Use Hooke's law equation to answer the question F_sp =-kx
WHat happens to the displacement vector x when the spring constant k has a higher value and the applied force F_sp remains constant
it remains the same
it changes its direction
it decreases in magnitude
it increases in magitude
The displacement vector x decreases in magnitude when the spring constant k has a higher value and the applied force F_sp remains constant.
When the spring constant (k) has a higher value and the applied force (F_sp) remains constant, the displacement vector (x) will decrease in magnitude. In other words, the amount the spring is stretched or compressed will be smaller when the spring constant is higher. Therefore, the correct answer is "it decreases in magnitude."
To determine the effect of a higher spring constant (k) on the displacement vector (x), we can use Hooke's Law equation, F_sp = -kx. Here, F_sp represents the applied force, k is the spring constant, and x is the displacement vector.
When the spring constant (k) has a higher value and the applied force (F_sp) remains constant, we can rearrange Hooke's Law equation to solve for x: x = -F_sp / k.
In this case, since the applied force remains constant, the change in displacement will solely depend on the spring constant. As the spring constant value increases, the displacement magnitude will decrease.
Therefore, the correct answer is: "it decreases in magnitude."