Pengantar Biomekanikadinus.ac.id/repository/docs/ajar/Pengantar_Biomekanika_Bio... · gaya dan percepatan sudut, dan beberapa besaran lain 𝐼= ... Hidrodinamika Laminer ... 𝜂=

Pengantar BiomekanikaDita Ayu Mayasari, ST., M.Biotech

Biomedical Engineering

Univ. Dian Nuswantoro

Dasar-Dasar Biomekanika

What is Biomechanics?

Applies mechanical principles to the human body in order to understand the

mechanical influences on bone and joint health

(Kelleys and Firestein’s Textbook of Rheumatology 10th Ed, 2017)

Why should we learn about

biomechanics?

Biomechanics

Ergonomic Utility

Medical Rehabilitation

Forensic

Sports

Why should we learn about

biomechanics?

Elements of Biomechanics

Statics: Studying systems that are in equilibrium, either at rest or moving at a

constant velocity.

Dynamics: Studying systems that are in motion with acceleration and

deceleration.

Kinetics: Studying what causes motion, the forces and moments at work.

Kinematics: Describing the effect of forces on a system, motion patterns

including linear and angular changes in velocity over time. Position,

displacement, velocity, and acceleration are studied.

Biomechanical Principles

Basic biomechanics relies heavily on Newtonian mechanics

Newton’s First Law – Law of Inertia

Objects tend to resist changes in their state of motion.

Newton’s Second Law – Law of Acceleration

Links the kinematics of a body to its kinetics

Newton’s Third law – Law of Reaction

There is an equal and opposite reaction force for every action (force)

Force

Gravitation

Spring

R2=

GMFg

m

Fs = kx

FN

Ff = Fc

Normal

Friction

Vector

Has magnitude and direction

Vectors are similarly represented in three dimensions in terms of their i, j,

and k components

A set of forces may be combined into an equivalent force denoted the

resultant R

Vector multiplication consists of two distinct operations: the dot and cross

products

|A x B|= AB sin A ∙ B = AB cos

Penjumlahan & Pengurangan Vektor

Torque

Forces describe changes in linear motion – which means changes in velocities,

while torques describe how these same forces can change angular motion –

which means changes in angular velocities

τ = r × F

Momen Inersia

ukuran kelembaman suatu benda untuk berotasi terhadap porosnya

analog rotasi daripada massa

berperan dalam dinamika rotasi seperti massa dalam dinamika dasar, dan

menentukan hubungan antara momentum sudut dan kecepatan sudut, momen

gaya dan percepatan sudut, dan beberapa besaran lain

𝐼 = 𝑚

𝑟2 𝑑𝑚

Static Equilibrium

∑F = 0

∑M = 0

Contoh Masalah :

Diketahui:

Seseorang dengan berat 160 lb

menahan beban bola 10 lb dengan

siku menekuk 90 derajat

Hitung:

Gaya yang harus dihasilkan oleh

otot bisep (Fb)

Jawab:

Biotransportasi

Mekanika Fluida

Zat Alir cairan, gas

Fluida statis & dinamis

Hidrostatika

TEKANAN HIDROSTATIKA

dF

Pm = P0 + ρgh

𝑃 =𝑑𝐹

𝑑𝐴

m

h

po

Tekanan terukur

P = P0 + ρgh

P – P0 = ρgh

misal h = 80 mm, berarti tekanan gas dlm tabung 80 mmHg

Hukum Archimedes

Sebuah benda bila berada dalam zat cair akan mendapat gaya ke atas (B)

sebesar berat zat cair yang dipindahkan

F2 – F1 = B = ρzat cair g vbenda

F1

F2

Hidrodinamika

Laminer : memiliki garis arus sendiri-sendiri kerapatan dan kompresibilitas

sama

Turbulen : garis arusnya saling berpotongan dan kerapatannya tidak merata

Bilangan Reynold

𝑅 =𝜌𝑣𝐷

𝜂

V = kecepatan aliran

D = diameter pipa

𝜂 = koefisien viskositas

bila R < 2000 aliran laminer

R > 3000 aliran turbulen

Persamaan kontinuitas

volume zat cair yang mengalir perdetik di setiap titik adalah sama

Q1 = Q2 = Q3 …

A1V1 = A2V2 = A3V3 …

A : luas penampang pipa

V : kecepatan aliran

Persamaan Bernuolli

Latihan Soal

1. Seorang anak (ρ=0,98 g/cm2) berada dalam keadaan terapung dengan

sebagian tubuhnya berada dalam kolam. Berapa bagian tubuh yang berada di

dalam air?

2. Sebuah bola ditengahnyan berongga , rdalam=10 cm dan rrongga =8cm. Bila

berada dalam keadaan melayang dalam air maka tentukan massa jenis bola

tersebut.

Diketahui:

Seseorang dengan berat 150 lb

(berat kaki 0.061 dari berat total

tubuh)

Hitung:

W?