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Chapter 6 Practice Problems

Practice problems involving trigonometric equations, vector components, and force calculations in physics. Solutions and explanations provided. Learn how to resolve forces, find resultant velocities, and apply equations in various scenarios.

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Chapter 6 Practice Problems

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  1. Chapter 6 Practice Problems

  2. Equations • Sin θ =opposite side • hypotenuse • Cos θ = adjacent side • hypotenuse • Tan θ = opposite side • adjacent side

  3. Equations • vR2 = vp2 + vw2 • R2 = A2 + B2 • Fv = F sin θ • Fh = F cosθ • Fnet2 = Fnetx2 + Fnety2 • A + B + W = 0

  4. Fll= W Sin θ • Fl = W cosθ • Ff = μFN

  5. Problem 1 • Finding a resultant velocity. • An airplane flying toward 0o at 90 km /h is being blown toward 90o at 50 km/h. What is the resultant velocity of the plane. • Given: vp = 90 km /h at 0o vw= 50 km/h at 90o tanΘ = side opposite /side adjacent • Unknown ; resultant velocity vr

  6. Problem 1 • Basic equation: R2 = A2 + B2 or • vR2 = vp2 + vw2

  7. Problem 1 • Answer: vR = 103 km/ h at 29o

  8. Problem 1 • Solution: • VR2 = (90 km/h)2 + (50 km/h)2 = • sq root 1.06 X 104 (km/h)2 • vR2 = 103 km /h • Tan θ = 50 km/h • 90 km/h • Tan θ -1= .556 = 29o

  9. Problem 2 • Resolving a Velocity Vector into its Components • A wind with a velocity of 40 km/h blows toward 30o. • A. What is the component of the wind’s velocity toward 90o • B. What is the component of the wind’s velocity toward 0o

  10. Problem 2 • Given: v= 40.0 km/h, 30.0o • Unknown: v90, v0 • Solution: Toward 0o and 90o are positive. Angles are measured from 0o. To find the component toward 90o use the following: • sin 30o = v90/v then v90 = 20 km/h at 90o

  11. Problem 2 • From 0ocos 30o =vo/v • V0 = 34.6 km/h at 0.0o

  12. Problem 3 • Adding Non perpendicular Vectors • Two ropes(F1 = 12.0 N at 10.0o) (F2= 8.0 N at 120o ) are pulling on a log. What is the net force on the log? • Given: F1 = 12.0 N at 10.0o • F2 = 8.0 N at 120o • Unknown: Fnet

  13. Problem 3 • Find the perpendicular components of each force.(figure 6-12) • F1x =(12 N) cos 30o = 11.8 N • F1y = (12 N) sin 30o = 2. N • F2x = ( 8.0 N) cos 120o = -4.0 N • F2y = (8.0 N) sin 120o = 6.9 N

  14. Problem 3 • Sum x and y components • Fnet x = F1x + F2x = 11.8 N + -4.0 N = 7.8 N • F nety = F1y + F2y= 2.0 N + 6 .9 N = 8.9 N • Find the magnitude of the net force • F net = sq root Fx2 +Fy2 = sq root of (7.8 N)2 + (8.9 N )2 = 11 N

  15. Problem 3 • Find the angle of the force • Tan θ = 1.14 • Θ = 49o

  16. Problem 4 • Finding Forces when Components are Known • A sign that weighs 168 N is supported by ropes a and b (figure6-16)that make 22.5o angles with the horizontal. The sign is not moving. What forces do the ropes exert on the sign?

  17. Problem 4 • Given: • The sign is in equilibrium • Weight = W = 168 N (down) • Angles ropes make with horizontal is 22.5o • Unknowns: • Force of rope a is A • Force of rope b is B

  18. Problem 4 • Basic equations: • In equilibrium net force is 0 • A + B + W = 0 • Fh = F Cos θ • Fv = F Sin θ

  19. Problem 4 • Since W is down the direction of A + B is up • Since the sum of A + B has no horizontal components . Therefore Ah and Bh have equal magnitude • Now, Ah = A Cos 22.5o and Bh = B cos 22.5o • Av + Bv = 168 N • Since A = B then Av + Bv

  20. Problem 4 • Thus • Av = Bv = ½ (168 N ) • = 84 N • A = Av • sin 22.5o = 220 N • B = A = 220 N

  21. Problem 5 • Finding F l and Fll • A trunk weighing 562 N is resting on a plane inclined at 30o from the horizontal (Figure 6-18 ) Find the components of the weight parallel and perpendicular to the plane.

  22. Problem 5 • Given: • W = 562 N • Θ = 30o • Unknown: • Fl • F ll

  23. Problem 5 • Solution: • Resolve the weight into components perpendicular and parallel to plane • Fll= W sin θ Fl= W Cos θ

  24. Problem 5 • F ll = (+562 N)( sin 30.0o) • = +(562 N) (0.500) • = +281 N • F l= + (562 N)(cos 30o) • = + (562 N) (.866 ) = + 487 N

  25. Problem 6 • Finding acceleration down a plane • The 562 N trunk is on a frictionless plane inclined at 30o from the horizontal . Find the acceleration of the trunk. What is its direction?

  26. Problem 7 • Finding the Coefficient of Static Friction

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