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Forces and the Laws of Motion

Forces and the Laws of Motion. Chapter 4. Forces and the Laws of Motion. 4.1 Changes in Motion Forces A force is a physical quantity that can affect the state of motion of an object. Forces are pushes or pulls. An unbalanced or net force causes acceleration.

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Forces and the Laws of Motion

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  1. Forces and the Laws of Motion Chapter 4

  2. Forces and the Laws of Motion 4.1 Changes in Motion • Forces • A force is a physical quantity that can affect the state of motion of an object. Forces are pushes or pulls. • An unbalanced or net force causes acceleration. • Balanced forces (net force = 0) do not cause acceleration. • Forces are measured innewtons (N). • 1 N = 1 kg.m/s2 • Forces can act through contact or at a distance. • Contact forces occur when objects touch. • Field forces occur when objects do not touch. • electric fields • magnetic fields • gravitational fields • Forces are vectors and are drawn with arrows.

  3. Forces and the Laws of Motion • Types of Forces Weight (Gravitational Force) Applied Force Normal Force Tension Force Friction Force (includes Air Resistance) Spring Force Electrical Force Magnetic Force

  4. Forces and the Laws of Motion • Gravity (Weight) Fg or FG or W or mg: On Earth the force of gravity is often referred to as the weight of an object. It is the attractive force of the earth on an object, and is always directed toward the center of the earth. It has a magnitude equal to the mass of the object times the acceleration due to gravity, or mg. The force of gravity is a field force.

  5. Forces and the Laws of Motion • Types of Contact Forces • Applied Force, Fapp: An applied force is a force exerted on an object by a person, by another object, or by an action which directly pushes or pulls on the object. - pushing a box across the floor • Spring Force, Fspring, is the force exerted on an object by a compressed or stretched spring.

  6. Forces and the Laws of Motion • Types of Contact Forces • Friction Force, Ffrict: The friction force opposes the applied force and is exerted by a surface on an object as it moves across or makes an effort to move across the surface. Air resistance, Fair is a friction force. • When pushing a box across the floor, the surface of the floor exerts friction on the object. • Tribology is defined as the science of interacting surfaces in relative motion.

  7. Forces and the Laws of Motion • Types of Contact Forces • Tension Force (T, Ftens or FT): This is the force exerted by a rope, cable, or string, when it is attached to an object and pulled taut. It is directed away from the object and along the rope at the point of attachment.

  8. Forces and the Laws of Motion • Types of Contact Forces • Normal Force (Fnormor Fn or FN) : The normal force is a support force that acts on an object at the surface in a direction perpendicular to the surface. (Don’t forget the normal.)

  9. Forces and the Laws of Motion 4.1 Free Body Diagrams (FBD) are used to analyze the forces on a single object. Force Diagrams show all force vectors as arrows.A free body diagram shows all of the external forces acting on a single object(not forces exerted by the object in question on other objects!). Identify (isolate) the object or system. Identify the forces acting on the object and the direction of the forces. Draw a diagram (a dot or box) to represent the isolated object. Draw and label vector arrows for all external forces acting on the object. Choose a coordinate system. Include critical angles and dimensions. Free body diagrams are used to determine the vector sum of all the forces acting on an object.

  10. Forces and the Laws of Motion • A book is at rest on a table top. Diagram the forces acting on the book. • A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on the girl. • 3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling. 4.1 Free Body Diagrams Practice FN FN Fg mg

  11. Forces and the Laws of Motion • 4. A flying squirrel is gliding (no wingflaps) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel. • A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. 4.1 Free Body Diagrams Practice

  12. Forces and the Laws of Motion • A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack. 4.1 Free Body Diagrams Practice

  13. Forces and the Laws of Motion 4.1 Free Body Diagrams Practice • A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver. • 8. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. Diagram the forces acting upon the sled.

  14. Forces and the Laws of Motion 4.1 Free Body Diagrams Practice • A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak. No air resistance. • A car is coasting to the right and slowing down. Diagram the forces acting upon the car.

  15. Steps for drawing a force diagram: • Identify the object you will draw a diagram for.  (If there are multiple objects of interest, you will need to draw multiple diagrams.) • Identify all the forces acting directly on the object and the object exerting them.  With the exception of gravity and certain other forces rarely used in first semester physics (magnetism, electric force), the two objects will be in direct contact.  Do not include forces by an object acting through another object--only include the force due to the intermediate object. • Draw a dot to represent the object of interest. • Draw a vector to represent each force.  Draw it in the direction the force is being exerted, and label it by (a) the type of force, (b) the object exerting the force, and (c) the object receiving the force (which will be you object of interest).  It will have the form F(type)exerting object -> object of interest • If the object is stationary or is moving at a constant velocity, the vectors should graphically add up to zero.  If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration. • Writing down the sum of the forces • Identify direction of every force and of acceleration. • Pick a coordinate system to minimize the number of things (forces and acceleration) that must be broken into components, especially unknown values • Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle that is given (or being looked for). • Pick one direction and write down all the forces or components of forces in that direction, using positive and negative signs to identify those in the positive and negative directions. • Set the sum of the forces in that direction as equal to the mass multiplied by the acceleration in that direction.  (If not moving or moving at a constant velocity in that direction, acceleration will be zero.) • Repeat for the other direction.

