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Aim: How can we explain forces at an angle?

Aim: How can we explain forces at an angle?. x = 5 N. x. Do Now: Solve for the x and y components:. 30°. y. 10 N. x = 8.7 N. Why do crazy football coaches say to get low?. Demo http://www.youtube.com/watch?v=eE6x1rfogIU&feature=related

eric-ayala
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Aim: How can we explain forces at an angle?

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  1. Aim: How can we explain forces at an angle? x = 5 N x Do Now: Solve for the x and y components: 30° y 10 N x = 8.7 N

  2. Why do crazy football coaches say to get low? • Demo • http://www.youtube.com/watch?v=eE6x1rfogIU&feature=related • If force is at an angle, some component of the force is in the x direction and some is in the y

  3. Forces at an Angle 50 N • A 12 kg box is pulled across a table with a force of 50 N at an angle of 40o above the horizontal. • Draw a free body diagram • Write a net force equation in the x and y direction • What is the normal force? • If the box moves at a constant velocity, what is the force of friction? • What is the coefficient of friction? 40o 12 kg

  4. Question 2 • A small child pulls a 25 kg wagon with 30 N of force over a frictionless surface. The angle that the handle makes with the ground is 27o • What is the horizontal component of the force? • What is the vertical component of the force? • Write a net force equation in the x and y direction • What is the acceleration of the wagon • If the wagon starts from rest, how far does the child go in 4 seconds?

  5. Normal Force Do you remember where the normal force is directed? What if the plane is inclined?

  6. On an incline:

  7. The problem with an incline: The object moves along the plane y y Everything would need to be resolved into x and y components That’s a lot of sins and cosines Solution – rotate the x and y axis x Fg x

  8. This way, only Fg needs to be resolved into x and y components - F║ and F┴

  9. FN How can we solve for F║ and F┴ FII Mathematically, these θ’s are equal θ F θ Fg = mg

  10. At rest or moving with a constant velocity: FF = ? FF = F║ FF = Fgsinθ FF = mgsinθ FN FN = ? FN = F┴ FN = Fgcosθ FN = mgcosθ FF FII θ F θ Fg

  11. FN As θ increases, FII increases, so Fnet increases, and the object accelerates faster On a frictionless incline: FNet = ma F║ = ma Fgsinθ = ma mgsinθ = ma gsinθ = a FF FII θ F θ Fg

  12. On a surface with friction… • The force of friction decreases as the angle increases since: Remember: cos(90o)= 0 and cos(0o) = 1 The higher the angle, the lower the value of cosine

  13. FII = Fgsinθ FII = mgsinθ FII = (50 kg)(9.8 m/s2)sin(25o) FII = 207 N F = Fgcosθ F = mgcosθ F = (50 kg)(9.8 m/s2)cos(25o) F = 444 N Ex: A 50 kg object rests on a table that is inclined 25o from the horizontal. (a) Determine the components of gravity acting on the object. (b) What is the Normal force? FN = F┴ = 444 N

  14. What is the force of friction if the object is at rest? FF = F║ FF = 207 N Assume the incline is now frictionless What is the acceleration down the incline? FNet = ma F║ = ma 207 N = (50 kg)a a = 4.14 m/s2

  15. What is the coefficient of static friction? FF = µFN 207 N = µ(444 N) µ = 0.47 How far will the object travel in 5 s? d = vit + ½at2 d = (0 m/s)(5 s) + ½(4.14 m/s2)(5 s)2 d = 51.75 m

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