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By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly 1/4 the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.

By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly 1/4 the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.

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By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0 − kg block is observed to be exactly 1 / 4 the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.

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As shown in Figure 3(a), a wooden block B with mass mB = 2.4 kg on a rough inclined plane is connected to a massless spring ( k = 160 N/m ) by a massless cord passing over a pulley P of radius R = 0.25 m and mass Mp = 0.60 kg. The angle of the inclined plane is θ = 37∘ and the coefficients of static and kinetic frictions are μs = 0.35 and μk = 0.30 respectively. The frictional force at the axle of the pulley is negligible. The pulley can be regarded as a solid disk. (a) The system is at rest and in this case, block B is on the verge of sliding down. Figure 3(a) i. Indicate (with labeled arrows) the forces acting on the pulley and the block. ii. Calculate the tension in the string and the extension of the spring. (You can assume that the tensions in the cord on either side of the pulley P are the same for this part.) (b) As shown in Figure 3(b), another wooden block A of mass mA = 1.2 kg made of the same material as block B is released from rest. It slides down a distance l down the rough inclined plane and collides with block B. The two blocks stick together and move down the incline with a common velocity v = 0.80 m/s immediately after collision and the pulley rotates. The cord does not stretch and does not slip on the pulley. Figure 3(b) i. Determine the distance l. ii. Determine the acceleration of the two blocks at the moment they move down together and the pulley starts to rotate. iii. Determine how much further down the slope the two blocks move together after they collide before the two blocks come to a momentary rest.
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The two blocks A and B have a mass mA and mB′, respectively, where mB > mA. If the pulley can be treated as a disk of mass M and radius r, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley. Hint: treat the pulley and the two blocks as a system. a. (10 points) Establish a coordinate system, specify the direction and sense of the accelerations aA and aB and the angular acceleration of the disk α. Draw the free-body-diagram and the kinetic diagram. b. (10 points) List the external forces acting on the system (the pulley and the two blocks) and calculate their moments about point O. c. (10 points) Calculate the mass moment of inertia of the pulley about point O. d. (10 points) Use kinematics to find the relation between aA, aB and α. e. (20 points) Establish the equation of motion and solve for aA. Hint: only consider the equation about the sum of moments about point O.
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A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh.

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