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REminders

REminders. Tomorrow is the second half of your exam!. Vector Applications. Monday, May 12 th. Free body diagrams. A free body diagram (FBD) is a picture of all the external forces acting on an object. Not internal forces Not forces that the object exerts on its surroundings.

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REminders

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  1. REminders • Tomorrow is the second half of your exam!

  2. Vector Applications Monday, May 12th

  3. Free body diagrams • A free body diagram (FBD) is a picture of all the external forces acting on an object. • Not internal forces • Not forces that the object exerts on its surroundings

  4. Net force ΣF = ma One of the things that this equation tells us is that if an object is moving at constant speed or standing still (aka. not accelerating) the sum of all the forces that act on the object must be zero.

  5. Is it in the Free body diagram? Sandy leans her head on Leanne’s shoulder to rest while both are seated. In a FBD of Sandy, you would expect to see: • A downward arrow indicating Sandy’s weight • A downward arrow indicating the force Sandy’s head exerts on Leanne’s shoulder • An upward arrow indicating the force of Sandy’s chair on her • An upward arrow indicating the force of Leanne’s shoulder on Sandy’s head.

  6. Is it in the Free body diagram? Sandy leans her head on Leanne’s shoulder to rest while both are seated. In a FBD of Sandy, you would expect to see: • A downward arrow indicating Sandy’s weight • A downward arrow indicating the force Sandy’s head exerts on Leanne’s shoulder • An upward arrow indicating the force of Sandy’s chair on her • An upward arrow indicating the force of Leanne’s shoulder on Sandy’s head.

  7. Is it in the Free body diagram? Sandy leans her head on Leanne’s shoulder to rest while both are seated. In a joint FBD of both Sandy and Leanne together, you would expect to see: • A downward arrow indicating Sandy + Leanne’s weight • A downward arrow indicating the force Sandy’s head exerts on Leanne’s shoulder • An upward arrow indicating the force of Sandy’s chair on her and Leanne’s chair on her • An upward arrow indicating the force of Leanne’s shoulder on Sandy’s head.

  8. Is it in the Free body diagram? Sandy leans her head on Leanne’s shoulder to rest while both are seated. In a joint FBD of both Sandy and Leanne together, you would expect to see: • A downward arrow indicating Sandy + Leanne’s weight • A downward arrow indicating the force Sandy’s head exerts on Leanne’s shoulder • An upward arrow indicating the force of Sandy’s chair on her and Leanne’s chair on her • An upward arrow indicating the force of Leanne’s shoulder on Sandy’s head.

  9. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N.

  10. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. Normal force Gravity Note, we are assuming that air resistance is negligible

  11. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. Normal force Gravity = 2000N

  12. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. Normal force has to balance out gravity in order for ΣF = 0. Gravity = 2000N

  13. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. If the normal force is > gravity Gravity = 2000N

  14. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. If the normal force < gravity Gravity = 2000N

  15. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. Normal force = 2000N up Gravity = 2000N down

  16. Draw the Free body diagram? A car drives at constant speed of 110km/h on the 401 outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N. Normal force = 2000N up Gravity = 2000N down Normal force vector + Force of gravity vector = 0

  17. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s2

  18. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up There is a force that must be pulling the car forward… what is it? Gravity = 2000N down

  19. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the engine? Gravity = 2000N down

  20. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the engine? No, because the force that the engine exerts on the axel is an internal force, which has no direct impact on acceleration Gravity = 2000N down

  21. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the force the axel exerts on the wheels? Gravity = 2000N down

  22. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the force the axel exerts on the wheels? Nope. That’s also an internal force Gravity = 2000N down

  23. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the force the wheels exert on the road? Gravity = 2000N down

  24. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Is it the force the wheels exert on the road? Nope. That would show up in an FBD of the road. Gravity = 2000N down

  25. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up It’s the force the road exerts on the wheels, which is… Gravity = 2000N down

  26. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up It’s the force the road exerts on the wheels, which is static friction! Gravity = 2000N down

  27. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Static friction = the only force that isn’t cancelled out Gravity = 2000N down

  28. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Static friction = ΣF Gravity = 2000N down

  29. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s Normal force = 2000N up Static friction = ΣF = ma Gravity = 2000N down

  30. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s2 Normal force = 2000N up Static friction = ΣF = (204kg)(2m/s2) = 408N Gravity = 2000N down

  31. Draw the Free body diagram? A car accelerates on the 401 onramp outside Chatham (this is flat). Draw the FBD for the car if the car weighs 2000N (mass of 204kg) and is accelerating forward at 2m/s2 Normal force = 2000N up Static friction = 408N Gravity = 2000N down

  32. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car.

  33. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. Normal force Friction force θ = 30o Gravity

  34. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, what is the normal force? What is the friction force? Normal force Friction force θ = 30o Gravity = 2000N down

  35. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components Gravity Friction θ = 30o Normal Gravity = 2000N down

  36. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components 0 –2000N Gravity Friction θ = 30o Normal Gravity = 2000N down

  37. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Friction force x-components y-components 0 –2000N Gravity Friction 30o Normal

  38. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Ffs x-components y-components 0 –2000N Gravity 30o Friction 30o Normal

  39. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Ffs x-components y-components Ffs sin(30) 0 –2000N Gravity 30o Ffscos(30) +Ffs sin(30) Friction +Ffscos(30) 30o Normal

  40. Draw the Free body diagram? A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components 0 –2000N Gravity +Ffs sin(30) Friction +Ffscos(30) 30o Normal Gravity

  41. Suggestion • When drawing free body diagrams that involve any angle, always draw a very shallow or very angle. Don’t draw anything close to a 45o angle.

  42. Suggestion • When drawing free body diagrams that involve any angle, always draw a very shallow or very steep. Don’t draw anything close to a 45o angle. Can you tell which angle in this triangle is supposed to be θ without doing bothersome trigonometry? Neither can I. θ

  43. Suggestion • When drawing freebody diagrams that involve any angle, always draw a very shallow or very steep. Don’t draw anything close to a 45o angle. θ θ Here, the tiny angle in the top corner is clearly θ Here, no one knows what’sθ and what’s not

  44. Suggestion • When drawing freebody diagrams that involve any angle, ALWAYS draw a shallow angle. Why? 30o 30o

  45. Suggestion • When drawing freebody diagrams that involve any angle, ALWAYS draw a shallow angle. Why? FN FNcos(30) 30o –FN sin(30) 30o

  46. Draw the Free body diagram A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components FNcos(30) 0 –2000N Gravity –FN sin(30) +Ffs sin(30) Friction +Ffscos(30) 30o Normal –FN sin(30) +FNcos(30) Gravity

  47. Draw the Free body diagram A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components FNcos(30) 0 –2000N Gravity –FN sin(30) √3/2 Ffs Friction ½Ffs 30o Normal –½FN √3/2FN Gravity

  48. Draw the Free body diagram A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components 0 –2000N Gravity √3/2 Ffs Friction ½Ffs 30o Normal –½FN √3/2FN Gravity Adds up to…

  49. Net force ΣF = ma Recall: this equation tells us is that if an object is moving at constant speed or standing still (aka. not accelerating) the sum of all the forces that act on the object must be zero.

  50. Draw the Free body diagram A car drives up a 30o incline at a constant 60km/h. Draw all the forces acting on the car. If the car’s weight is 2000N, calculate all of the other forces. Normal force Friction force x-components y-components 0 –2000N Gravity √3/2 Ffs Friction ½Ffs 30o Normal –½FN √3/2FN Gravity Adds up to… 0 0

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