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chapter 8 answers

chapter 8 answers - Problem 8.1 The coefficients of static...

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Problem 8.1 The coefficients of static and kinetic fric- tion between the 0.4-kg book and the table are µ s = 0 . 30 and µ k = 0 . 28 . A person exerts a horizontal force on the book as shown. (a) If the magnitude of the force is 1 N and the book remains stationary, what is the magnitude of the fric- tion force exerted on the book by the table? (b) What is the largest force the person can exert without causing the book to slip? (c) If the person pushes the book across the table at a constant speed, what is the magnitude of the friction force? Solution: F x : F f = 0 F y : N W = 0 (a) F = 1 N Solving f = 1 N (b) f max = µ s N, µ s = 0 . 3 N = 3 . 92 N , f max = 1 . 18 N F max = 1 . 18 N (c) For constant speed, f = µ k N = (0 . 28)(3 . 92) f = 1 . 10 N Thus, since F f = 0 F = 1 . 10 N F N W = mg = (0.4) 9.81 = 3.92 N f

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Problem 8.2 The 10.5-kg Sojourner rover, placed on the surface of Mars by the Pathfinder Lander on July 4, 1997, was designed to negotiate a 45 slope without tipping over. (a) What minimum static coefficient of friction between the wheels of the rover and the surface is necessary for it to rest on a 45 slope? The acceleration due to gravity at the surface of Mars is 3 . 69 m/s 2 . (b) Engineers testing the Sojourner on Earth want to confirm that it will negotiate a 45 slope without tipping over. What minimum static coefficient of friction between the wheels of the rover and the sur- face is necessary for it to rest on a 45 slope on Earth? Solution: (a) Assume that slip is impending when the rover is on a 45 slope. The friction force f = µ s N , and the free-body diagram is: The equilib- rium equations are: F x = µ s N + mg sin 45 = 0 , F y = N mg cos 45 = 0 . Summing the two equations, we obtain N µ s N = 0 so µ s = 1 is the minimum static coefficient of friction. (b) the solution in (a) is independent of the value of g so µ s = 1 is the minimum on earth also. N mg x y 45 ° s N µ Problem 8.3 The coefficient of static friction between the tires of the 8000-kg truck and the road is µ s = 0 . 6 . (a) If the truck is stationary on the incline and α = 15 , what is the magnitude of the total friction force exerted on the tires by the road? (b) What is the largest value of α for which the truck will not slip? Solution: f y x N W = mg α α α (a) F x : f mg sin α = 0 F y : N mg cos α = 0 g = 9 . 81 m/s 2 , α = 15 , m = 8000 kg Solving, f = 20 . 3 kN also N = 75 . 8 kN (b) Set f = µ s N and solve for α in the basic eqns. F x : µ s N mg sin α = 0 F y : N mg cos α = 0 m = 8000 kg, g = 9 . 81 m/s 2 Solving, α = 30 . 96
Problem 8.4 The coefficient of static friction between the 5-kg box and the inclined surface is µ s = 0 . 3 . The force F is horizontal and the box is stationary. (a) If F = 40 N, what friction force is exerted on the box by the inclined surface? (b) What is the largest value of F for which the box will not slip? 30 ° F Solution: f N x F y mg 30 ° 30 ° 30 ° (a) F = 40 N F x : f + F cos 30 mg sin 30 = 0 F y : N F sin 30 mg cos 30 = 0 f = 10 . 1 N (down the plane) (b) In the equilibrium eqns, set f = µ s N and treat F as unknown.

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chapter 8 answers - Problem 8.1 The coefficients of static...

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