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Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β. Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration. Let down define the positive direction for the hanging bag. What is ay, the vertical component of the acceleration of the hanging bag? ay = Enter your expression in terms of given quantities and integers.

Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β. Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration. Let down define the positive direction for the hanging bag. What is ay, the vertical component of the acceleration of the hanging bag? ay = Enter your expression in terms of given quantities and integers.

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Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β .
Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration.
Let down define the positive direction for the hanging bag. What is a y , the vertical component of the acceleration of the hanging bag?
a y =
◻ Enter your expression in terms of given quantities and integers.

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Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β. Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration. Let down define the positive direction for the hanging bag. What is ay, the vertical component of the acceleration of the hanging bag? ay = Enter your expression in terms of given quantities and integers.
Solution
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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. 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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.

Solution
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This problem is identical to the second problem of Test 5 , except now you will solve it using an energy method. Three masses mA, mB and mC are initially at rest. The masses mB and mC are connected to each other with a taut and massless rope which is guided over a massless and frictionless pulley. The masses mA and mB are connected to each other with a second taut and massless rope which is guided over a second massless and frictionless pulley. The masses mB and mC are on frictionless inclines of angles θB and θC, respectively, while mass mA hangs vertically, as shown in Figure 1 . The force of gravity acts vertically downward. Figure 1. Diagram for Problem 1. a. (30 pts) The masses are released from rest. Using the Principle of Conservation of Mechanical Energy, derive an equation for the common velocity v of the masses at the moment they have moved through distance L. Express your equation for v in terms of only the aforementioned variables and g. You must make a drawing showing the various configurations of the system and labeling them. You may draw directly on Figure 1 adding all the required elements for a system configuration diagram. Simplify your equation.

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