Suppose that 2 ? of work is needed to stretch a spring from its natural length o

Question

Suppose that 2 ? of work is needed to stretch a spring from its natural length of 24 cm to a length of 35 cm. (a) How much work is needed to stretch the spring from 29 cm to 33 cm? (Round your answer to two decimal places.) cm 64.015. A cable that weighs 4 Ib/ft is used to lift 650 tb of coal up a mine shaft 450 ft deep. Find the work done. to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter x as ) lim Ax Express the work as an integral and evaluate. 450 4r Need Help? chTlkto a Tuter MacBook Air

Explanation / Answer

a)

Initial length = natural length = 24 cm = 0.24m

Final length = 35 cm = 0.35 cm

Stretched = 0.35m - 0.24m = 0.11m

Work Done = 1/2 * k * x^2 = 2

k * (0.11)^2 = 4

k = 4/(0.11)^2 = 330.57

Work Done = 1/2 * k * (x2^2 - x1^2) = 1/2 * 330.57 * (0.08^2 - 0.05^2) = 0.64J

b)

25= 330.57 * x

x = 25/330.57 = 0.075m = 7.5 cm

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