SM1 Physics Practical Solids Mechanics Statics 12 13

7/26/2019 SM1 Physics Practical Solids Mechanics Statics 12 13

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Solid mechanics: Statics and dynamics 1-1

Practical 1 SOLID MECHANICS:

STATICS AND DYNAMICS

Foreword

This practical work in an open one. The text below describes the experiments that have to be

performed. Since the duration is limited to 4 hours, they have to be performed before the time

is elapsed. If you have some time left, it is up to you to imagine additional exeri!ent"with

the material at hand.

The material at hand has purposely been chosen to be rudimentary. Thus the measurements

will not be very precise and for each measurement you should estimate the uncertainty

(uncertainty rea"ona#leupper limit of the measurement error!.

I$ INT%OD&CTION

The field of mechanics describes bodies that are at rest (statics! or moving (dynamics!.This

practical work uses simple experiments to illustrate the mechanics course. "or an efficient

preparation for this practical work you are recommended to review the fundamentals of the

mechanics course.

II$ MODELIN'

To model a physical phenomenon, you are recommended to start with the simplest description

before making it more complex (if necessary!. "or example, in your first approximation, themass of certain ob#ects may be neglected. It is only if the difference between the calculated

results and the experiment is too large that the other masses are taken into account.

III$ P%O(LEM 1

III$1$ T)e "teel*ard

On a market the goods are weighed with a steelyard (also known as steelyard balance or

roman balance1) (seeFigure 1). It is hangs from a hook (A) and the mass M is moved along

the beam until the latter reaches a horiontal !osition.

$hat is the working principle of the steelyard% &oes the measurement depend on the gravity

field%

'The roman balance that consists of a straightbeambalancewith arms of une)ual length, is

older than the roman empire. In *rabic it is called +roummana literally after the pomegranate,because of the mobile mass that can be translated along the beam. It is a straightbeam

balancewith arms of une)ual length.
http://en.wikipedia.org/wiki/Weighing_scalehttp://en.wikipedia.org/wiki/Weighing_scalehttp://en.wikipedia.org/wiki/Weighing_scalehttp://en.wikipedia.org/wiki/Weighing_scale


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"igure ' Steelyard.

III$+$ Exeri!ent: !ea",re!ent o- a #od*." !a"" /

* magnetic board with holes enables various elements to be attached

The body - that represents the unknown mass it is a cylindrical steel tube with

density /.0 g1cm23

* beam with holes that can be mounted on an axis3

* set of bodies (each of known mass! with a total mass less than the unknown mass.

'. easure the unknown mass - with a setup similar to the steelyard. $hat is the

uncertainty on the measurement%

5. $hat are the conditions to achieve the most precise measurement%

2. 6se a vernier caliper to measure the dimensions of the unknown mass - (see

chapters 4.' and 4.5 of the 7methods8 textbook!. &educe its mass from its volume

and density.4. &o the uncertainty domains overlap% If not, identify the causes and if possible try

to improve your results.

I0$ P%O(LEM +

I0$1$ Deice to 2ee a #ea! )ori3ontal

A beam A" can rotate freely around an a#is O##9 . In order to kee! this beam horiontal

when a mass M is attached at !oint " with a string (rigid and of negligible mass)$ a s!ring is

attached between the other end A of the slab and a fi#ed !oint % (Figure &).

'he settings are the following

%istance OA a$ distance O" b (with b*a)+

'he s!ring has a length l,when unloaded and a s!ring constant k+

'he direction (%A) builds an angle with the u!right direction.

$hat is the expression of the spring constant k%


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"igure 5 Sketch of the experimental setup.

I0$+$ Exeri!ent"

I0$+$1$ 1"treli!inar* "t,d*: !ea",re!ent o- t)e "rin4 con"tant #* !ean"o- a "tatic exeri!ent

:eminder a spring with a spring constant k generates a restoring force ' proportional to its

elongation

( );llk'' ==

*ttach different bodies of known mass to the spring held in vertical position (the other end of

the spring being attached to a fixed point!.


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Compare the values and uncertainties obtained by the 2 methods and draw conclusions

from them.

0$ P%O(LEM 5

0$1$ 6inc) and cran2 7e8,ili#ri,! o- a !ec)anical deice t)at li-t"wei4)t" erticall*9

* winch is made of a cylinder of radius : (free to rotate around an axis O9 ! on which a

crank of mass is welded. The crank is e)uivalent to a straight and inextensible rod A* of

length D. Its mass can be neglected. * flexible inextensible string of negligible mass is

attached and wound on the cylinder. The other end of the string carries a body of mass that

is sub#ect only to vertical displacements. *nother mass is fixed at point *. *ny friction can

be neglected ("ig. 2!.

"igure 2 Schematic view of a winch and crankbased mechanical device.

'. &etermine the positions of e)uilibrium of the system by giving the values of the angle E

that makes the crank A* with respect to the direction O9 .

5. Examine the existence and the stability of these positions depending on the values for

and . The values of D and : have to be determined experimentally.

*ssuming that the mass of the winchs cylinder can be neglected, what is the period of the

oscillations around the e)uilibrium position%

0$+$ Exeri!ent

6se the premounted assembly schematically shown in "igure 2.

'. &etermine experimentally the threshold mass Mfrom which on it is possible to observe

e)uilibrium for a given value of .

5.


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-Eclose to ; (approximately ';>!

-Eclose to G;> (approximately 0;>!

Explain where the difference comes from.

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SM1 Physics Practical Solids Mechanics Statics 12 13