Chapter_6_09 - Problems from Chapter 6 6.3 A person pushes...

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Problems from Chapter 6 6.3 A person pushes horizontally with a force of 220 N on a 55 kg crate to move it across a level floor. The coefficient of kinetic friction is 0.35. What is the magnitude of (a) the frictional force and (b) the crate’s acceleration. F F f N mg ma y = 0 = N mg N = mg F f = μ N = μ mg = 0.35 55 kg 9.8 m / s 2 = 188.65 N ma x = F F f a x = F F f m = 220 N 188.65 N 55 kg = 0.57 m / s 2 6.7. A 3.5 kg block is pushed along a horizontal floor by a force F of magnitude 15N at an angle of 40 degrees with the horizontal. The coefficient of kinetic friction between the block and the floor is 0.25. Calculate the magnitudes of (a) The frictional force on the block from the floor and (b) the acceleration of the block. N F mg F f N F mg F f θ We can now write the forces in the vertical and horizontal directions: Vertical 0 = N mg F sin θ N = mg + F sin θ Horizontal ma = F cos θ F f = F cos θ μ N a = F cos θ μ ( mg + F sin θ ) m
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F f = μ ( mg + F sin θ ) = 0.25 (3.5 kg 9.8 m / s 2 + 15 N sin40 ° ) = 10.99 N a = F cos θ μ ( mg + F sin θ ) m = 15 N cos40 ° 10.99 N 3.5 kg = 0.143 m / s 2 6.20 A loaded penguin sled weight 80N rests on a plane inclined at 20 degrees to the horizontal. Between the sled and the plane, the coefficient of static friction is 0.25, and the coefficient of kinetic friction is 0.15. (a) What is the minimum magnitude of the force F, parallel to the plane, that will prevent the sled from slipping down the plane. (b) What is the minimum magnitude F that will start the sled moving up the plane? (c) What value F is required to move the sled with constant velocity up the incline. a) We begin by drawing the forces. Since the motion would be downward if F is too small, we draw Friction as pointing UP the incline for part a.
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