Question

multiple choice question
which best describes the reason for the negative sign in hookes law, $f = -kx$.

• the force is in a direction that will always be opposite to the force of gravity.
• the force is in the direction opposite to the stretch or compression direction.
• all spring forces are negative.
• the value of $k$ is always negative, so a negative sign is needed for the force to be a positive value.

Explanation:

Hooke's law \( F = -kx \) describes the restoring force of a spring. The negative sign indicates the force is opposite to the displacement (stretch or compression direction). The first option is wrong as spring force isn't always opposite to gravity. The third is incorrect (spring force direction determines sign, not all are negative). The fourth is wrong as \( k \) (spring constant) is positive for most springs. So the correct reason is the force opposes stretch/compression.

Answer:

The force is in the direction opposite to the stretch or compression direction.