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

Question

Suppose that 2 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 54 cm.

(a) How much work is needed to stretch the spring from 44 cm to 49 cm? (Round your answer to two decimal places.) in J

(b) How far beyond its natural length will a force of 25 N keep the spring stretched? (Round your answer one decimal place.) cm

Suppose that 2 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 54 cm (a) How much work is needed to stretch the spring from 44 cm to 49 cm? (Round your answer to two decimal places.) (b) How far beyond its natural length will a force of 25 N keep the spring stretched? (Round your answer one decimal place.) cm

Explanation / Answer

Length it was extended from natural length = 0.54 - 0.36 = 0.18 m

2 = 1/2 . k . 0.18^2

k = 4 / 0.18^2 = 123.456 N/m

Work to stretch 49 = 0.5 . 123.456 . 0.13^2 = 1.043 J

Work to stretch 44 = 0.5 . 123.456 . 0.8^2 = 0.395 J

Work to go from 44 to 49 = 1.43 - 0.395 = 0.65 J ----> Answer

b) F = k . x

x = 25 / 123.456 = 0.202 = 20.2 cm

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