A hanging weight, with a mass of m₁ = 0.360 kg, is attached by a cord to a block with mass m₂ = 0.840 kg as shown in the figure below. The cord goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R₁ = 0.0200 m, and an outer radius of R₂ = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μ = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the cord does not stretch and does not slip on the pulley, and that the mass of the cord is negligible. R₂ Mo R₁ m/s 201 (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s

A hanging weight, with a mass of m₁ = 0.360 kg, is attached by a cord to a block with mass m₂ = 0.840 kg as shown in the figure below. The cord goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R₁ = 0.0200 m, and an outer radius of R₂ = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μ = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the cord does not stretch and does not slip on the pulley, and that the mass of the cord is negligible. R₂ Mo R₁ m/s 201 (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s

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 40P: In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2...

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Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of = 30.0 as shown in Figure P10.16. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley. Figure P10.16
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
As shown in Figure OQ10.9, a cord is wrapped onto a cylindrical reel mounted on a fixed, frictionless, horizontal axle. When does the reel have a greater magnitude of angular acceleration? (a) When the cord is pulled down with a constant force of 50 N. (b) When an object of weight 50 N is hung from the cord and released. (c) The angular accelerations in parts (a) and (b) are equal. (d) It is impossible to determine. Figure OQ10.9
A rod 7.0 m long is pivoted at a point 2.0 m from the left end. A downward force of 50 N acts at the left end, and a downward force of 200 N acts at the right end. At what distance to the right of the pivot can a third force of 300 N acting upward be placed to produce rotational equilibrium? Note: Neglect the weight of the rod. (a) 1.0 m (b) 2.0 m (c) 3.0 m (d) 4.0 m (e) 3.5 m
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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 turntable (disk) of radius r = 26.0 cm and rotational inertia0.400 kg m2 rotates with an angular speed of 3.00 rad/s arounda frictionless, vertical axle. A wad of clay of mass m =0.250 kg drops onto and sticks to the edge of the turntable.What is the new angular speed of the turntable?
A force of F=(2.00i+3.00j) N is applied to an object that is pivoted about a fixed axle aligned along the z coordinate axis. The force is applied at the point r=(4.00i+5.00j)m. Find (a) the magnitude of the net torque about the z axis and (b) the direction of the torque vector .
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 reel shown in Figure P10.71 has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and the reel is then released from rest. Find the angular speed of the reel when the spring is again unstretched. Figure P10.71
A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. (a) If they are released from rest and roll without slipping, which object reaches the bottom first? (b) Verify your answer by calculating their speeds when they reach the bottom in terms of h.