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A uniform beam of length L and mass m shown in Figure P12.8 is inclined at an angle θ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is μs. Assume the angle θ is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of
Figure P12.8
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Chapter 12 Solutions
Physics for Scientists and Engineers
- A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = ℓ. A painter of mass m stands on the ladder a distance d from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately. Figure P10.73 Problems 73 and 74.arrow_forwardA 215-kg robotic arm at an assembly plant is extended horizontally (Fig. P14.32). The massless support rope attached at point B makes an angle of 15.0 with the horizontal, and the center of mass of the arm is at point C. a. What is the tension in the support rope? b. What are the magnitude and direction of the force exerted by the hinge A on the robotic arm to keep the arm in the horizontal position? FIGURE P14.32arrow_forwardA uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28arrow_forward
- A massless, horizontal beam of length L and a massless rope support a sign of mass m (Fig. P14.78). a. What is the tension in the rope? b. In terms of m, g, d, L, and , what are the components of the force exerted by the beam on the wall? FIGURE P14.78arrow_forwardA One end of a metal rod of weight Fg and length L presses against a corner between a wall and the floor (Fig. P14.64). A rope is attached to the other end of the rod. Find the magnitude of the tension in the rope if the angle between the rod and the rope is 90.arrow_forwardA stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.arrow_forward
- A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 740 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. (a) What is the maximum friction force that the ground can exert on the ladder at its lower end? (b) What is the actual friction force when the man has climbed 1.0 m along the ladder? (c) How far along the ladder can the man climb before the ladder starts to slip?arrow_forwardThe figure below shows a beam of uniform density with a mass of 33.0 kg and a length l = 4.45 m. It is suspended from a cord at a distance d = 1.20 m from its left end, while its right end is supported by a vertical column. (a) What is the tension (in N) in the cord? N (b) What is the magnitude of the force (in N) that the column exerts on the right end of the beam? N Need Help? Read Itarrow_forwardA uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.1 m, a weight of WL = 61.0 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 = N N2 = N f1 = N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 = N N2 = N f1 = Narrow_forward
- A uniform beam of length L = 1.5 m with a mass of 11 kg is attached to a wall by a cable as shown in the figure. The board is free to pivot at the point where it attached to the wall. What is the tension in the cable? The angle = 26°arrow_forwardA uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.4 m, a weight of WL = 53.5 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 = ? N N2 = ? N f1 = ? N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 = ? N N2 = ? N f1 = ? Narrow_forwardA uniform 36.0-kg beam of length ℓ = 4.20 m is supported by a vertical rope located d = 1.20 m from its left end as in the figure below. The right end of the beam is supported by a vertical column. Answer parts a-b.arrow_forward
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