Suppose that 6 J of work is needed to stretch a spring from its natural length o

Question

Suppose that 6 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 44 cm.
(a) How much work is needed to stretch the spring from 37 cm to 39 cm? (Round your answer to two decimal places.)
b)(b) How far beyond its natural length will a force of 50 N keep the spring stretched? (Round your answer one decimal place.)

Explanation / Answer

work done = 1/2 * K * x^2 were x is change in length , here 6 = k/2 * 144 * 10^-4 => K =10^4/12 work needed for stretching 37 to 39 => 1/2 * 10^4/12 * [(39-32)^2 - (37-32)^2]* 10^-4 = 12/12= 1J Force = K* x where x is elongation, = 50 = 10^4/12 * x = 6 cm => Length of spring = 38 for elongation or 26 cm for compression

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