Answer
The restoring force is $3F$ when the spring is stretched to a length of 13 cm.
The restoring force is $2F$ when the spring is compressed to a length of 8 cm.
Work Step by Step
The magnitude of a spring's restoring force is $F = kx$, where $x$ is the length that the spring is stretched or compressed. The problem statement tells us that the restoring force is $F$ when $x = 1~cm$. That is: $F = k~(1~cm)$
(a) We can find the distance the spring is stretched when the restoring force is $3F$.
$3F = 3\times k~(1~cm)$
$3F = k~(3~cm)$
The restoring force is $3F$ when the spring is stretched 3 cm. That is, the restoring force is $3F$ when the spring is stretched to a length of 13 cm.
(b) We can find the distance the spring is compressed when the restoring force is $2F$.
$2F = 2\times k~(1~cm)$
$2F = k~(2~cm)$
The restoring force is $2F$ when the spring is compressed 2 cm. That is, the restoring force is $2F$ when the spring is compressed to a length of 8 cm.
