Question

the spring constant \k\ is measured in units of...
meters squared
it is unitless
newtons per meter
newtons
meters per second

Explanation:

Hooke's Law states \( F = kx \), where \( F \) is force (in Newtons, \( N \)), \( k \) is the spring constant, and \( x \) is displacement (in meters, \( m \)). Rearranging for \( k \) gives \( k=\frac{F}{x} \). Substituting units: \( k \) has units \( \frac{N}{m} \) (Newtons per meter).

• Meters Squared (\( m^{2} \)) is an area unit, not relevant.
• Spring constant is not unitless as it relates force and displacement.
• Newtons (\( N \)) is a force unit, not for \( k \).
• Meters per second (\( m/s \)) is a velocity unit, incorrect.

Answer:

Newtons per meter