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Mountain Climbing. Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rapelling). They do this with their body nearly horizontal and their feet pushing against the cliff (Fig. P11.45). Suppose that an 82.0-kg climber, who is 1.90 m tall and has a center of gravity 1.1 m from his feet, rappels down a vertical cliff with his body raised 35.0° above the horizontal. He holds the rope 1.40 m from his feet, and it makes a 25.0° angle with the cliff face. (a) What tension does his rope need to support? (b) Find the horizontal and vertical components of the force that the cliff face exerts on the climber’s feet. (c) What minimum coefficient of static friction is needed to prevent the climber’s feet from slipping on the cliff face if he has one foot at a time against the cliff?
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- Why is the following situation impossible? A worker in a factory pulls a cabinet across the floor using a rope as shown in Figure P12.36a. The rope make an angle = 37.0 with the floor and is tied h1 = 10.0 cm from the bottom of the cabinet. The uniform rectangular cabinet has height = 100 cm and width w = 60.0 cm, and it weighs 400 N. The cabinet slides with constant speed when a force F = 300 N is applied through the rope. The worker tires of walking backward. He fastens the rope to a point on the cabinet h2 = 65.0 cm off the floor and lays the rope over his shoulder so that he can walk forward and pull as shown in Figure P12.36b. In this way, the rope again makes an angle of = 37.0 with the horizontal and again has a tension of 300 N. Using this technique, the worker is able to slide the cabinet over a long distance on the floor without tiring. Figure P12.36 Problems 36 and 44.arrow_forwardA horizontal, rigid bar of negligible weight is fixed against a vertical wall at one end and supported by a vertical string at the other end. The bar has a length of 50.0 cm and is used to support a hanging block of weight 400.0 N from a point 30.0 cm from the wall as shown in Figure P14.81. The string is made from a material with a tensile strength of 1.2 108 N/m2. Determine the largest diameter of the string for which it would still break. FIGURE P14.81arrow_forwardA 10.0-kg monkey climbs a uniform ladder with weight 1.20 102 N and length L = 3.00 m as shown in Figure P12.14. The ladder rests against the wall and makes an angle of = 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. (a) Draw a force diagram for the ladder. (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. (d) Find the maximum distance d 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)? Figure P12.14arrow_forward
- A bridge of length 50.0 m and mass 8.00 104 kg is supported on a smooth pier at each end as shown in Figure P12.25. A truck of mass 3.00 104 kg is located 15.0 m from one end. What are the forces on the bridge at the points of support? Figure P12.25arrow_forwardA bridge of length 50.0 m and mass 8.00 X 104 kg is supported on a smooth pier at each end as in Figure P12.39. A truck of mass 3.00 X 104 kg is located 15.0 m from one end. What are the forces on the bridge at the points of support?arrow_forwardA uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40 kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.20 m from the left-hand end of the rod?arrow_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_forwardConsider a nanotube with a Youngs modulus of 2.130 1012 N/m2 that experiences a tensile stress of 5.3 1010 N/m2. Steel has a Youngs modulus of about 2.000 1011 Pa. How much stress would cause a piece of steel to experience the same strain as the nanotube?arrow_forwardConsider the sketch of a portion of a roller-coaster track seen in Figure P14.5. Identify places on the track that could be considered possible locations of static equilibrium for a rollercoaster car were the car to be placed at any spot on the track.Which places are candidate locations for stable, unstable, andneutral static equilibrium? FIGURE P14.5arrow_forward
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