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Newton’s Laws

Newton’s Laws. Inertia. Inertia. Newton’s 1 st Law An object wants to keep on doing what it is already doing In order to change, it needs a net force not equal to zero sum of all forces. Exploring 1 st Law: Torque. Force: a push or pull [units: Newton (N) ]

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Newton’s Laws

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  1. Newton’s Laws

  2. Inertia

  3. Inertia • Newton’s 1st Law • An object wants to keep on doing what it is already doing • In order to change, it needs a net force not equal to zero • sum of all forces

  4. Exploring 1st Law: Torque • Force: • a push or pull [units: Newton (N)] • Translational motion: motion without rotation • Fulcrum: point of rotation (ex. hinge) • If a force is applied to an object with a fulcrum, you get rotational motion Fulcrum

  5. Exploring 1st Law: Torque • Force: • a push or pull • Translational motion: motion without rotation • Fulcrum: point of rotation (ex. hinge) • If a force is applied to an object with a fulcrum, you get rotational motion Fulcrum

  6. Torque • Rotational Force is most effective far from the fulcrum • Torque is the combination of force and distance from fulcrum (lever arm =r) r r A B r = 0 Which lever arm has greatest torque? C

  7. Torque • Only the perpendicularpart of the force is applied to the torque. • This requires a touch of trig. r

  8. Rotational Stability • 1st Law, rotational style: • “In the absence of a net torque, an object not rotating will continue to not rotate and an object rotating will continue to rotate at a constant rotational velocity” • This means that if a rotational system is in balance (not moving), the net torque is zero.

  9. Rotational Stability • 1st Law, rotational style: • All torques add to zero • Convention: CW is positive, CCW is negative • Which dog has a positive torque?

  10. Center of Mass • Concentration of mass • Where the weight force of the object is located • This weight force can add a torque if it is not at the fulcrum.

  11. Center of Mass • Concentration of mass • This weight force can add a torque if it is not at the fulcrum. What is applying the torque on the left side?

  12. Center of Mass • Where is the woman’s COM? • In her upper body there are two main torques. • To compensate she needs to lean back.

  13. Check Yourself! Go to pg. 349

  14. Newton’s 2nd Law: Acceleration • Recap of 1st law: • involves objects with no net force • When you do have a net force: • object will accelerate in same direction • This acceleration is proportional to the net force and inversely proportional to its mass

  15. Exploring 2nd Law • Put the two together: • mass units: kg • acceleration units: m/s2 • This makes force units: kg•m/s2 • Let’s call 1 kg•m/s2a Newton (N) 

  16. Freefalling: 2nd Law • Weightis a very common force • In freefalling the only force is weight • In freefall, the acceleration is -9.8 m/s2 (g) • So, if a = 9.8 m/s2and m =mass of object

  17. 2nd Law • Let’s look back at the original eqn • Pay close attention to the “net” • This is a reminder you need to add all the forces present upon that object • Let’s look at an example…

  18. 2nd Law Hanging mass pulling a block on a frictionless tabletop • How does the acceleration of m1 change by connecting it to m2? • Why? • Accelerationdecreases because m2 is pulling more mass • Moreinertia

  19. 2nd Law: Example The Batman, with a mass of 70-kg, rappels down a rope from hisbat-copter with a downward acceleration of 3.5 m/s2. What vertical force does the rope exert on Batman?

  20. 2nd Law: Example The Batman, with a mass of 70-kg, rappels down a rope from his bat-copter with a downward acceleration of 3.5 m/s2. What vertical force does the rope exert on Batman? Start all force questions with a diagram showing the forces Pick the positive direction (make direction of motion positive) Identify all givens with symbols

  21. 2nd Law: Example The Batman, with a mass of 70-kg, rappels down a rope from his bat-copter with a downward acceleration of 3.5 m/s2. What vertical force does the rope exert on Batman? Given: Want:

  22. 2nd Law: Example Calculations:

  23. Lab Go to pg. 359

  24. 2nd Law Lab Prep To be able to complete the lab you need to be able to find acceleration in the situation below:

  25. 2nd Law Lab Prep Draw diagram of the moving “body” (in this case: both masses connected by string) m1 m2

  26. 2nd Law Lab Prep Draw diagram of the moving “body” (in this case: both masses connected by string) m1 m2 m2g Draw in all forces acting on the body Which forces affect the motion?

  27. 2nd Law Lab Prep m1 m2 m2g Use Newton’s 2ndLaw

  28. Begin Lab Go to pg. 359

  29. Free Body Diagrams • Identifies all forces acting upon an object • Shows direction and relative sizes Scenario 1: 10 kg block in freefall (no air resistance) 10 kg

  30. Free Body Diagrams Scenario 2: 10 kg block in freefall with air resistance 10 kg

  31. Free Body Diagrams Scenario 3: 10 kg block pulled across a frictionless floor by a string Y Does it fall through the floor? Just like projectiles, we treat x and yseparately 10 kg Normal Force • perpendicular () to the surface • equal to the force acting on the opposite side of surface

  32. Free Body Diagrams Scenario 3: 10 kg block pulled across a frictionless floor by a string X 3 Forces 10 kg net force only in x direction

  33. Free Body Diagrams Scenario 4: 10 kg block on a frictionless ramp at 30° 10 kg

  34. Free Body Diagrams Scenario 4: 10 kg block on a frictionless ramp at 30° 10 kg There are 2 forces

  35. Free Body Diagrams Scenario 4: 10 kg block on a frictionless ramp at 30° Choose x and y to line up with movement y x 10 kg There are 2 forces

  36. Free Body Diagrams Scenario 4: 10 kg block on a frictionless ramp at 30° Choose x and y to line up with movement 10 kg There are 2 forces Weight has both an x and y component

  37. Free Body Diagrams y x The angle between the weight and Fy is the same as the angle between the ramp and the ground

  38. Free Body Diagrams Scenario 4: 10 kg block on a frictionless ramp at 30° The y forces cancel out (block does not move in the y direction) 10 kg Only force left is: thexcomponent of the weight

  39. Air Resistance • Twothings determine amount of air resistance • surface area (shape) • speed

  40. Time to practice Turn to pg. 371

  41. 2nd Law: Rotational Style • Translational motion takes you from place to place • Rotational motion moves about an axis (spinning) • for every type of translational measurement there is rotational one

  42. Rotational Symbols • Measurements • The angles (θ) are in radians

  43. Radians • s = arc length (sector) • r = radius • radians are just the ratio of arc length to the radius

  44. Radians • For a whole circle, s is just the circumference • One whole circle makes 2π radians • 2π = 360°

  45. Converting Radians

  46. Rotational Equations • Each translational equation has a rotational version

  47. Rotational Inertia • α = τnet/ I • Which shapes accelerate faster? • The ones with smaller I

  48. relief

  49. Rotational Motion • Example: Two dumbbells are spun about their center axis with a torque of 5.0 N•m. Both consist of a 50 cm long rod with a mass of 0.20 kg and two 1.0 kg spheres. Calculaterotational acceleration of each. #1 #2

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