Presentation on theme: "Forces and Newton’s Laws of Motion"— Presentation transcript:
1 Forces and Newton’s Laws of Motion Chapter 4Forces and Newton’s Laws of Motion
2 4.1 The Concepts of Force and Mass A force is a push or a pull.Contact forces arise from physicalcontact .Action-at-a-distance forces do notrequire contact and include gravity and electrical forces.
3 4.1 The Concepts of Force and Mass Arrows are used to represent forces. The length of the arrowis proportional to the magnitude of the force.15 N5 N
4 4.1 The Concepts of Force and Mass Mass is a measure of the amountof “stuff” contained in an object.
5 4.2 Newton’s First Law of Motion An object continues in a state of restor in a state of motion at a constantspeed along a straight line, unlesscompelled to change that state by anet force.The net force is the vector sum of allof the forces acting on an object.
6 4.2 Newton’s First Law of Motion The net force on an object is the vector sum of all forces acting on that object.The SI unit of force is the Newton (N).Individual ForcesNet Force4 N10 N6 N
7 4.2 Newton’s First Law of Motion Individual ForcesNet Force5 N3 N4 N
8 4.2 Newton’s First Law of Motion Inertia is the natural tendency of anobject to remain at rest in motion ata constant speed along a straight line.The mass of an object is a quantitativemeasure of inertia.SI Unit of Mass: kilogram (kg)
9 4.2 Newton’s First Law of Motion An inertial reference frame is one inwhich Newton’s law of inertia is valid.All accelerating reference frames arenoninertial.
10 4.3 Newton’s Second Law of Motion Mathematically, the net force iswritten aswhere the Greek letter sigma denotes the vector sum.
11 4.3 Newton’s Second Law of Motion When a net external force acts on an objectof mass m, the acceleration that results isdirectly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.
12 4.3 Newton’s Second Law of Motion SI Unit for ForceThis combination of units is called a newton (N).
14 4.3 Newton’s Second Law of Motion A free-body-diagram is a diagram thatrepresents the object and the forces thatact on it.
15 4.3 Newton’s Second Law of Motion The net force in this case is:275 N N – 560 N = +110 Nand is directed along the + x axis of the coordinate system.
16 4.3 Newton’s Second Law of Motion If the mass of the car is 1850 kg then, byNewton’s second law, the acceleration is
17 4.4 The Vector Nature of Newton’s Second Law The direction of force and acceleration vectorscan be taken into account by using x and ycomponents.is equivalent to
18 4.4 The Vector Nature of Newton’s Second Law The direction of force and acceleration vectorscan be taken into account by using x and ycomponents.is equivalent to
19 Example3. In the amusement park ride known as Magic Mountain Superman, powerful magnets accelerate a car and its riders from rest to 45 m/s (about 100 mi/h) in a time of 7.0 s. The mass of the car and riders is . Find the average net force exerted on the car and riders by the magnets.
20 Example6. Interactive LearningWare 4.1 at reviews the approach taken in problems such as this one. A 1580-kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 50.0 m?
27 4.6 Types of Forces: An Overview In nature there are two general types of forces,fundamental and nonfundamental.Fundamental Forces1. Gravitational force2. Strong Nuclear force3. Electroweak force
28 4.6 Types of Forces: An Overview Examples of nonfundamental forces:frictiontension in a ropenormal or support forces
29 4.7 The Gravitational Force Newton’s Law of Universal GravitationEvery particle in the universe exerts an attractive force on everyother particle.A particle is a piece of matter, small enough in size to beregarded as a mathematical point.The force that each exerts on the other is directed along the linejoining the particles.
30 4.7 The Gravitational Force For two particles that have masses m1 and m2 and areseparated by a distance r, the force has a magnitudegiven by
33 4.7 The Gravitational Force Definition of WeightThe weight of an object on or above the earth is the gravitational force that the earth exerts on the object.The weight always acts downwards, toward the centerof the earth.On or above another astronomical body, the weight is thegravitational force exerted on the object by that body.SI Unit of Weight: newton (N)
34 Example18. On earth, two parts of a space probe weigh N and 3400 N. These parts are separated by a center-to-center distance of 12 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.
