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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 1 Chapter 2: Force Forces Newton’s First and Third Laws Vector Addition Gravity Contact Forces Tension Fundamental Forces

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 2 §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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 3 Simply, a force is a “push” or “pull” on an object.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 4 How can a force be measured? One way is with a spring scale. By hanging masses on a spring we find that the spring stretch applied force. The units of force are Newtons (N).

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 5 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 6 Notation: Vector: The magnitude of a vector: Scalar: m (not bold face; no arrow) The direction of vector might be “35 south of east”; “20 above the +x-axis”; or….

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 7 §2.2 Net Force The net force is the vector sum of all the forces acting on a body.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 8 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 9 To add vectors graphically they must be placed “tip to tail”. The result (F 1 + F 2 ) points from the tail of the first vector to the tip of the second vector. For collinear vectors: F1F1 F net F2F2 F1F1 F2F2

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 10 §2.3 Newton’s First Law Newton’s 1 st 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 11 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 12 An object is in translational equilibrium if the net force on it is zero.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 13 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 14 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 15 §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).

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 16 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). A x y B 120 C

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 17 and A x = 5.00 m and A y = 0.00 m A x y B 120 60 ByBy BxBx Example continued:

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 18 The components of C: x y C C x = 3.50 m C y = 2.60 m The length of C is: The direction of C is: From the +x-axis Example continued:

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 19 § 2.5 Newton’s Third Law Newton’s 3 rd 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:

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 20 Example: Consider a box resting on a table. F1F1 (a) If F 1 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 21 F2F2 (b) If F 2 is the force of the box on the table, what is the interaction partner of this force? Example continued: The force of the table on the box.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 22 External forces: Any force on a system from a body outside of the system. F Pulling a box across the floor

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 23 Internal forces: Force between bodies of a system. F ext Pulling 2 boxes across the floor where the two boxes are attached to each other by a rope.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 24 §2.6 Gravity Gravity is the force between two masses. Gravity is a long- range or field force. No contact is needed between the bodies. The force of gravity is always attractive! r is the distance between the two masses M 1 and M 2 and G = 6.67 10 -11 Nm 2 /kg 2. M2M2 r M1M1 F 12 F 21

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 25 Let M 1 = mass of the Earth. Here F = the force the Earth exerts on mass M 2. This is the force known as weight, w. Near the surface of the Earth

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 26 What is the direction of g? Note that 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 w?

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 27 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: In low Earth orbit: Their weight is reduced by about 10%. The astronaut is NOT weightless!

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 28 §2.7 Contact Forces Contact forces: these forces arise because of an interaction between the atoms in the surfaces in contact.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 29 Normal force: this force acts in the direction perpendicular to the contact surface. Force of the ground on the box Force of the ramp on the box N w N w

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 30 Example: Consider a box on a table. FBD for box This just says the magnitude of the normal force equals the magnitude of the weight; they are not Newton’s third law interaction partners. Apply Newton’s 2 nd law N w x y

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 31 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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 32 Static Friction: The force of static friction is modeled as where s is the coefficient of static friction and N is the normal force.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 33 Kinetic Friction: The force of kinetic friction is modeled as where k is the coefficient of kinetic friction and N is the normal force.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 34 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? FBD for box N w x y F fsfs Apply Newton’s 2 nd Law

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 35 Example continued: From (2): 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):

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 36 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? FBD for box N w x y F fkfk Apply Newton’s 2 nd Law From 2:

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 37 An ideal cord has zero mass, does not stretch, and the tension is the same throughout the cord. This is the force transmitted through a “rope” from one end to the other. §2.8 Tension

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 38 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 . FDB for the mass M w T x y Apply Newton’s 2 nd Law to the mass M.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 39 FBD for the pulley: x y T T F Apply Newton’s 2 nd Law: This statement is true only when = 45 and Example continued:

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 40 §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.

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 41 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)

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 42 What is the net force acting on the object shown below? 15 N 10 N x y a.40 N b.0 N c.10 N down d.10 N up

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Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 43 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?

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