21. A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?
A) Horizontal
B) 60? above the horizontal
C) 30? above the horizontal
D) 27? above the horizontal
E) 30? below the horizontal
22. A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if he:
A) pushes with slightly greater force
B) pushes with slightly less force
C) stops pushing
D) pushes so his force is slightly downward but has the same magnitude
E) pushes so his force is slightly upward but has the same magnitude
23. A horizontal force of 12 N pushes a 0.5-kg bookk against a vertical wall. The book is initially at rest. If the coefficients of friction are ??s = 0.6 and ??k = 0.8 which of the following is true?
A) The frictional force is 4.9 N
B) The frictional force is 7.2 N
C) The normal force is 4.9 N
D) The block will start moving and accelerate
E) If started moving downward, the block will decelerate
24. A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If ??s = 0.6 and ??k = 0.80, the frictional force is:
A) 0
B) 4.9 N
C) 3.0 N
D) 5.0 N
E) 4.0 N
25. A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If ??s = 0.6 and ??k = 0.80, the acceleration of the book in m/s2 is:
A) 0
B) 9.4 m/s2
C) 9.8 m/s2
D) 14.4 m/s2
E) 19.2 m/s2
26. A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If ??s = 0.60 and ??k = 0.80, the acceleration of the block in m/s2 is:
A) 0
B) 1.8
C) 6.0
D) 8.0
E) 9.8
27. A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slide. The coefficient of static friction is:
A) 0.8
B) 0.25
C) 0.4
D) 0.6
E) 0.75
28. A heavy wooden block is dragged by a force 
along a rough steel plate, as shown below for two possible situations. The magnitude of is the same for the two situations. The magnitude of the frictional force in (ii), as compared with that in (i) is:
A) the same
B) greater
C) less
D) less for some angles and greater for others
E) can be less or greater, depending on the magnitude of the applied force.
29. A block is first placed on its long side and then on its short side on the same inclined plane. The block slides down the plane on its short side but remains at rest on its long side. A possible explanation is:
A) the short side is smoother
B) the frictional force is less because the contact area is less
C) the center of gravity is higher in the second case
D) the normal force is less in the second case
E) the force of gravity is more nearly down the plane in the second case
30. A block is placed on a rough wooden plane. It is found that when the plane is tilted 30? to the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction of the block with the plane is:
A) 0.500
B) 0.577
C) 1.73
D) 0.866
E) 4.90
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