35 4.7 The Gravitational Force Relation Between Mass and Weight
36 4.7 The Gravitational Force On the earth’s surface:
37 Example26. A space traveler weighs 540 N on earth. What will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth?
38 Definition of the Normal Force The normal force is one component of the force that a surfaceexerts on an object with which it is in contact – namely, thecomponent that is perpendicularto the surface.
40 Example34. A 35-kg crate rests on a horizontal floor, and a 65-kg person is standing on the crate. Determine the magnitude of the normal force that (a) the floor exerts on the crate and (b) the crate exerts on the person.
41 4.8 The Normal ForceApparent WeightThe apparent weight of an object is the reading of the scale.It is equal to the normal force the man exerts on the scale.
43 Example36. A 95.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.80 m/s2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.30 m/s2?
44 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface there is a forceacting on that object. The component of this force that isparallel to the surface is called thefrictional force.
45 4.9 Static and Kinetic Frictional Forces When the two surfaces arenot sliding across one anotherthe friction is calledstatic friction.
46 4.9 Static and Kinetic Frictional Forces The magnitude of the static frictional force can have any valuefrom zero up to a maximum value.is called the coefficient of static friction.
47 4.9 Static and Kinetic Frictional Forces Note that the magnitude of the frictional force doesnot depend on the contact area of the surfaces.
48 4.9 Static and Kinetic Frictional Forces Static friction opposes the impending relative motion betweentwo objects.Kinetic friction opposes the relative sliding motion motions thatactually does occur.is called the coefficient of kinetic friction.
50 4.9 Static and Kinetic Frictional Forces The sled comes to a halt because the kinetic frictional forceopposes its motion and causes the sled to slow down.
51 4.9 Static and Kinetic Frictional Forces Suppose the coefficient of kinetic friction is 0.05 and the totalmass is 40kg. What is the kinetic frictional force?
52 Example39. ssm A 60.0-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are and 0.410, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?
53 Cables and ropes transmit forces through tension. 4.10 The Tension ForceCables and ropes transmitforces through tension.
54 A massless rope will transmit tension undiminished from one 4.10 The Tension ForceA massless rope will transmittension undiminished from oneend to the other.If the rope passes around amassless, frictionless pulley, thetension will be transmitted tothe other end of the ropeundiminished.
55 4.11 Equilibrium Application of Newton’s Laws of Motion Definition of EquilibriumAn object is in equilibrium when it has zero acceleration.
56 4.11 Equilibrium Application of Newton’s Laws of Motion Reasoning StrategySelect an object(s) to which the equations of equilibrium areto be applied.Draw a free-body diagram for each object chosen above.Include only forces acting on the object, not forces the objectexerts on its environment.Choose a set of x, y axes for each object and resolve all forcesin the free-body diagram into components that point along theseaxes.Apply the equations and solve for the unknown quantities.
57 4.11 Equilibrium Application of Newton’s Laws of Motion
58 4.11 Equilibrium Application of Newton’s Laws of Motion
59 4.11 Equilibrium Application of Newton’s Laws of Motion Forcex componenty component
60 4.11 Equilibrium Application of Newton’s Laws of Motion The first equation givesSubstitution into the second gives
61 4.11 Equilibrium Application of Newton’s Laws of Motion
62 4.12 Nonequilibrium Application of Newton’s Laws of Motion When an object is accelerating, it is not in equilibrium.
63 4.12 Nonequilibrium Application of Newton’s Laws of Motion The acceleration is along the x axis so
64 4.12 Nonequilibrium Application of Newton’s Laws of Motion Forcex componenty component
65 4.12 Nonequilibrium Application of Newton’s Laws of Motion
66 4.12 Nonequilibrium Application of Newton’s Laws of Motion