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One end of a light spring with spring constant k₁ is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k₂. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: K₁, K₂, m, and g, the gravitational acceleration.) Xtotal = X Because the springs are light, you can treat them as essentially massless, so the only downward force acting on them is mg. Use |FI = kx to find the amount of stretch, x, for each spring, and then find the sum. (b) What is the effective spring constant of the spring system? (Use the following as necessary: k₁, k₂, m, and g, the gravitational acceleration.) Keff = X Use your result from part (a), and recast it into the form |F| = Keff* total. Solve for Keff (c) What If? Two identical light springs with spring constant k3 are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of k3. (Use the following as necessary: K3, M, the mass of the symmetric object, and g, the gravitational acceleration.) Keff =

One end of a light spring with spring constant k₁ is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k₂. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: K₁, K₂, m, and g, the gravitational acceleration.) Xtotal = X Because the springs are light, you can treat them as essentially massless, so the only downward force acting on them is mg. Use |FI = kx to find the amount of stretch, x, for each spring, and then find the sum. (b) What is the effective spring constant of the spring system? (Use the following as necessary: k₁, k₂, m, and g, the gravitational acceleration.) Keff = X Use your result from part (a), and recast it into the form |F| = Keff* total. Solve for Keff (c) What If? Two identical light springs with spring constant k3 are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of k3. (Use the following as necessary: K3, M, the mass of the symmetric object, and g, the gravitational acceleration.) Keff =

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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One end of a light spring with spring constant k₁ is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k₂. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: k₁, k₂, m, and g, the gravitational acceleration.) Xtotal = X Because the springs are light, you can treat them as essentially massless, so the only downward force acting on them is mg. Use |F| = kx to find the amount of stretch, x, for each spring, and then find the sum. (b) What is the effective spring constant of the spring system? (Use the following as necessary: K₁, K₂, m, and g, the gravitational acceleration.) Keff X Use your result from part (a), and recast it into the form |F| = Keff* total Solve for keff. = (c) What If? Two identical light springs with spring constant k3 are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of k3. (Use the following as necessary: K3, M, the mass of the symmetric object, and g, the gravitational acceleration.) Keff =
Transcribed Image Text:One end of a light spring with spring constant k₁ is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k₂. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: k₁, k₂, m, and g, the gravitational acceleration.) Xtotal = X Because the springs are light, you can treat them as essentially massless, so the only downward force acting on them is mg. Use |F| = kx to find the amount of stretch, x, for each spring, and then find the sum. (b) What is the effective spring constant of the spring system? (Use the following as necessary: K₁, K₂, m, and g, the gravitational acceleration.) Keff X Use your result from part (a), and recast it into the form |F| = Keff* total Solve for keff. = (c) What If? Two identical light springs with spring constant k3 are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of k3. (Use the following as necessary: K3, M, the mass of the symmetric object, and g, the gravitational acceleration.) Keff =
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