Question

The distance d that a spring stretches varies directly as the weight w on the spring. A weight of 100 Ib stretches the spring six inches. How far will a weight of 75 lb stretch a spring?

          The distance d that a spring stretches varies directly as the weight w on the spring. A weight of 100 Ib stretches the spring six inches. How far will a weight of 75 lb stretch a spring?
        

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The distance d that a spring stretches varies directly as the weight w on the spring. A weight of 100 Ib stretches the spring six inches. How far will a weight of 75 lb stretch a spring?
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Transcript

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00:02 In this problem, we're given a coiled spring that is stretched 40 centimeters by a 5 -newton force.
00:09 And in the first part, we're asked how much is it stretched by a weight that is 15 newtons.
00:18 So first, let's calculate the spring constant of the spring.
00:22 So hook's law states that f is equal to k times x.
00:33 Now to solve for k, we can just substitute in our values for f, that is 5 newtons, and for x, that is 40 centimeters, and that gives k is equal to 1 by 8.
00:57 Now, that gives f equals 1 by 8x, and we're given our required force to be 15, and that gives our extension as 15 times 8, and that results in our extension being equal to 120 centimeters...
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