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Two bodies of mass m1 = 1 kg and m2 = 3 kg are connected to each other by a rope as in the figure; m1 is also attached to a spring with spring constant k = 100 N/m and rest length d = 1 m. At the instant t = 0, with the spring at rest and with zero initial velocity, the system is left free to move. In the absence of friction, determine: a) the equations of motion for the system of the bodies x(t); b) the maximum value of the tension in the rope.

Two bodies of mass m1 = 1 kg and m2 = 3 kg are connected to each other by a rope as in the figure; m1 is also attached to a spring with spring constant k = 100 N/m and rest length d = 1 m. At the instant t = 0, with the spring at rest and with zero initial velocity, the system is left free to move. In the absence of friction, determine: a) the equations of motion for the system of the bodies x(t); b) the maximum value of the tension in the rope.

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Two bodies of mass m 1 = 1 k g and m 2 = 3 k g are connected to each other by a rope as in the figure; m 1 is also attached to a spring with spring constant k = 100 N / m and rest length d = 1 m . At the instant t = 0 , with the spring at rest and with zero initial velocity, the system is left free to move. In the absence of friction, determine: a) the equations of motion for the system of the bodies x ( t ) ; b) the maximum value of the tension in the rope.

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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. 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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. 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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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