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Chap 05 SM - Chapter 5 Additional Applications of Newtons...

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387 Chapter 5 Additional Applications of Newton’s Laws Conceptual Problems 1 [SSM] Various objects lie on the bed of a truck that is moving along a straight horizontal road. If the truck gradually speeds up, what force acts on the objects to cause them to speed up too? Explain why some of the objects might stay stationary on the floor while others might slip backward on the floor. Determine the Concept Static and kinetic frictional forces are responsible for the accelerations. If the coefficient of static friction between the truck bed and the object is sufficiently large, then the object will not slip on the truck bed. The larger the acceleration of the truck, the larger the coefficient of static friction that is needed to prevent slipping. 2 Blocks made of the same material but differing in size lie on the bed of a truck that is moving along a straight horizontal road. All of the blocks will slide if the truck’s acceleration is sufficiently great. How does the minimum acceleration at which a small block slips compare with the minimum acceleration at which a much heavier block slips? Determine the Concept The forces acting on an object are the normal force exerted by the floor of the truck, the gravitational force exerted by Earth, and the friction force; also exerted by the floor of the truck. Of these forces, the only one that acts in the direction of the acceleration (chosen to be to the right) is the static friction force. Apply Newton’s second law to the object to determine how the critical acceleration depends on its weight. x y n F r g F r s f r Taking the + x direction to be to the right, apply Σ F x = ma x to the object: x ma mg F f = = = s g s s μ g a x s = Because x a is independent of m and F g , the critical accelerations are the same. 3 A block of mass m rests on a plane that is inclined at an angle θ with the horizontal. It follows that the coefficient of static friction between the block and plane is ( a ) s g , ( b ) s = tan , ( c ) s tan , ( d ) s tan .
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Chapter 5 388 Determine the Concept The forces acting on the block are the normal force n F r exerted by the incline, the weight of the block g F r exerted by Earth, and the static friction force s f r also exerted by the incline. We can use the definition of μ s and the conditions for equilibrium to determine the relationship between s and θ . s f r g F r n F r x y Apply x x ma F = to the block: 0 sin g s = F f or, because F g = mg, 0 sin s = mg f (1) Apply y y ma F = in the y direction: 0 cos n = mg F (2) Divide equation (1) by equation (2) to obtain: n s tan F f = Substitute for f s ( s F n ) and simplify to obtain: s n n s tan = F F and ) ( d is correct. 4 A block of mass m is at rest on a plane that is inclined at an angle of 30º with the horizontal, as shown in Figure 5-56. Which of the following statements about the magnitude of the static frictional force f s is necessarily true?
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