$$ \newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor} \newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil} \renewcommand{\mod}{\,\mathrm{mod}\,} \renewcommand{\div}{\,\mathrm{div}\,} \newcommand{\metar}{\,\mathrm{m}} \newcommand{\cm}{\,\mathrm{cm}} \newcommand{\dm}{\,\mathrm{dm}} \newcommand{\litar}{\,\mathrm{l}} \newcommand{\km}{\,\mathrm{km}} \newcommand{\s}{\,\mathrm{s}} \newcommand{\h}{\,\mathrm{h}} \newcommand{\minut}{\,\mathrm{min}} \newcommand{\kmh}{\,\mathrm{\frac{km}{h}}} \newcommand{\ms}{\,\mathrm{\frac{m}{s}}} \newcommand{\mss}{\,\mathrm{\frac{m}{s^2}}} \newcommand{\mmin}{\,\mathrm{\frac{m}{min}}} \newcommand{\smin}{\,\mathrm{\frac{s}{min}}} $$

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Monocycle robot

../_images/monocycle-background.png ../_images/monocycle-robot&Wheel.png ../_images/monocycle-robotWheelBox.png

Introduction

The main task of the monocycle robot is to make package deliveries. Every day it traverses the same hills multiple times to acomplish its task. Some of the hills are quite steep and are not so easy to climb. Bellow, you can run the program to see how the robot moves without any package. Can you help our robot figure out what is the maximum mass of the load it can carry and manage to climb all of the hills on its road? By knowing this, the robot will group multiple packages and reduce number of trips accross the hills.

To help you solve the main task, lets warm up first with a few simpler problems.

Moving at a constant velocity

The robot is moving with a constant velocity of 7.2km/h. What is the distance the robot moves in 30 seconds?

Force and acceleration

The robot is moving on a flat surface. Forces acting on the robot are the pull force of its motor and friction force between the robot wheel and the ground. Pull force is equal to \(F_m = 150N\). Mass of the robot is \(m = 50kg\). Friction coefficient is \(\mu = 0.2\). What is the acceleration of the robot?

Decomposition of forces

The robot is moving on the ground which is inclined. The inclination of the ground is \(\alpha = 10 degrees\). Mass of the robot is \(50kg\). Gravitational acceleration is \(9.81m/s^2\). Pull force of the engine is equal to 100N. Friction coefficient is \(\mu = 0.15\). Determine the force acting on the robot in the direction parallel to the ground.

Max package mass

To help the robot figure out what is the maximum package mass it can carry accross the hill, first you need to implement the physics laws governing the robot motion. Then you can run the simulation multiple times with different package mass to come to the needed answer.