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One end of a uniform meter stick is placed against a vertical wall (Fig. P11.66). The other end is held by a lightweight cord that makes an angle θ with the stick. The coefficient of static friction between the end of the meter stick and the wall is 0.40. (a) What is the maximum value the angle θ can have if the stick is to remain in equilibrium? (b) Let the angle θ be 15°. A block of the same weight as the meter stick is suspended from the stick, as shown, at a distance x from the wall. What is the minimum value of x for which the stick will remain in equilibrium? (c) When θ = 15°, how large must the coefficient of static friction be so that the block can be attached 10 cm from the left end of the stick without causing it to slip?
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- A 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 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_forwardChildren playing pirates have suspended a uniform wooden plank with mass 15.0 kg and length 2.50 m as shown in Figure P14.27. What is the tension in each of the three ropes when Sophia, with a mass of 23.0 kg, is made to walk the plank and is 1.50 m from reaching the end of the plank? FIGURE P14.27arrow_forward
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- A 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_forwardWhy is the following situation impossible? A uniform beam of mass mk = 3.00 kg and length = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown in Figure P12.2. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero. Figure P12.2arrow_forwardA 800 N man is standing on a 4 m long plank of wood that is supported at each end by vertical ropes. The plank has a weight of 500 N and the man is standing 1 m from the left end. Find the force of tension in the rope at the left end of the plank.arrow_forward
- Any time you have to climb a ladder, you want the ladder to remain in static equilibrium. At what angle should a 60-kg painter place his ladder against the wall in order to climb two-thirds of the way up the ladder and have the ladder remain in static equilibrium? The ladder's mass is 10 kg and its length is 6.0 m. The exterior wall of the house is very smooth, meaning that it exerts a negligible friction force on the ladder. The coefficient of static friction between the floor and the ladder is 0.50.arrow_forwardA uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. N2 mg d b Since the floor is rough, it exerts both a normal force N, and a frictional force f, on the ladder. However, since the wall is frictionless, it exerts only a normal force N, on the ladder. The ladder has a length of L = 4.70 m, a weight of W = 68.0 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 N2 = f1 %3D (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 = f1arrow_forwardA 11.0-kg monkey climbs a uniform ladder with weight w = 1.40 × 102 N and length L = 2.60 m as shown in the figure below. The ladder rests against the wall and makes an angle of 0 = 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N. Rope (a) Draw a force diagram for the ladder. Choose File no file selected This answer has not been graded yet. (b) Find the normal force exerted on the bottom of the ladder. (c) Find the tension in the rope when the monkey is two-thirds of the way up the ladder. N (d) Find the maximum distance d (along the ladder) that the monkey can climb up the ladder before the rope breaks. (e) If the horizontal surface were rough and the rope were removed, how would your analysis of the problem change? What other information would you need to answer parts (c) and (d)? This answer has not been graded yet.…arrow_forward
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