MTH404 Assignment 1

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Questionl:

A particle ofmass m moves undertheforceF inxy -planesuchthatat any timet itspolar

coordinates(r, 0)aregivenby (t,t'). Findthetransverse componentofforce.

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Solution:

Tofindthetransverse componentoftheforceF actingon theparticle moving inthexy -plane

we startwiththegivenpolarcoordinates(r, 0)

r(t)=t

r(0)= 2

componentoftheforceisrelated totheangularcomponentofthemotion. First we

needtoexpressthevelocity andacceleration

Velocity

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Q2. A forceof(4+ 5)N actsonaparticle

whichdisplaces theparticle withthevelocity(2i+ 7j)

Findthepowerappliedon theparticle.

Solution:

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Tofindthepowerappliedon theparticle we usetheformula:

Power = ForceVelocity

= F.S

P= Åi

First expresstheforceandvelocity vectorsintermsoftheircomponents:

Givenforce=(41+ 5/)N

Givenvelocity = 21 + 7)

Now letcalculate thedotproductoftheforceand velocity vectors:

F.i=(4 · + 5)(21+7j) · Fi=(2t. · 48 + 5j.7)

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Determine whethertheforcefieldF= (xyz)i+ 2yz+ y'k isconservative or not?

Solution:

TodeterminewhethertheforcefieldF = (x²y-z)i + 2yzj+ yk isconservative ornotwe can

useatheoremfromvectorcalculus: A vectorfieldF isconservative ifandonlyifitscurlV XFis

thezerovector

So letcalculate thecurlof F

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Ix²y-z 2yz y'l|

Expanding thisdeterminant:

vx-()-(

Oy

VXF= (o)t+j+ x²k

Sincethecurl of F isnotthezerovectorie.V X F*#0theforcefieldF isnotconservative.

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