# Trampoline Park

## Introduction

In this course you will learn how different disciplines are needed to build and maintain a trampoline park.

## Forces

### Gravity

Gravity is a mutually force that attracts two objects with a certain mass. Gravity is discovered by Isaac Newton, by having observed how an apple fell from a tree, he found that the power of the gravity of the earth is strong enough to attract us all towards it. Gravity is often found in many situations, for example a trampoline. The suspension level is always connected to the level of hight that the trampoline can bring you at and to make sure the trampoline is in a safe distance from the ground beneath. The level of gravity also depends on the level of mass that includes a certain object. Gravity is always present, no matter how far in space you go. There is always, somewhere in the distance, a certain force that attracts other objects and beings. There is always a force from some planet or star. The level of gravity that a certain objects has, can be calculated by the two masses of the objects that attract each other and the distance between them.

Newton's gravitational law is

${\displaystyle F=G\cdot {\frac {m_{1}\cdot m_{2}}{r^{2}}}}$

where

• F is the gravity between two objects in Newton
• m1 the mass of the first object (in kg)
• m2 the mass of the second object (in kg)
• r the distance between the centers of gravity of those objects (in meters)
• G the gravity constant = (6,67428 ± 0,00067) × 10-11 Nm2 kg-2.

An example is the gravity between a person of 40 kg and 100 kg with the distances between their centers of gravity of 1 meter.

${\displaystyle F=6,7\cdot 10^{-11}\cdot {\frac {Nm^{2}}{kg^{2}}}\cdot {\frac {40kg\cdot 100kg}{1m^{2}}}=2,7\cdot 10^{-7}N}$

For the gravity the earth exerts on a person where ${\displaystyle a=acceleration}$

${\displaystyle F=m_{person}\cdot a_{earth}=G\cdot {\frac {m_{person}\cdot m_{earth}}{r_{earth}^{2}}}=m_{person}\cdot G\cdot {\frac {m_{earth}}{r_{earth}^{2}}}}$

so ${\displaystyle a_{earth}}$ which we abbreviate to ${\displaystyle g}$ obvious equals to

${\displaystyle g=G\cdot {\frac {m_{earth}}{r_{earth}^{2}}}=6,7\cdot 10^{-11}\cdot {\frac {N\cdot m^{2}}{kg^{2}}}\cdot {\frac {6\cdot 10^{24}kg}{6.371.000^{2}m^{2}}}=6,7\cdot 10^{-11}\cdot {\frac {{\frac {kg\cdot m}{s^{2}}}\cdot m^{2}}{kg^{2}}}\cdot {\frac {6\cdot 10^{24}kg}{4.1\cdot 10^{13}m^{2}}}\approx 9.81m/s^{2}}$

### Spring Force

Simple harmonic oscillator

The Spring Force is a mechanical forse that occurs is pushed in or pulled out to resist to that motion. This force in a trampoline can occur in the springs attached to the canvas (pullspring) and in the canvas (leaf spring) it self. The spring constant can be calculated by dividing the applied force by the extension of the spring. A good spring extends a lot but does not distort. The energy it stores will than be returned to the jumper as much as possible. Hooke discovered that as long a a string is not distorded the spring force equals the spring constant times the extension. In the picture below the spring has been stretched beyond the elasticity limit.