Question

A pan hangs from a 50 cm spring. When a 10 kg mass is placed in the pan, it stretches the spring 6 cm. What is a function rule l(w) that models the length of the spring based on the mass of the object in the pan?

Answer 1

Answer:

Explanation:

A Spring stretches / compresses when force is applied on them and they are governed by the Hookes Law which states that the force required to stretch or compress a spring is directly proportional to the distance it is stretched.

$F = -kx$

F is the force applied and x is the elongation of the spring

k is the spring constant.

negative sign indicates the change in direction from equilibrium position.

In the given question, we dont have force but we know that the pan is hanging. We also know from the Newton's second law of motion that

$F=mg$

Inserting this into Hooke's Law

$mg=-kx$

computing it for x,

$-x=mg/k$

This is the model which will tell the length of the spring against change in the mass located in the pan.