Question

Dont understand how to do this problem, please help

If 6J of work is needed to strech a spring from 10cm to 12cm and another 10 J is needed to strech it from 12 cm to 14cm, what is the natural length of the spring?

Answer 1

potentai energy = 0.5*k*dx^2

at 10 cm U1 = 0.5*k*(0.1-a)^2

at 12 cm   U2 = 0.5*k*(0.12-a)^2

at 14 cm    U3 = 0.5*k*(0.14-a)^2

work done from 10 cm to 12 cm

U2 - U1 = 6

0.5*k*( (0.12-a)^2 - (0.1-a)^2 ) = 6.....(1)

work done fron 12 to 14 cm

U3 - U2 = 10

0.5*k*( (0.14-a)^2 - (0.12-a)^2 ) = 10........(2)

solving 1 & 2

original length = a = 0.08 m = 8 cm <<<---answer