1. Chapter 4 : Laws of Motion Weerachai Siripunvaraporn Department of Physics, Faculty of Science Mahidol University email&FB : wsiripun2004@hotmail.com

2. What is in this chapter? Force is the causes of motion.

3. In previous chapter, we described motion in terms of position, velocity, and acceleration. But we have not considered the causes of motion. Here, we begin our investigation of the causes of motion. Definition: 1. a force is a push or a pull that causes an object to move. 2. a force is something that causes an object to accelerate. Forces have both magnitude and direction, so forces are vector quantities. Force

4. Contact and Field Forces CH5 No physical contact is required

5. Fundamental Forces Gravitational force Between objects Electromagnetic forces Between electric charges Nuclear force Between subatomic particles Weak forces Arise in certain radioactive decay processes Note: These are all field forces. Section 5.1 CH5

6. ∑F = F 1 + F 2

7. Net Force FF1F1 F2F2 ∑F = F 1 + F 2

8. Net Force Each force and net force can be divided into components.

10. Sir Isaac Newton 1642 – 1727 Formulated basic laws of mechanics Discovered Law of Universal Gravitation Invented form of calculus Many observations dealing with light and optics Section 5.1 CH5

11. Inertial frames are frames of reference that are not accelerating (i.e. not moving or moving at constant velocity) A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame, and for our purposes we can consider the Earth as being such a frame. The Earth is not really an inertial frame because of its orbital motion around the Sun and its rotational motion about its own axis, both of which result in centripetal accelerations. However, these accelerations are small compared with g and can often be neglected. For this reason, we assume that the Earth is an inertial frame, as is any other frame attached to it.

12. If there is no force acting on it, it remains the same.

13. Newton’s First Law – Alternative Statement In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. Newton’s First Law describes what happens in the absence of a force. Does not describe zero net force Also tells us that when no force acts on an object, the acceleration of the object is zero Can conclude that any isolated object is either at rest or moving at a constant velocity Section 5.2 CH5

14. Applications of Newton’s first law

16. Which is easier to pull, a shredder or a fire truck? A fire truck is more resistant to changes in its velocity than the shredder. How can we quantify this concept? Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity. The SI unit of mass is the kilogram (kg). The greater the mass of an object, the less that object accelerates under the action of a given applied force.

17. More About Mass Mass is an inherent property of an object. Mass is independent of the object’s surroundings. Mass is independent of the method used to measure it. Mass is a scalar quantity. Obeys the rules of ordinary arithmetic The SI unit of mass is kg. Mass and weight are two different quantities. Section 5.3 CH5

18. Notice that the acceleration is in the same direction as the resultant force. Force is the cause of changes in motion, as measured by the acceleration. Remember, an object can have motion in the absence of forces. Do not interpret force as the cause of motion.

19. Newton’s Second Law  is the net “external” force This is the vector sum of all the forces acting on the object. May also be called the total force, resultant force, or the unbalanced force. Newton’s Second Law can be expressed in terms of components: Remember that ma is not a force. The sum of the forces is equated to this product of the mass of the object and its acceleration. The SI unit of force is the newton (N). 1 N = 1 kg·m / s 2 Section 5.4 CH5

22. action force reaction force action force reaction force

24. action force reaction force

27. Free Body Diagrams and the Particle Model The particle model is used by representing the object as a dot in the free body diagram. The forces that act on the object are shown as being applied to the dot. The free body helps isolate only those forces acting on the object and eliminate the other forces from the analysis. Section 5.6 CH5

28. External and Internal Forces and System We only care about the external forces. To tell which forces are external forces, we must define system of interest first. If dog is system, External force …

29. F m1m1 m2m2 External and Internal Forces Force F acting on m 1 and m 2, there is internal force between m 1 and m 2. F1’F1’F2’F2’ If m 1 and m 2 are our system of interest, F is external force and F 1 ’ and F 2 ’ are internal forces. If m 1 is our system of interest, F and F 2 ’ are external force. If m 2 is our system of interest, F 1 ’ is external force.

32. 130 N

34. Forces in every day Gravitational force and weight Normal force Tension force Friction

35. Gravitational Force & Weight The gravitational force,, is the force that the earth exerts on an object. This force is directed toward the center of the earth. From Newton’s Second Law: Its magnitude is called the weight of the object. Weight = F g = mg Because it is dependent on g, the weight varies with location. g, and therefore the weight, is less at higher altitudes. This can be extended to other planets, but the value of g varies from planet to planet, so the object’s weight will vary from planet to planet. Weight has a unit of Newton. CH5

36. But g is not constant, decrease with increasing distance from the surface. Therefore, weight is not constant. g near the surface is about 9.8 m/s 2 and vary from point to point. g  1/r 2

37. Mass vs. Weight Mass and weight are two different quantities. Weight is equal to the magnitude of the gravitational force exerted on the object. Weight will vary with location. Section 5.3 CH5

38. g near Earth’s surface is about 10 m/s 2 g near Moon’s surface is about 10/6 m/s 2 What is your mass on Earth and on Moon? What is your weight on Earth and on Moon? Mass = 60 kgMass = 60 kg Weight = 60 kg x 10 m/s 2 Weight = 60 kg x 10/6 m/s 2 = 600 N = 100 N

40. Normal Force N N N

42. Tension Force String tension is an electromagnetic force. The molecules in the string are pulling one another. Each portion of the string transmits the force undiminished from end to end. A light smooth pulley

43. If the acceleration of an object that can be modeled as a particle is zero, the particle is in equilibrium.

44.  F x = ma x  F y = ma y

45. Problem-Solving Hints – Applying Newton’s Laws Conceptualize Draw a diagram Choose a convenient coordinate system for each object Categorize Is the model a particle in equilibrium? If so,  F = 0 Is the model a particle under a net force? If so,  F = m a Section 5.7 CH5

46. Problem-Solving Hints – Applying Newton’s Laws, cont. Analyze Draw free-body diagrams for each object Include only forces acting on the object Find components along the coordinate axes Be sure units are consistent Apply the appropriate equation(s) in component form Solve for the unknown(s) Finalize Check your results for consistency with your free-body diagram Check extreme values Section 5.7 CH5

50. If we try to drag a box with an increasing force F, what would happen?

62. Example A mass m is attached to a tread and suspended from a ceiling. A force F pulls the mass sideway such that the tread is deviated by an angle  from the vertical. Find the magnitude of F and the tension in the string in terms of m, g and .

63. Example 4kg6kg Two bodies of mass 4kg and 6kg are tied with a string, and put on a smooth floor. A force 10N pulls 6kg mass to the right. Find the acceleration of the two bodies and the string tension. 10N 4kg T a 6kg a 10N T

64. Example A body slides on a rough surface with a kinetic friction constant of 0.4. How far does the body move before it comes to rest? u = 10 m/s a N mg

65.  y x  T W Example A small ball is suspended from a ceiling of a moving car. The car moves with a constant acceleration a. Find the angle  through which the string is deviated from the vertical.

66.  Example A small disc is resting on an inclined plane making an a small angle  with the horizontal. The inclination angle  is then slowly increased. Find the critical angle  c at which the disc starts to slide down. The static friction constant is  s. Ans.

67. M m A force F pushes onto M. Attached to the front of M is m, which is not glued to M. The static friction between M and m is  s. Find the minimum magnitude of F that still keeps m attached to the front of M without slipping down. The floor is smooth. Example