Lab Report - 3D Equilibrium Engineering Dynamics, Lab Reports of Dynamics

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National University of Sciences and Technology (NUST)

SMME

Lab Report

THREE DIMENSIONAL EQUILIBRIUM

COURSE : Mechanics Lab

SUBMITTED B Y : Altaf Ahmad (250282)

SECTION : ME-10 A

3D Equilibrium

Objective:

The purpose of the experiment is to study the equilibrium conditions of five forces in 3d.

Apparatus:

The apparatus consists of a cube shaped frame having angled sections and rods which are vertically placed. It also consists of two mirrors placed on one adjacent pair of the box while two transparent sheets of plastic with centimeter markings on the other pair of sides. The mirrors and the grids can be aligned with each other on right angles at vertical sides. The vertical rods extend below the cube as 4 levelling feet. At the top four corners of the box, there are swiveling pulleys on which cords are placed which in turn support hanger and a vertical cord.

Totally there are 5 cords and all of them carry two beads set 100 mm apart from one another. The set of five cords is arranged concurrent to the space.

Theory:

The apparatus can be arranged in three dimensional as required i.e. Concurrent or non- Concurrent.

For a body being in a 3d space:

ΣF = 0 and ΣM = 0

In a totally balanced 3d system, the forces along any axis must equal zero.

ΣF (^) x = 0 ΣF (^) y = 0 ΣF (^) z = 0

Procedure:

1. Place the 4 longer cords of the 5 cords assembly over the given four pulleys which are at the top corners of the box. Now attach hangers to the ends of these cords, which makes the 5th^ cord to hang in the middle of the box, in such a way that all the marker beards present on the cords are within the limits of both graphic grids.
2. Make sure that the pulleys are in the same plane as the cords. Make them swivel in the housing until they are positioned in the best equilibrium position.
3. Choose one cord and note down the total weight attached to it with the color of the beads.