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.)

(a) The work done is 0.05 J

(b) The  force will stretch the spring by 3.8 cm

Explanation:

Given;

work done in stretching the spring from 30 cm to 45 cm, W = 3 J

extension of the spring, x = 45 cm - 30 cm = 15 cm = 0.15 m

The work done is given by;

W = ¹/₂kx²

where;

k is the force constant of the spring

k = 2W / x²

k = (2 x 3) / (0.15)²

k = 266.67 N/m

(a) the extension of the spring, x = 37 cm - 35 cm = 2 cm = 0.02 m

work done is given by;

W = ¹/₂kx²

W = ¹/₂ (266.67)(0.02)²

W = 0.05 J

(b) force = 10 N

natural length L = 30 cm

F = kx

x = F / k

x = 10 / 266.67

x = 0.0375 m

x = 3.75 cm = 3.8 cm

Thus a force of 10 N will stretch the spring by 3.8 cm