A spring has a natural length of 30 cm. If a 24-N force is required to keep it stretched to a length of 40 cm, how much work W is required to stretch it from 30 cm to 35 cm? (Round your answer to two decimal places.)
W = J

If 0.6 J of work are needed to stretch a spring from 9 cm to 11 cm and 1 J are needed to stretch it from 11 cm to 13 cm, what is the natural length of the spring?

L = 7 cm

Step-by-step explanation:

Given,

natural length,L = 30 cm

Force to stretch the spring to 40 cm, F = 24 N

We know,

F = k Δ x

24 = k × (0.4 - 0.3)

0.1 k = 24

k = 240 N/m

now,

Work done calculation to stretch it from 30 cm to 35 cm

 W = 0.3 J

b) Work done to stretch from 9 cm to 11 cm

   W = 0.6 J

Let L be the natural length

.........(1)

When spring is stretched from 11 cm to 13 cm

   W = 1 J

......(2)

Form equation (1) and (2)

on solving

L = 7 cm

Hence, the natural length of the spring is equal to 7 cm.

x = 23.78

step-by-step explanation: