Question
What is the force exerted by a spring?
Answers
GPT-4o mini
The force exerted by a spring is described by Hooke's Law, which states that the force exerted by a spring is proportional to the displacement (stretch or compression) of the spring from its equilibrium position. Mathematically, this can be expressed as:
\[ F = -kx \]
Where:
- \( F \) is the force exerted by the spring (in newtons, N),
- \( k \) is the spring constant (in newtons per meter, N/m), which measures the stiffness of the spring,
- \( x \) is the displacement from the equilibrium position (in meters, m),
- The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement (restoring force).
So, if \( x \) is positive (meaning the spring is stretched), the force is negative (pulling back towards the equilibrium position), and if \( x \) is negative (meaning the spring is compressed), the force is positive (pushing back towards equilibrium).
\[ F = -kx \]
Where:
- \( F \) is the force exerted by the spring (in newtons, N),
- \( k \) is the spring constant (in newtons per meter, N/m), which measures the stiffness of the spring,
- \( x \) is the displacement from the equilibrium position (in meters, m),
- The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement (restoring force).
So, if \( x \) is positive (meaning the spring is stretched), the force is negative (pulling back towards the equilibrium position), and if \( x \) is negative (meaning the spring is compressed), the force is positive (pushing back towards equilibrium).