A plank of mass 87 kg and length 7.8 m is supported by, but not affixed to, two posts which are shown in the figure below. A 62 kg person starts walking along the plank to the right end. How close can the person get to the right end of the plank before the plank tips over? 7.8m a.8m

A plank of mass 87 kg and length 7.8 m is supported by, but not affixed to, two posts which are shown in the figure below. A 62 kg person starts walking along the plank to the right end. How close can the person get to the right end of the plank before the plank tips over? 7.8m a.8m

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 36P: A crane of mass m1 = 3 000 kg supports a load of mass m2 = 10 000 kg as shown in Figure P10.36. The...

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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 P10.28
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.
A 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.
The fishing pole in Figure P10.22 makes an angle of 20.0 with the horizontal. What is the torque exerted by the fish about an axis perpendicular to the page and passing through the anglers hand if the fish pulls on the fishing line with a force F=100N at an angle 37.0 below the horizontal? The force is applied at a point 2.00 m from the anglers hands. Figure P10.22
A wooden door 2.1 m high and 0.90 m wide is hung by two hinges 1.8 m apart. The lower hinge is 15 cm above the bottom of the door. The center of mass of the door is at its geometric center, and the weight of the door is 260 N, which is supported equally by both hinges. Find the horizontal force exerted by each hinge on the door.
A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates through more than 180? (a) 3 rad, 6 rad; (b) 1 rad, 1 rad; (c) 1 rad, 5 rad.
What force must be applied to end of a rod along the x-axis of length 2.0 m in order to produce a torque on the rod about the origin of 8.0k Nm ?
Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23
The Iron Cross When a gymnast weighing 750 N executes the iron cross as in Figure lN.91a, the primary muscles involved in supporting this position are the latissimus dorsi (lats") and the pectoralis major (pecs"). The rings exert an upward force on the aims and support the weight of the gymnast. The force exerted by the shoulder joint on the arm is labeled Fs, while the two muscles exert a total force Fw on the arm. Estimate the magnitude of the force Fw. Note that one ring supports half the weight of the gymnast, which is 375 N as indicated in Figure P8.91b. Assume that the force Fw acts at an angle of 45 below the horizontal at a distance of 4.0 cm from the shoulder joint In your estimate, take the distance from the shoulder joint to the hand to be L = 70 cm and ignore the weight of the arm.
As shown in Figure 10.13 on page 306, toppling chimneys often break apart in midfall because the mortar between the bricks cannot withstand much shear stress. As the chimney begins to fall, shear forces must act on the topmost sections to accelerate them tangentially so that they can keep up with the rotation of the lower part of the stack. For simplicity, let us model the chimney as a uniform rod of length pivoted at the lower end. The rod starts at rest in a vertical position (with the frictionless pivot at the bottom) and falls over under the influence of gravity. What fraction of the length of the rod has a tangential acceleration greater than g sin , where is the angle the chimney makes with the vertical axis?