Essential University Physics, 3e (Wolfson) Chapter 12 Static Equilibrium 12.1 Conceptual Questions 1) If the torque on an object adds up to zero A) the forces on it also add up to zero. B) the object is at rest. C) the object cannot be turning. D) the object could be accelerating linearly but it could not be turning. E) the object could be both turning and accelerating linearly. 2) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses. A) It is impossible to say without knowing the masses. B) It is impossible to say without knowing the distances. C) The side the boy is sitting on will tilt downward. D) Nothing will happen; the seesaw will still be balanced. E) The side the girl is sitting on will tilt downward. 12.2 Problems 1) A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A small 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board? 2) An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B.
3) A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor.
(a) What is the tension in the rope? (b) What is the magnitude of the force that the floor exerts on the plank? 4) A 3.00-kg ball rests in a frictionless groove as shown in the figure.
(a) What is the magnitude of the force that the left side of the groove exerts on the ball? 1 Copyright © 2016 Pearson Education, Inc.
(b) What is the magnitude of the force that the right side of the groove exerts on the ball? 5) A nonuniform, 80.0-g, meterstick balances when the support is placed at the 51.0-cm mark. At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark? A) 16.0 cm B) 67.0 cm C) 66.0 cm D) 35.0 cm E) 34.0 cm 6) A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam? A) 2.12 m B) 1.98 m C) 1.93 m D) 2.07 m E) 2.20 m 7) In the figure, the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot. How much force FM must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?
A) 100 N B) 500 N C) 750 N D) 1000 N E) 1500 N 8) A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip? A) 4.0 m B) 3.7 m C) 1.7 m D) 1.3 m E) 3.3 m 9) A stepladder consists of two halves, hinged at the top, and connected by a tie rod that keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.
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A) 140 N B) 240 N C) 280 N D) 360 N E) 560 N 10) Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a horizontal rope, 1.0 m above the smooth floor forming a symmetric "A" arrangement. The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint. What is the tension in the rope? A) 240 N B) 300 N C) 220 N D) 260 N E) 280 N 11) A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide, has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide? A) 0.710 m B) 1.00 m C) 1.21 m D) 1.42 m E) 1.63 m 12) A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in the figure. What is the maximum possible overhang distance d?
A) 5 cm B) 6 cm C) 7 cm D) 8 cm E) 9 cm
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13) A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square a side and its mass is what is the magnitude of the horizontal force that the wall at P experiences?
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A) 20 N B) 0.00 N C) 7.8 N D) 98 N 14) A uniform 300-kg beam, 6.00 m long, is freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. The maximum mass M of the load is closest to
A) 789 kg. B) 554 kg. C) 1020 kg. D) 1090 kg. E) 1320 kg. 15) A uniform 300-kg beam, 6.00 m long, is freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. Under maximum load, find the magnitude of the x component of the force exerted on the beam by the pivot at P.
A) 13,800 N B) 12,800 N C) 11,200 N D) 14,400 N E) 16,000 N 16) A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder?
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A) 538 N B) 706 N C) 1290 N D) 833 N E) 601 N 17) A dump truck has a large cubical concrete block in its bed. The coefficients of friction between this block and the floor of the bed are µk = 0.450 and µs = 0.650. As the bed is slowly tilted above the horizontal, will the brick first begin to slide or will it first tip over? A) It will first tip over. B) It will first begin to slide. C) It will tip over just as it begins to slide. D) It is impossible to answer without knowing the mass of the block. E) It is impossible to answer without knowing the dimensions of the block. 18) A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure), you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick?
A) 5.18 cm B) 6.09 cm C) 6.81 cm D) 9.40 cm E) 10.5 cm 19) A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m. The door is mounted on a post by a pair of hinges, marked 1 and 2 in the figure, at the top and bottom of the door. An external force of 60.0 N, at an angle of 30.0° above the horizontal, is applied to the small doorknob, as shown in the figure. The doorknob is 1.00 m above the bottom of the door. (a) Find the x component of the force that hinge 1 exerts on the door at the top. (b) Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.
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20) In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.
21) In the figure, a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53° with the bar. The bar is uniform and weighs 39.9 N. How far from the hinge should a 10.0-kg mass be suspended for the tension T in the rope to be 125 N?
22) In the figure, a uniform ladder 12 meters long rests against a vertical frictionless wall. The ladder weighs 400 N and makes an angle θ of 79° with the floor. A man weighing 790 N climbs slowly up the ladder When he has climbed to a point that is 7.8 m from the base of the ladder, the ladder starts to slip. What is the coefficient of static friction between the floor and the ladder?
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