Final answer:
The function rule that models the length of the spring based on the mass of the object in the pan is l(w) = 1633.33w, where w is the mass in kilograms.
Step-by-step explanation:
To find a function rule that models the length of the spring based on the mass of the object in the pan, we can use Hooke's law. Hooke's law states that the force exerted by a spring is directly proportional to the amount the spring is stretched or compressed. The formula for Hooke's law is F = kx, where F is the force exerted by the spring, k is the force constant, and x is the displacement of the spring from its equilibrium position.
In this case, we are given that a 10 kg mass stretches the spring 6 cm. We can use this information to find the force constant. First, we need to convert the displacement to meters: 6 cm = 0.06 m. Then we can rearrange Hooke's law to solve for k: k = F/x. Plugging in the values, we get k = (10 kg * 9.8 m/s^2) / 0.06 m = 1633.33 N/m.
Therefore, the function rule l(w) that models the length of the spring based on the mass of the object in the pan is l(w) = 1633.33w, where w is the mass in kilograms.