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 \( F = -kx \) has a negative sign because the spring force (restoring force) acts opposite to the displacement (stretch or compression direction). Let's analyze each option:

• Option 1: The spring force opposes displacement, not necessarily gravity. Eliminate.
• Option 2: This matches the restoring force concept (opposite to stretch/compression). Correct.
• Option 3: Spring forces can be positive or negative based on direction; the negative sign is about restoring, not all forces being negative. Eliminate.
• Option 4: \( k \) (spring constant) is positive (it's a magnitude of stiffness), the negative sign is for direction of force relative to displacement, not to make force positive. Eliminate.

Answer:

The force is in the direction opposite to the stretch or compression direction. (The third option in the list, i.e., the option with text "The force is in the direction opposite to the stretch or compression direction.")