In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by AA= 1.7 AB; the Young's moduli of the cylinders are related by EA= 1.8 Eg. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are defor cylinder A and dg for cylinder B. (c) What is the ratio dд/de?

In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by AA= 1.7 AB; the Young's moduli of the cylinders are related by EA= 1.8 Eg. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are defor cylinder A and dg for cylinder B. (c) What is the ratio dд/de?

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 28P: A uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under...

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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 horizontal plank 4.00 m long and having mass 20.0 kg rests on two pivots, one at the left end and a second 1.00 m from the right end. Find the magnitude of the force exerted on the plank by the second pivot. (See Section 8.4.)
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.
In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. (b) Find the angular speed of the pulley at the same moment. Figure P10.40
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 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 P12.14
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 P12.25
A brass wire and a steel wire, both of the same length, are extended by 1.0 mm under the same force. Is the cross-sectional radius of the brass wire more, less, or equal to the cross-sectional radius of the steel wire? Explain. Youngs moduli for brass and steel are 1.0 1010 N/m2 and 2.0 1011 N/m2, respectively.
In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by AA= 1.7 AB; the Young's moduli of the cylinders are related by EA= 1.9 EB. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are dAfor cylinder A and dB for cylinder B. (c) What is the ratio dA/dB?
A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm, what is the tension in the wire?
Two uniform planks, each of mass m = 7.45 kg and length L = 2.51 m, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape of an A, on a frictionless surface without collapsing. If the chain has the length 0.81 m, find each of the following: a) the absolute value of the tension in the chain, b) the absolute magnitude of the force on the hinge of each p lank