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Learning Goal: Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead you to a solution. One such prescription is the following: • Visualize the problem and identify special cases. • Isolate each body and draw the forces acting on it. • Choose a coordinate system for each body. Apply Newton's 2nd law to each body. • Write equations for the constraints and other given information. • Solve the resulting equations symbolically. • Check that your answer has the correct dimensions and satisfies special cases. • If numbers are given in the problem, plug them in and check that the answer makes sense. • Think about generalizations or simplifications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass m2 that is pulled up a frictionless plane inclined at angle 0 with respect to the horizontal by a massless string that passes over a massless, frictionless pulley to a block of mass m₁ that is hanging vertically. (Figure 1) Part H Solve and check In the previous parts, you obtained the following equations using Newton's 2nd law and the constraint on the motion of the two blocks: m2a2x T-m2g sin(0), (1) = m1a1yTm1g, (2) a2x = -aly. (3) and Solve these equations to find aly. Before you enter your answer, make sure it satisfies the special cases you already identified: Figure block 2 block 1 1 of 2 > • aly -g if m2 = 0 and . aly = 0 if m1 = m2 and 0 = π/2. Also make sure that your answer has dimensions of acceleration. Express aly in terms of some or all of the variables m1, M2, 0, and g. ▸ View Available Hint(s) aly = Submit ΕΠΙ ΑΣΦ ?

Learning Goal: Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead you to a solution. One such prescription is the following: • Visualize the problem and identify special cases. • Isolate each body and draw the forces acting on it. • Choose a coordinate system for each body. Apply Newton's 2nd law to each body. • Write equations for the constraints and other given information. • Solve the resulting equations symbolically. • Check that your answer has the correct dimensions and satisfies special cases. • If numbers are given in the problem, plug them in and check that the answer makes sense. • Think about generalizations or simplifications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass m2 that is pulled up a frictionless plane inclined at angle 0 with respect to the horizontal by a massless string that passes over a massless, frictionless pulley to a block of mass m₁ that is hanging vertically. (Figure 1) Part H Solve and check In the previous parts, you obtained the following equations using Newton's 2nd law and the constraint on the motion of the two blocks: m2a2x T-m2g sin(0), (1) = m1a1yTm1g, (2) a2x = -aly. (3) and Solve these equations to find aly. Before you enter your answer, make sure it satisfies the special cases you already identified: Figure block 2 block 1 1 of 2 > • aly -g if m2 = 0 and . aly = 0 if m1 = m2 and 0 = π/2. Also make sure that your answer has dimensions of acceleration. Express aly in terms of some or all of the variables m1, M2, 0, and g. ▸ View Available Hint(s) aly = Submit ΕΠΙ ΑΣΦ ?

Principles of Physics: A Calculus-Based Text
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
Chapter5: More Applications Of Newton’s Laws
Section: Chapter Questions
Problem 1CQ: A car is moving forward slowly and is speeding up. A student claims that the car exerts a force on...
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Learning Goal: Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead you to a solution. One such prescription is the following: • Visualize the problem and identify special cases. • Isolate each body and draw the forces acting on it. • Choose a coordinate system for each body. Apply Newton's 2nd law to each body. • Write equations for the constraints and other given information. • Solve the resulting equations symbolically. • Check that your answer has the correct dimensions and satisfies special cases. • If numbers are given in the problem, plug them in and check that the answer makes sense. • Think about generalizations or simplifications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass m2 that is pulled up a frictionless plane inclined at angle 0 with respect to the horizontal by a massless string that passes over a massless, frictionless pulley to a block of mass m₁ that is hanging vertically. (Figure 1) Part H Solve and check In the previous parts, you obtained the following equations using Newton's 2nd law and the constraint on the motion of the two blocks: m2a2x T-m2g sin(0), (1) = m1a1yTm1g, (2) a2x = -aly. (3) and Solve these equations to find aly. Before you enter your answer, make sure it satisfies the special cases you already identified: Figure block 2 block 1 1 of 2 > • aly -g if m2 = 0 and . aly = 0 if m1 = m2 and 0 = π/2. Also make sure that your answer has dimensions of acceleration. Express aly in terms of some or all of the variables m1, M2, 0, and g. ▸ View Available Hint(s) aly = Submit ΕΠΙ ΑΣΦ ?
Transcribed Image Text:Learning Goal: Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead you to a solution. One such prescription is the following: • Visualize the problem and identify special cases. • Isolate each body and draw the forces acting on it. • Choose a coordinate system for each body. Apply Newton's 2nd law to each body. • Write equations for the constraints and other given information. • Solve the resulting equations symbolically. • Check that your answer has the correct dimensions and satisfies special cases. • If numbers are given in the problem, plug them in and check that the answer makes sense. • Think about generalizations or simplifications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass m2 that is pulled up a frictionless plane inclined at angle 0 with respect to the horizontal by a massless string that passes over a massless, frictionless pulley to a block of mass m₁ that is hanging vertically. (Figure 1) Part H Solve and check In the previous parts, you obtained the following equations using Newton's 2nd law and the constraint on the motion of the two blocks: m2a2x T-m2g sin(0), (1) = m1a1yTm1g, (2) a2x = -aly. (3) and Solve these equations to find aly. Before you enter your answer, make sure it satisfies the special cases you already identified: Figure block 2 block 1 1 of 2 > • aly -g if m2 = 0 and . aly = 0 if m1 = m2 and 0 = π/2. Also make sure that your answer has dimensions of acceleration. Express aly in terms of some or all of the variables m1, M2, 0, and g. ▸ View Available Hint(s) aly = Submit ΕΠΙ ΑΣΦ ?
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