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Chapter 5 Forces in Two Dimensions

Chapter 5 Forces in Two Dimensions. Vectors Again! How do we find the resultant in multiple dimensions? Pythagorean Theorem- if the two vectors are at right angles R 2 = A 2 + B 2 At an angle other than 90 ° a. Law of Cosines R 2 = A 2 +B 2 –2AB cos 

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Chapter 5 Forces in Two Dimensions

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  1. Chapter 5Forces in Two Dimensions Vectors Again! How do we find the resultant in multiple dimensions? • Pythagorean Theorem- if the two vectors are at right angles R2= A2 + B2 • At an angle other than 90° a. Law of Cosines R2 = A2 +B2 –2AB cos  b. Law of Sines R = A = B sin  sin a sin b

  2. Examples • A car is driven 125.0 km due west, then 65.0 km due south. What is the magnitude of its displacement? • Find the magnitude of the sum of two forces, one 20.0 N and the other 7.0 N, when the angle between them is 30.0 °.

  3. Does a vector have components? A = Ax + Ay A  Ay Ax

  4. Vector Resolution • The process of breaking a vector into its components How can we determine the vector components? By using Trigonometry

  5. Trig. Functions • SOH sin  = opposite/hyp. • CAH cos  = adj./ hyp. • TOA tan  = opp./adj.

  6. Example As the 60-Newton tension force acts upward and rightward on Fido at an angle of 40 degrees, the components of this force can be determined using trigonometric functions.

  7. Adding 2/more Vectors • By resolving each vector into its x and y components then add the x components to form the x component of the resultant then add the y components to form the y component of the resultant • Rx= Ax + Bx + Cx • Ry= Ay + By + Cy • Then • R2 = Rx2 + Ry2

  8. How do we find the angle of the resultant? • Use the Angle of Resultant Vector = tan-1 (Ry/Rx) Example: A hiker travels 4.0 m South then 7.3 m Northwest. Find the displacement and angle of the hiker.

  9. What is Friction? • A force opposing motion 2 Types of Friction • Kinetic Friction(Ffk)- friction created between moving surfaces • Static Friction(Ffs)-force between 2 nonmoving surfaces

  10. What does Frictional Force depend upon? • Surface materials- depends on the nature of the surfacesCoefficient of Friction- value describing the nature of the surfaces in contact • Normal force- perpendicular contact force exerted by a surface on an object

  11. How is it Determined? • Kinetic Friction(Ffk) Ffk= kFN • Static Friction(Ffs) Ffs sFN

  12. Example Problem 3 p.128 You push a 25.0 kg wooden box across a wooden floor at a constant speed of 1.0 m/s. How much force do you exert on the box? What do we know? M= 25.0 kg Fapp.=? V= 1.0 m/s a= 0.0m/s/s = .20(Table 5-1)

  13. Practice Problem p.130, #22 • A 1.4 kg block slides across a rough surface that it slows down with an acceleration of 1.25 m/s/s. What is the coefficient of friction between the block and the surface?

  14. Motion Along an Inclined Plane A crate weighing 562 N is resting on a plane inclined 30.0° above the horizontal. Find the components of the weight forces that are parallel and perpendicular to the plane.

  15. Example Problem #6, p.134 • A 62 kg person on skis is going down a hill sloped at 37°. The coefficient of kinetic friction between the skis and the snow is 0.15. How fast is the skier going after 5.0 s after starting from rest?

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