Essential University Physics
Essential University Physics
4th Edition
ISBN: 9780134988559
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 4, Problem 64P

Two springs have the same unstretched length but different spring constants, k1 and k2. (a) If they’re connected side by side and stretched a distance x, as shown in Fig. 4.25a, show that the force exerted by the combination is (k1 + k2)x. (b) If they’re connected end to end (Fig. 4.25b) and the combination is stretched a distance show that they exert a force k1k2x/(k1 + k2).

Chapter 4, Problem 64P, Two springs have the same unstretched length but different spring constants, k1 and k2. (a) If

FIGURE 42.5 Problem 62

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One end of a light spring with spring constant k, is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k,. 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: k,, k,, m, and g, the gravitational acceleration.) Xtotal = (b) What is the effective spring constant of the spring system? (Use the following as necessary: k,, k,, m, and g, the gravitational acceleration.) keff = (c) What If? Two identical light springs with spring constant k, 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 k2. (Use the following as necessary: ka, M, the mass of the…
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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,…

Chapter 4 Solutions

Essential University Physics

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