Motion, in physics, changes with the time of the position or orientation of a body. Motion along a line or a curve is called translation.
1. Physics 111: Mechanics Lecture 4 Dale Gary NJIT Physics Department
2. The Laws of Motion Newton’s first law Force Mass Newton’s second law Newton’s third law Examples Isaac Newton’s work represents one of the greatest contributions to science ever made by an individual. Feb. 11-15, 2013
3. Dynamics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Language of Dynamics Force: The measure of interaction between two objects (pull or push). It is a vector quantity – it has a magnitude and direction Mass: The measure of how difficult it is to change object’s velocity (sluggishness or inertia of the object) Feb. 11-15, 2013
4. Forces The measure of interaction between two objects (pull or push) Vector quantity: has magnitude and direction May be a contact force or a field force Contact forces result from physical contact between two objects Field forces act between disconnected objects Also called “action at a distance” Feb. 11-15, 2013
5. Forces Gravitational Force Archimedes Force Friction Force Tension Force Spring Force Normal Force Feb. 11-15, 2013
6. Vector Nature of Force Vector force: has magnitude and direction Net Force: a resultant force acting on object Fnet F F1 F2 F3 ...... You must use the rules of vector addition to obtain the net force on an object | F | F12 F22 2.24 N F1 tan 1 ( ) 26.6 F2 Feb. 11-15, 2013
7. Newton’s First Law An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force An object at rest remains at rest as long as no net force acts on it An object moving with constant velocity continues to move with the same speed and in the same direction (the same velocity) as long as no net force acts on it “Keep on doing what it is doing” Feb. 11-15, 2013
8. Newton’s First Law An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force When forces are balanced, the acceleration of the object is zero Object at rest: v = 0 and a = 0 Object in motion: v 0 and a = 0 The net force is defined as the vector sum of all the external forces exerted on the object. If the net force is zero, forces are balanced. When forces are balances, the object can be stationary, or move with constant velocity. Feb. 11-15, 2013
9. Mass and Inertia Every object continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by unbalanced forces impressed upon it Inertia is a property of objects to resist changes is motion! Mass is a measure of the amount of inertia. Mass is a measure of the resistance of an object to changes in its velocity Mass is an inherent property of an object Scalar quantity and SI unit: kg Feb. 11-15, 2013
10. Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass a F Fnet m m Fnet F ma Feb. 11-15, 2013
11. Units of Force Newton’s second law: Fnet F ma SI unit of force is a Newton (N) kg m 1 N 1 s2 US Customary unit of force is a pound (lb) 1 N = 0.225 lb Weight, also measured in lbs. is a force (mass x acceleration). What is the acceleration in that case? Feb. 11-15, 2013
12. More about Newton’s 2nd Law You must be certain about which body we are applying it to Fnet must be the vector sum of all the forces that act on that body Only forces that act on that body are to be included in the vector sum Net force component along an axis gives rise to the acceleration along that same axis Fnet , x ma x Fnet , y ma y Feb. 11-15, 2013
13. Sample Problem One or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 and are directed along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle = 30° and has magnitude F3 = 1.0 N. In each situation, what is the acceleration a) F1 ma xof the puck? a 1 F 4.0 N 20 m/s 2 x m 0.2 kg b) F1 F2 ma x F1 F2 4.0 N 2.0 N ax 10 m/s 2 m 0.2 kg c) F3, x F2 max F3, x F3 cos Fnet , x ma x F3 cos F2 1.0 N cos 30 2.0 N ax 5.7 m/s 2 m 0.2 kg Feb. 11-15, 2013
14. Gravitational Force Gravitational force is a vector Expressed by Newton’s Law of Universal Gravitation: mM Fg G R2 G – gravitational constant M – mass of the Earth m – mass of an object R – radius of the Earth Direction: pointing downward Feb. 11-15, 2013
15. Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object: w = mg g can also be found from the Law of Universal Gravitation Weight has a unit of N mM Fg G 2 w Fg mg R M g G 2 9.8 m/s 2 R Weight depends upon location R = 6,400 km Feb. 11-15, 2013
16. Normal Force Force from a solid surface which keeps object from w Fg mg falling through Direction: always perpendicular to the surface N Fg ma y Magnitude: N mg ma y depends on situation N mg Feb. 11-15, 2013
17. Tension Force: T A taut rope exerts forces on whatever holds its ends Direction: always along the cord (rope, cable, string ……) T1 and away from the T1 = T = T2 object T2 Magnitude: depend on situation Feb. 11-15, 2013
18. Newton’s Third Law If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1 Fon A Fon B Equivalent to saying a single isolated force cannot exist Feb. 11-15, 2013
19. Newton’s Third Law cont. F12 may be called the action force and F21 the reaction force Actually, either force can be the action or the reaction force The action and reaction forces act on different objects Feb. 11-15, 2013
20. Some Action-Reaction Pairs mM Fg G R2 GM Fg mg m 2 mM R Fg G 2 Gm R Fg Ma M 2 R Feb. 11-15, 2013
21. Free Body Diagram The most important step in solving problems involving F hand on book Newton’s Laws is to draw the free body diagram Be sure to include only the forces acting on the object of interest Include any field forces F Earth on book acting on the object Do not assume the normal force equals the weight Feb. 11-15, 2013
22. Hints for Problem-Solving Read the problem carefully at least once Draw a picture of the system, identify the object of primary interest, and indicate forces with arrows Label each force in the picture in a way that will bring to mind what physical quantity the label stands for (e.g., T for tension) Draw a free-body diagram of the object of interest, based on the labeled picture. If additional objects are involved, draw separate free-body diagram for them Choose a convenient coordinate system for each object Apply Newton’s second law. The x- and y-components of Newton second law should be taken from the vector equation and written individually. This often results in two equations and two unknowns Solve for the desired unknown quantity, and substitute the numbers F ma F ma net , x x net , y y Feb. 11-15, 2013
23. Objects in Equilibrium Objects that are either at rest or moving with constant velocity are said to be in equilibrium a 0 of an object can be modeled Acceleration as zero: Mathematically, the F net 0 force acting on the object is zero Equivalent to the set of component Fx by equations given 0 Fy 0 Feb. 11-15, 2013
24. Equilibrium, Example 1 A lamp is suspended from a chain of negligible mass The forces acting on the lamp are the downward force of gravity the upward tension in the chain Applying equilibrium gives Fy 0 T Fg 0 T Fg Feb. 11-15, 2013
25. Equilibrium, Example 2 A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37° and 53° with the horizontal. Find the tension in each of the three cables. Conceptualize the traffic light Assume cables don’t break Nothing is moving Categorize as an equilibrium problem No movement, so acceleration is zero F 0 Fy 0 Model xas an object in equilibrium Feb. 11-15, 2013
26. Equilibrium, Example 2 Need 2 free-body diagrams Apply equilibrium equation to light Fy 0 T3 Fg 0 F y 0 T3 Fg 0 T3 Fg 100 N T3 Fg 100 N Apply equilibrium equations to F knot x T1x T2x T1 cos 37 T2 cos 53 0 F y T1 y T2 y T3 y T1 sin 37 T2 sin 53 100 N 0 cos 37 T2 T1 1.33T1 cos 53 T1 60 N T2 1.33T1 80 N Feb. 11-15, 2013
27. Accelerating Objects If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it Draw a free-body diagram Apply Newton’s Second Law in component form F ma F x ma x F y ma y Feb. 11-15, 2013
28. Accelerating Objects, Example 1 A man weighs himself with a scale in an elevator. While the elevator is at rest, he measures a weight of 800 N. What weight does the scale read if the elevator accelerates upward at 2.0 m/s2? a = 2.0 m/s2 What weight does the scale read if the elevator accelerates Upward: Fy downward at 2.0 m/s2? a = - 2.0 m/s2 N mg ma N N mg ma m( g a ) N 80(2.0 9.8) 624 N N w 800 N m g 9.8 m/s 2 80 N N mg Downward: N 80( 2.0 9.8) 624 N N mg mg mg Feb. 11-15, 2013
+1-315-636-4485
+91 98151-74050 
