g uppose that 3 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 45 cm. (a) How much work is needed to stretch the spring from 35 cm to 37 cm? (Round your answer to two decimal places.) .02 Incorrect: Your answer is incorrect. J (b) How far beyond its natural length will a force of 10 N keep the spring stretched? (Round your answer one decimal place.)

W= 0.319992 J  and distance is 3.75 cm

Explanation:

The energy needed to stretch the spring from 30 cm to 45 cm = 3 J

Now we required to find the requirement of energy when the spring is stretched from 35 cm to 37 cm.

So first find the work done to stretch the spring from 35 cm to 45 cm.

Work done, w = (1/2) kx^2

3 = (1/2)k(0.45 – 0.30)^2

k = 266.66 N/m

now, x1 = 0.35 – 0.30 = 0.05m

x2 = 0.37 – 0.30 = 0.07m

Now the amount of work done to stretch from 35cm to 37.

w = (1/2) k (x2^2 – x1^2)

w = (1/2) (266.66) (0.07^2 – 0.05^2 )

w= 0.319992 J

(b). Given F = 10 N

F = kx

x = F / k

x = 10 / 266.66

x = 0.0375m

x = 3.75 cm

Thus, distance is 3.75cm