Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Fisica Generale - Alan Giambattista, Betty McCarty Richardson Chapter 2: Force •Forces •Newton’s First and Third Laws •Vector Addition •Gravity •Contact Forces •Tension •Fundamental Forces Copyright © 2008 – The McGraw-Hill Companies s.r.l. 1 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.1 Forces Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies. Over the next few chapters we will study how bodies interact with one another. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 2 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Simply, a force is a “push” or “pull” on an object. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 3 Fisica Generale - Alan Giambattista, Betty McCarty Richardson How can a force be measured? One way is with a spring scale. By hanging masses on a spring we find that the spring stretchapplied force. The units of force are Newtons (N). Copyright © 2008 – The McGraw-Hill Companies s.r.l. 4 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Vectors versus scalars: A vector is a quantity that has both a magnitude and a direction. A force is an example of a vector quantity. A scalar is just a number (no direction). The mass of an object is an example of a scalar quantity. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 5 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Notation: Vector: F or F The magnitude of a vector: F or F or F . The direction of vector might be “35 south of east”; “20 above the +x-axis”; or…. Scalar: m (not bold face; no arrow) Copyright © 2008 – The McGraw-Hill Companies s.r.l. 6 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.2 Net Force The net force is the vector sum of all the forces acting on a body. Fnet F F1 F2 F3 Copyright © 2008 – The McGraw-Hill Companies s.r.l. 7 Fisica Generale - Alan Giambattista, Betty McCarty Richardson To graphically represent a vector, draw a directed line segment. The length of the line can be used to represent the vector’s length or magnitude. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 8 Fisica Generale - Alan Giambattista, Betty McCarty Richardson To add vectors graphically they must be placed “tip to tail”. The result (F1 + F2) points from the tail of the first vector to the tip of the second vector. F2 F1 Fnet For collinear vectors: F1 F2 Fnet Copyright © 2008 – The McGraw-Hill Companies s.r.l. 9 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.3 Newton’s First Law Newton’s 1st Law (The Law of Inertia): If no force acts on an object, then its speed and direction of motion do not change. Inertia is a measure of an object’s resistance to changes in its motion. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 10 Fisica Generale - Alan Giambattista, Betty McCarty Richardson If the object is at rest, it remains at rest (speed = 0). If the object is in motion, it continues to move in a straight line with the same speed. No force is required to keep a body in straight line motion when effects such as friction are negligible. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 11 Fisica Generale - Alan Giambattista, Betty McCarty Richardson An object is in translational equilibrium if the net force on it is zero. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 12 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Free Body Diagrams: •Must be drawn for problems when forces are involved. •Must be large so that they are readable. •Draw an idealization of the body in question (a dot, a box,…). You will need one free body diagram for each body in the problem that will provide useful information for you to solve the given problem. •Indicate only the forces acting on the body. Label the forces appropriately. Do not include the forces that this body exerts on any other body. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 13 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Free Body Diagrams (continued): •A coordinate system is a must. •Do not include fictitious forces. Remember that ma is itself not a force! •You may indicate the direction of the body’s acceleration or direction of motion if you wish, but it must be done well off to the side of the free body diagram. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 14 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.4 Vector Addition Vector Addition: Place the vectors tip to tail as before. A vector may be moved any way you please provided that you do not change its length nor rotate it. The resultant points from the tail of the first vector to the tip of the second (A+B). Copyright © 2008 – The McGraw-Hill Companies s.r.l. 15 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example: Vector A has a length of 5.00 meters and points along the x-axis. Vector B has a length of 3.00 meters and points 120 from the +x-axis. Compute A+B (=C). y B C 120 A x Copyright © 2008 – The McGraw-Hill Companies s.r.l. 16 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: opp sin hyp adj cos hyp sin opp tan cos adj y B By 60 Bx sin 60 By 120 A x B y B sin 60 3.00m sin 60 2.60 m B Bx cos60 Bx Bcos60 3.00m cos60 1.50 m B and Ax = 5.00 m and Ay = 0.00 m Copyright © 2008 – The McGraw-Hill Companies s.r.l. 17 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: C x Ax Bx 5.00 m - 1.50 m 3.50 m The components of C: C y Ay By 0.00 m 2.60 m 2.60 m y The length of C is: C Cy = 2.60 m C C Cx C y 2 x Cx = 3.50 m The direction of C is: tan Cy Cx 2 3.50 m 2 2.60 m 2 4.36 m 2.60 m 0.7429 3.50 m tan 1 0.7429 36.6 From the +x-axis Copyright © 2008 – The McGraw-Hill Companies s.r.l. 18 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.5 Newton’s Third Law Newton’s 3rd Law: When 2 bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction. Or, forces come in pairs. Mathematically: F21 F12. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 19 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example: Consider a box resting on a table. F1 (a) If F1 is the force of the Earth on the box, what is the interaction partner of this force? The force of the box on the Earth. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 20 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: F2 (b) If F2 is the force of the box on the table, what is the interaction partner of this force? The force of the table on the box. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 21 Fisica Generale - Alan Giambattista, Betty McCarty Richardson External forces: Any force on a system from a body outside of the system. F Pulling a box across the floor Copyright © 2008 – The McGraw-Hill Companies s.r.l. 22 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Internal forces: Force between bodies of a system. Fext Pulling 2 boxes across the floor where the two boxes are attached to each other by a rope. