Highschool Diving board distortion problem

[Soccerface]

Homework Statement

A physics teacher (mass 80.0 kg) stands at the end of his 2.0 m long diving board. The distortion of the free end is 22.5 cm. when his noisy neighbor comes over and stands at the end he distorts it by 32.0 cm. what is the mass of the noisy neighbor?

Mass of teacher = 80.0 kg
Force = 780N
L = 2.0m
Distortion of Teacher = 22.5cm
Distortion of neighbour = 32.0cm
Mass of Neighbour = ?

Homework Equations

Cannot figure out equation.

The Attempt at a Solution

22.5cm / 80.0 kg = 0.28125 cm/kg
Diving board can handle 0.28125 cm/kg
So if neighbour distorts 32.0 cm
32.0cm / 0.28125cm/kg = 113.777777kg


Our teacher never gave us any equations or sample problems to go off of, so I'm just winging it, Please help!

 

[cepheid]

Welcome to PF Soccerface!

The only way I can think of to approach this problem is to assume the the board is springy i.e. it acts like a spring under bending, in the sense that the more you bend it downward, the harder it pushes up on you (trying to unbend). Maybe you are meant to assume that Hooke's law applies in this case, and therefore the force is proportional to the displacement, i.e. it's equal to some constant k, times the displacement? If so, you should be able to solve for k given the first pair of force and displacement, and that k will then allow you to solve for the second force given the second displacement.

 

[PhanthomJay]

In which case, your answer is correct. Force is proportional to displacement for materials that obey Hooke's law.