Hooke's law is described mathematically using the formula F_sp=-kx. Which statement is correct about the spring force, F_sp
it is the force that displaces the spring
it is a vector quantity
it is larger than the applied force
it is always a positive force
The correct statement about the spring force, F_sp, is: it is the force that displaces the spring.
The correct statement about the spring force, F_sp, is that it is always a positive force.
The correct statement about the spring force, F_sp, is that it is the force that displaces the spring.
To explain how to arrive at this answer, let's break down Hooke's law and analyze the variables in the formula F_sp = -kx:
- F_sp represents the spring force, which is the force exerted by the spring when it is stretched or compressed.
- -kx indicates that the spring force is proportional to the displacement, x, of the spring from its equilibrium position. The negative sign represents the direction of the force, which opposes the displacement.
Now, let's examine the given options:
1. "It is the force that displaces the spring" - This statement is correct because the spring force is indeed the force that causes the spring to be displaced from its equilibrium position. When a spring is stretched or compressed, it exerts a force to restore itself to its original state.
2. "It is a vector quantity" - This statement is incorrect. The spring force is not a vector quantity as it does not have a specific direction associated with it. It is only dependent on the magnitude and the displacement of the spring.
3. "It is larger than the applied force" - This statement might be true or false depending on the specific scenario. The magnitude of the spring force can be greater or smaller than the applied force, depending on factors such as the stiffness of the spring (represented by the constant k) and the amount of displacement (x).
4. "It is always a positive force" - This statement is false. The spring force can be positive or negative depending on the direction of the displacement. If the spring is stretched (positive displacement), the spring force will be in the opposite direction (negative) to restore the spring to equilibrium. If the spring is compressed (negative displacement), the spring force will be in the opposite direction (positive) to bring the spring back to its equilibrium.
Therefore, by the process of elimination and understanding the concept of Hooke's law, we can conclude that the correct statement is: "It is the force that displaces the spring."