  16. Forces and the Laws of Motion 4.2 Newton’s First Law – The Law of Inertia In the absence of a net external force, an object will continue in a state of uniform motion (including rest) in a straight line. (1687, The Mathematical Principles of Natural Philosophy or PhilosophiaeNaturalisPrincipiaMathematica ) An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by an unbalanced force or a net external force. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (Galileo, in the 1630’s, had recognized this about motion.)

  17. Forces and the Laws of Motion • Uniform Motion • not changing • no acceleration • at rest or moving at constant velocity • no change in speed • no change in direction • all forces balance • no net force • Fnet = 0 • equilibrium • Nonuniform Motion • changing motion • acceleration • changing velocity • change in speed • change in direction • change in speed and direction • unbalanced force • net force • Fnet = 0 or 4.2 Newton’s First Law – The Law of Inertia

  18. Forces and the Laws of Motion 4.2 Newton’s First Law – The Law of Inertia • An object maintains constant velocity until acted upon by a net force. • When the net external force on an object is zero, the object does not accelerate. • Analyze the forces acting on an object using free body diagrams to determine the sum of all the forces acting on the object. This is the net force.

  19. Forces and the Laws of Motion 4.2 Determining Net Force • Define the problem. • Select a coordinate system, and apply it to the free-body diagram. (Make the x-axis parallel to the incline and the y-axis perpendicular to it.) • Find the x and y components of all vectors. • Find the net force in both the x and y directions. (Sum the forces in the x direction and sum the forces in the y direction. SFx and SFy • Find the net force. If there is a net force in both the x and y directions, use vector addition (Pythagorean theorem) to find the total (or single) net force on the object. Use tan-1q to determine the direction of the net force and thus the direction of the acceleration.

  20. Flift Ffriction Fforward Fgravity Forces and the Laws of Motion Net force is the vectorsum of forces acting on an object. 4.2 Determining Net Force SFx = Fforward–Ffriction= 0 SFy=Flift- Fgravity= 0 Fnet = 0 N

  21. Forces and the Laws of Motion • 4.2 Equilibrium • Fnet = 0 • Equilibrium is the state in which the net force on an object is zero. (Acceleration is zero.) • Objects at rest or at constant velocity are in equilibrium. • When there is a net force acting on an object, the equilibrant force is the single force that if applied to an object would balance or cancel the net force and produce equilibrium.

  22. Forces and the Laws of Motion 4.2 Newton’s First Law – The law of Inertia • Inertia is the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction. • Inertia is the tendency of an object not to accelerate. • Mass (the amount of matter in an object) is a measure of inertia. • Inertia is directly proportional to mass. The greater mass an object has then the greater the inertia of that object.

  23. Forces and the Laws of Motion Fnet = 20 N, left Fnet = 400 N, up Fnet = 200 N, down

  24. Forces and the Laws of Motion Fnet = 0 N Fnet = 5 N, left Fnet = 0 N Fnet = 15 N, up

  25. Forces and the Laws of Motion F = 22 N* G = 50 N H = 22 N* A = 50 N B = 200 N D = 20 N E = 300 N C = 1100 N *Any number you choose as long as F = H.

  26. Fx = F.cosq Fy = F.sinq F q Forces and the Laws of Motion • Vector Review • The resultant vector is the sum of two or more vectors and can be determined trigonometrically or graphically. • A single vector can be resolved into two or more components that have the same effect. • Concurrent forces act through the same point at the same time • and can be combined to find the resultant vector.

  27. Forces and the Laws of Motion 4.2 Determining Net Force on Inclines • FII= Fgrav.sinq • Fperp= Fgrav.cosq Remember Fgrav = mg http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm

  28. q Forces and the Laws of Motion y 4.2 Determining Net Force on Inclines FN Ffrict Fg.sinq Fg.cosq x Fg 35o 35o 55o q = 35o 35o Coordinate System: X-axis is parallel to the slope. Y-axis is perpendicular to the slope.

  29. q Forces and the Laws of Motion y 4.2 Determining Net Force on Inclines FN Ffrict Fg.sinq Fg.cosq x Fg 35o q = 35o • SFx = Fg.sinq- Ffrict • SFy= FN - Fg.cosq Right is +. Left is -. Up is +. Down is -. Remember Fg = mg

  30. Forces and the Laws of Motion http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm 4.2 Determining Net Force Fnet = 5 N down the ramp

  31. Forces and the Laws of Motion Draw a free body diagram for a block on a 25o incline ignoring friction. Show the x and y (parallel and perpendicular) components of gravity. 4.2 Determining Net Force - YOU TRY! FN Fgcos25o 25o 25o FG Fgsin25o

  32. Forces and the Laws of Motion http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm 4.2 Determining Net Force 100 kg crate Ffrict = 255 N Determine Fnet . 255 Fperp 30o 981 Fnorm– Fperp= 0 Fnet = FII - Ffrict Fnet = 491 N – 255 N Fnet = 236 N down the ramp Fgrav = mg = 100 kg x 9.81 m/s2 = 981 N Fperp= Fgrav.cosq = 981 N . cos30o = 850 N Fnorm = Fgrav.cosq = 981 N . cos30o = 850 N • FII= Fgrav.sinq= 981 N . sin 30o = 491 N

  33. Forces and the Laws of Motion http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm 4.2 Determining Net Force 6937 4905 9810 9810 8.50 6.9 4 8496 6937

  34. Forces and the Laws of Motion A 10kg sculpture is hanging stationary by two cables as shown in the diagram. What is the tension in the cables? 4.2 Determining Net Force Analyze: The forces are balanced because the object is stationary. Vertical forces cancel or add to zero and so do horizontal forces. T1 and T2 have vertical and horizontal components. T1 and T2 horizontal components cancel each other. What part of the tension force is holding up the structure? The vertical component of the two tension forces. So, T1,y + T2,y = Fg . T2 T1 10 kg Fg = 98.1 N Fg = mg Fg = 10 kg x 9.81 m/s2 = 98.1 N Vertical T1,y = T1 x sin 45o and T2,y = T2x sin 45o Horizontal T1,x + T2,x = 0 or T1,x = -T2,x T1.cos45o = T2.cos45o T1 = T2 Fg = T1,y + T2,y = T1.sin 45o + T2.sin 45o T1 =T2 98.1 N = T1.sin 45o + T1.sin 45o 98.1 N = 2(T1.sin 45o) T1 = 69 N

  35. Forces and the Laws of Motion • Practice • p. 128 1-3 • p. 129 1-5

  36. Forces and the Laws of Motion • 4.3Newton’sSecond Law of Motion • According to Newton’s first law when a net force does act on an object its motion changes, that is, it accelerates. • The Law of Acceleration The acceleration of an object is directly proportional to the net force acting on an object and inversely proportional to the object’s mass. F = ma a = F/m m = F/a SF = ma or net force = mass x acceleration

  37. 2 2 • vf = vi + 2aDx Forces and the Laws of Motion SF = ma What do we know about acceleration? Acceleration is the rate of change in velocity. Acceleration occurs when an object speeds up, slows down, or changes direction (at constant speed or changing speed). a = Dv/t = (vf-vi)/t Acceleration is zero if velocity is constant. vf = vi + at When acceleration is constant: Dx = vit + ½ at2

  38. Forces and the Laws of Motion 4.3Newton’sSecond Law of Motion F = ma Fg = mg = weight

  39. Forces and the Laws of Motion • 4.3Newton’sThird Law of Motion – The Law of Recoil • If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. • For every action force there exists an equal in size and opposite in direction reaction force. • Forces always exist in pairs. • Action and reaction forces are two forces that act on two different objects. • Field forces also exist in pairs. The earth exerts a force of gravity on you and you exert a force of gravity on the earth. • Practice with handout.

  40. Forces and the Laws of Motion • 4.4 Everyday Forces • Weight • magnitude of the gravitational force exerted on an object • depends on location • W = Fg = mag = mg = m.9.81 m/s2 on Earth • The greater the distance between Earth and the object the less weight the object has because the force of gravity decreases with increasing distance.

  41. Forces and the Laws of Motion • 4.4 Everyday Forces • The Normal Force • normal means perpendicular • is the support force perpendicular to an object and the surface it touches

  42. Forces and the Laws of Motion • 4.4 Everyday Forces • Friction • Friction opposes the applied force. • Static friction opposes the initiation of motion between two surfaces in contact and at rest. Static friction must be overcome before an object will move. • Fs = Fapp until Fs = Fs,max and a greater Fapp will cause motion.

  43. 4.4 Everyday Forces • Kinetic friction, Fk, is the retarding force on an object in motion. • Fnet = Fapp – Fk • Kinetic friction is less than static friction.

  44. Forces and the Laws of Motion • 4.4 Everyday Forces • Friction • Friction results from complex interactions between contacting surfaces which include electrostatic forces between the molecules and atoms. • The force of friction, Ff, is proportional to the normal force. • The force of friction between two surfaces is approximately equal to the normal force multiplied by the coefficient of friction for the two surfaces. Ff = mFn • Fk = mkFn Fs = msFn The coefficient of friction is a ratio of forces. mk = Fk/Fn ms = Fs,max/Fn

  45. The coefficient of friction is a ratio of forces. mk = Fk/Fn ms = Fs,max/Fn

  46. Forces and the Laws of Motion • 4.4 Air Resistance, FR • a form of fluid friction • FR increases with increasing speed.

  47. Net Force Fnet = Fapp – Ff Fnet = Fapp - mFN Fnet = Fapp – mFg Fnet = Fapp - mmg

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