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Forces and the Problem of Motion

Forces and the Problem of Motion. How do we describe our world?. Physicists use numbers. Mathematics is the language of science Allows precise description and definite prediction Sometime need something more complicated than a pure number. How do we describe our world?.

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Forces and the Problem of Motion

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  1. Forcesand the Problem of Motion

  2. How do we describe our world? Physicists use numbers. Mathematics is the language of science Allows precise description and definite prediction Sometime need something more complicated than a pure number.

  3. How do we describe our world? I have a meeting 150 miles away on the Thruway. Direction? Where am I? Numbers + direction

  4. Vectors versus scalars: A scalar is just a number (no direction). The mass of an object is an example of a scalar quantity.Volume is a scalar A vector is a quantity that has both a magnitude and a direction. Velocity is an example of a vector quantity. Force is a vector

  5. Vectors 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.

  6. Notation: Scalar: m (not bold face; no arrow) Vector: The magnitude of a vector: The direction of vector might be “35 south of east”; “20 above the +x-axis”; or….

  7. Adding vectors 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. F1 F2 For collinear vectors: Fnet ? F1 F2 Fnet ?

  8. Units Our normal unit of force is pounds lb. Metric system uses Newtons 1N = .225 lbs. 1 lb = 4.45 N Get used to it. We will define later.

  9. Adding Vectors Lengthb Lengtha c Θ b a a2+ b2 = c2 Tan θ =b/a

  10. Adding Vectors • Same result as before Can also add

  11. Components a=c cosθ b=c sinθ c b θ a2+b2 = c2 a

  12. How fast is this plane moving? 200 100 Cross wind

  13. Motorboats cross a river pointing in the three directions shown. The boats all have the same speed relative to the water, and all experience the same water flow. Which boat reaches the opposite shore first? A) a B) b C) c

  14. Scalar ? Vector? Length Force Speed Temperature Time A) Scalar B) Vector

  15. A force is a “push” or “pull” on an object. Forces are vectors How can a force be measured?

  16. One way is with a spring scale. By hanging masses on a spring we find that the spring stretch  applied force. The unit of force is the newton (N).

  17. Page 68

  18. Motion Are we moving? As the Earth spins? Around the sun? What is natural motion?

  19. Newton’s First Law of Motion. (Law of Inertia) 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.

  20. Newton’s First Law More concisely If nonetforce acts on an object, then its speed and direction of motion do not change. The net force is the vector sum of all the forces acting on a body. Inertiais a measure of an object’s resistance to changes in its motion.

  21. Examples Difference between mass and weight Mass is a measure of inertia. Quantity of matter Weight is the force on an object due to gravity. Where does it hurt more to kick a cinder block A) In this room? B) In space?`

  22. Newton’s First Law More concisely If nonetforce acts on an object, then its speed and direction of motion do not change. The net force is the vector sum of all the forces acting on a body. Inertiais a measure of an object’s resistance to changes in its motion.

  23. Compare a 2 kg. bar of gold (A) to a 2 kg. box of grapes (B) Which has more inertia? Which has more mass? Which has more weight? Which has more volume?

  24. An object is in translational equilibrium if the net force on it is zero.

  25. Translational EquilibriumExamples Stopped car Car moving at constantspeed in straight line

  26. Translational Equilibrium A hawk weighing 8 N. glides due N at a constant speed. What is the force acting on the hawk due to the air? Equilibrium; net force = 0 W = 8 (down) Fair = ? Fair= 8(up)

  27. Free Body Diagrams (FBD): • Drawn for problems when forces are involved. • Must be LARGE so that they are readable. • Draw an idealization of 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 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.

  28. 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.

  29. A chest W =750 N, is pushed horizontally with F = 450N and moves across the floor with constant velocity. What is the contact force C of the floor on the chest? Equiibrium: 3 Forces W, F, C

  30. F2 + W2 = C2 C= 870 Nθ = Tan F/W =450/750

  31. An airplane heads E. The forces acting on it are: Gravity 16kN down Lift 16kN up Thrust 1.8 kN E Drag 0.8 kN W Ftot = ? Ftot = 1.0 kN E

  32. Page 68

  33. 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:

  34. Newton’s Third Law To every action there is always an equal and opposite reaction Can you hurt your hand hitting a heavy punching bag? apiece of tissue paper? Even if you swing hard?

  35. Bend fingers Hit desk What is the force? Where does it act? What is its magnitude

  36. Newton’s Third Law Action and reaction always act on different objects Two external forces acting on the same object can be equal and opposite but they are not an action reaction pair

  37. Newton’s Third Law You pull on spring (Action) The spring pulls on you (Reaction) I walk on floor. I push on the floor(Action) The floor pushes on me (Reaction) Can you walk on ice?

  38. Does the scale read: A. 100 N, B. 200 N, or C. Zero?

  39. F1 Example: Consider a box resting on a table. (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.

  40. F2 Example continued: (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.

  41. Arnold Strongman and Suzie Small pull on opposite ends of a rope in a tug of war. The greater force exerted on the rope is by A. Arnold. B. Suzie. C. Neither. The force is the same.

  42. Fig. 02.27

  43. Newton’s Third Law Smart horse. If I pull harder on the sleigh the sleigh will pull harder on me (with the same magnitude) so I won’t be able to move faster. I might as well stop pulling and rest! Fxyis the force of y on x

  44. Free body diagram for horse

  45. Fig. 02.29

  46. Fig. 02.30

  47. F External forces: Any force on a system from a body outside of the system. Pulling a box across the floor

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