x-direction) (y-direction) N T Mg

30. Falling block • Consider the falling block: • Newton’s 2nd law for the y direction: a T mg

31. List of equations (1) (2) (3)

32. Using equations 1 and 3, we eliminate T: (1) (3)

33. Using equations 1 and 3, we eliminate T: • Substituting into equation 1: (1) (3)

34. Therefore: • and,

35. More about friction

36. Here we will be considering the friction between dry solid surfaces.

37. Here we will be considering the friction between dry solid surfaces. • We recall that there are two types of friction for this case: kinetic and static friction.

38. Here we will be considering the friction between dry solid surfaces. • We recall that there are two types of friction for this case: kinetic and static friction. • Consider the following example when each case occurs.

39. Consider a book resting on a table. The forces acting on it are shown below. FN Halliday/ Resnick/ Walker Fundamentals of Physics W

40. An external force F is applied to the book. Again the forces acting on it are shown below. FN Halliday/ Resnick/ Walker Fundamentals of Physics fs F (Stationary) The applied force is not large enough to overcome friction W

41. The friction at this point is static friction.

42. As the magnitude of the external force F is increased so does the friction. • NB: The applied force must balance the friction. FN Halliday/ Resnick/ Walker Fundamentals of Physics F fs (Stationary) The applied force is still not large enough to overcome friction W

43. The friction increases with the applied force until it reach a maximum. • At this point the book will move when a greater external force is applied.

44. When the external force is greater than the friction the book is moving. At this point the friction acting on the book is kinetic friction. a FN Halliday/ Resnick/ Walker Fundamentals of Physics F fk (Moving) The book begins to accelerate when the friction is overcome. W

45. Definition • Static Friction: the friction that occurs between the two surface when the two surfaces are at rest relative to each other. • Kinetic Friction: when there is relative motion between surfaces.

46. Properties of Friction • For static friction, the static frictional force balances the component of the net external force parallel to the surface. • When the static friction reaches a maximum: • Where is the coefficient of static friction. • a measure of the relative amount of adhesion between the surfaces

47. Properties of Friction • When the body is moving the kinetic friction is given by: • Where is the coefficient of kinetic friction.

48. Example • A 75kg roller is pulled at angle of 42° along a cricket pitch at constant velocity. If the coefficient of friction between the roller and pitch is 0.1, find the tension T in the handle.

49. The free body diagram: N T fr mg

50. The free body diagram: T sin42 N T fr T cos42 mg