Two light springs and have force constants and respectively

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two light springs

S_{1}

and

S_{2}

have force constants

k

and

2k

respectively. (a) The springs are compressed by distances

x

(for

S_{1}

) and

y

(for

S_{2}

) such that the elastic potential energies stored in them are equal. Derive the relation between

x

and

y

. (b) If

y = 4.0\,\text{cm}

, calculate the corresponding value of

x

. (c) The first spring

S_{1}

is now further compressed to a distance

1.5x

. Find the ratio of the new energy stored in

S_{1}

to the energy originally stored in

S_{2}

(which remained at compression

y

). Show all the steps in your calculation.