How to Predict the New Length of a Spring Based on Hooke's Law
What is Hooke's Law and how can it be used to predict the new length of a spring?
Hooke's Law states that the force needed to extend or compress a spring by a certain distance is proportional to that distance. Based on this law, how can we predict the new length of a spring when a mass is attached to it?
Answer:
To predict the new length of a spring based on Hooke's Law, we need to use the formula: F = k * dx. Where F is the force applied to the spring, k is the spring constant, and dx is the change in length of the spring. By rearranging the formula, we can calculate the new length of the spring when a mass is attached to it.
Explanation:
Hooke's Law can be expressed in the formula F = k * dx, where F is the force applied to the spring, k is the spring constant in Newton per meter (N/m), and dx is the change in length of the spring.
When a mass is attached to the spring, we can calculate the new length of the spring using the formula mg = k * (L2 - L1). Where m is the mass, g is the acceleration due to gravity (9.8 m/s²), L2 is the new length of the spring, and L1 is the initial length of the spring.
By rearranging the formula, we can solve for the new length of the spring: L2 = (mg + k * L1) / k. Substituting the given values into the formula will allow us to predict the new length of the spring when a mass is attached to it.
Therefore, Hooke's Law can be used to accurately predict the new length of a spring when external forces are applied, making it a valuable tool in physics and engineering calculations.