Homework_2_Solutions

# Homework_2_Solutions - 14:125:308 Introduction to Biomechanics Homework Assignment#2 Problem 1(Center of Gravity and Coordinate Transform NOTE:This

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14:125:308: Introduction to Biomechanics Spring 2007 Homework Assignment #2 Due 2/06/07 Problem 1: (Center of Gravity and Coordinate Transform) NOTE:This is an old exam question You are preparing to run some tests on cadaveric femur bones with a stainless steel bone plate attached, and you need to find the center of mass of the bone plate/bone composite in the x-y plane. If you assume that the bone can be approximated as a small, hollow ellipse (representing the medullary canal) and a bigger ellipse (representing cortical bone), and that the bone and plate are uniform and identical in thickness into the page, and you are given the information below, find : A) the center of mass of bone plate/bone composite in the original (unprimed) coordinate frame AND B) the location of the center of mass in the translated, rotated, primed frame, where the origin is (7,2.5) relative to original frame and rotated as indicated. . Some useful information Bone density: 1.3 g/cm 3 Marrow density: 0 g/cm 3 (the marrow is removed prior to testing) Stainless steel density: 7.5 g/cm3 Area of outer ellipse: 8.0 cm2 Area of inner ellipse: 1.6 cm2 Area of bone plate: 0.9 cm2 Center of outer ellipse (cm) (x,y): (0,0) Center of inner ellipse (cm) (x,y): (0.2, -0.4) Center of bone plate (cm) (x,y): (-1.6, 0) Note: Schematic not to scale x y x' y' 40 ° (7cm,2.5cm) x y

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14:125:308: Introduction to Biomechanics Spring 2007 Homework Assignment #2 Due 2/06/07 A) In order to find the center of mass of the bone plate/bone system we need to find the center of mass of the bone (The center of mass of the plate is given). We first have to Mass of the bone ( ) ( ) kg t t cm cm t cm g A A t M e innerelips e outerelips bone bone 32 . 8 4 . 6 3 . 1 6 . 1 0 . 8 / 3 . 1 2 2 3 = = = = ρ Now the COM of the bone is ( ) ( ) () cm COM cm t t M A Y A Y t Y cm t t M A X A X t X bone bone relipse Centerinne relipse Centerinne relipse Centeroute relipse Centeroute bone COMbone bone relipse Centerinne relipse Centerinne relipse Centeroute relipse Centeroute bone COMbone ) 10 . 0 , 05 . 0 ( 10 . 0
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## This note was uploaded on 01/31/2012 for the course BIOMEDICAL 208 taught by Professor Zhann during the Spring '11 term at Rutgers.

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Homework_2_Solutions - 14:125:308 Introduction to Biomechanics Homework Assignment#2 Problem 1(Center of Gravity and Coordinate Transform NOTE:This

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