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 23 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.6 Gravity Gravity is the force between two masses. Gravity is a longrange or field force. No contact is needed between the bodies. The force of gravity is always attractive! GM1M 2 F r2 M1 r is the distance between the two masses M1 and M2 and G = 6.6710-11 Nm2/kg2. F12 F21 M2 F21 F12. r Copyright © 2008 – The McGraw-Hill Companies s.r.l. 24 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Let M1 = mass of the Earth. GM E F 2 r M 2 Here F = the force the Earth exerts on mass M2. This is the force known as weight, w. GM E w 2 rE M 2 gM 2 . GM E 2 where g 9 . 8 N/kg 9 . 8 m/s 2 rE M E 5.98 1024 kg rE 6400 km Near the surface of the Earth Copyright © 2008 – The McGraw-Hill Companies s.r.l. 25 Fisica Generale - Alan Giambattista, Betty McCarty Richardson F Note that g m is the gravitational force per unit mass. This is called the gravitational field strength. It is often referred to as the acceleration due to gravity. What is the direction of g? What is the direction of w? Copyright © 2008 – The McGraw-Hill Companies s.r.l. 26 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example: What is the weight of a 100 kg astronaut on the surface of the Earth (force of the Earth on the astronaut)? How about in low Earth orbit? This is an orbit about 300 km above the surface of the Earth. On Earth: w mg 980 N GM E 890 N In low Earth orbit: w mg (ro ) m RE h Their weight is reduced by about 10%. The astronaut is NOT weightless! Copyright © 2008 – The McGraw-Hill Companies s.r.l. 27 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.7 Contact Forces Contact forces: these forces arise because of an interaction between the atoms in the surfaces in contact. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 28 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Normal force: this force acts in the direction perpendicular to the contact surface. N Force of the ground on the box w N Force of the ramp on the box w Copyright © 2008 – The McGraw-Hill Companies s.r.l. 29 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example: Consider a box on a table. y N FBD for box x w Apply Newton’s 2nd law F y N w0 So that N w mg This just says the magnitude of the normal force equals the magnitude of the weight; they are not Newton’s third law interaction partners. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 30 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Friction: a contact force parallel to the contact surfaces. Static friction acts to prevent objects from sliding. Kinetic friction acts to make sliding objects slow down. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 31 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Static Friction: The force of static friction is modeled as f s s N . where s is the coefficient of static friction and N is the normal force. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 32 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Kinetic Friction: The force of kinetic friction is modeled as f k k N . where k is the coefficient of kinetic friction and N is the normal force. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 33 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example (text problem 2.91): A box full of books rests on a wooden floor. The normal force the floor exerts on the box is 250 N. (a) You push horizontally on the box with a force of 120 N, but it refuses to budge. What can you say about the coefficient of friction between the box and the floor? y N FBD for box F x fs w Apply Newton’s 2nd Law (1) Fy N w 0 (2) Fx F f s 0 Copyright © 2008 – The McGraw-Hill Companies s.r.l. 34 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: From (2): F F f s s N s 0.48 N This is the minimum value of s, so s > 0.48. (b) If you must push horizontally on the box with 150 N force to start it sliding, what is the coefficient of static friction? Again from (2): F F f s s N s 0.60 N Copyright © 2008 – The McGraw-Hill Companies s.r.l. 35 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: (c) Once the box is sliding, you only have to push with a force of 120 N to keep it sliding. What is the coefficient of kinetic friction? y N FBD for box F x fk Apply Newton’s 2nd Law (1) Fy N w 0 (2) Fx F f k 0 w From 2: F f k k N F 120 N k 0.48 N 250 N Copyright © 2008 – The McGraw-Hill Companies s.r.l. 36 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.8 Tension This is the force transmitted through a “rope” from one end to the other. An ideal cord has zero mass, does not stretch, and the tension is the same throughout the cord. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 37 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example (text problem 2.73): A pulley is hung from the ceiling by a rope. A block of mass M is suspended by another rope that passes over the pulley and is attached to the wall. The rope fastened to the wall makes a right angle with the wall. Neglect the masses of the rope and the pulley. Find the tension in the rope from which the pulley hangs and the angle . y T FDB for the mass M x w Apply Newton’s 2nd Law to the mass M. F y T w 0 T w Mg Copyright © 2008 – The McGraw-Hill Companies s.r.l. 38 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Example continued: Apply Newton’s 2nd Law: FBD for the pulley: F F y F T x F cos T 0 y F sin T 0 T F cos F sin x T This statement is true only when = 45 and F 2T 2 Mg Copyright © 2008 – The McGraw-Hill Companies s.r.l. 39 Fisica Generale - Alan Giambattista, Betty McCarty Richardson §2.9 Fundamental Forces The four fundamental forces of nature are: •Gravity which is the force between two masses; it is the weakest of the four. •Strong Force which helps to bind atomic nuclei together; it is the strongest of the four. •Weak Force plays a role in some nuclear reactions. •Electromagnetic is the force that acts between charged particles. Copyright © 2008 – The McGraw-Hill Companies s.r.l. 40 Fisica Generale - Alan Giambattista, Betty McCarty Richardson Summary •Newton’s First and Third Law’s •Free Body Diagrams •Adding Vectors •Contact Forces Versus Long-Range Forces •Different Forces (friction, gravity, normal, tension) Copyright © 2008 – The McGraw-Hill Companies s.r.l. 41 Fisica Generale - Alan Giambattista, Betty McCarty Richardson What is the net force acting on the object shown below? y 15 N 15 N x 10 N a. 40 N b. 0 N c. 10 N down d. 10 N up Copyright © 2008 – The McGraw-Hill Companies s.r.l. 42 Fisica Generale - Alan Giambattista, Betty McCarty Richardson The gravitational field strength of the Moon is about 1/6 that of Earth. If the mass and weight of an astronaut, as measured on Earth, are m and w respectively, what will they be on the Moon? a. m, w 1 b. m, w 6 1 c. m, w 6 1 1 d. m, w 6 6 Copyright © 2008 – The McGraw-Hill Companies s.r.l. 43