Elasticity Mechanics Problem
Anyone got any hints or tips for this question? Really stuck! Many thanks!
Original post by marinacalder
Anyone got any hints or tips for this question? Really stuck! Many thanks!
Original post by marinacalder
...
What can/have you done/tried? Where are you stuck?
Original post by ghostwalker
What can/have you done/tried? Where are you stuck?
Unsure whether I need the radius? and wondered since the string is inelastic that it would be 2m vertically... but that makes no sense..
Original post by marinacalder
Unsure whether I need the radius? and wondered since the string is inelastic that it would be 2m vertically... but that makes no sense..
Yes, you will need the radius, since you're told the particle will move in a horizontal circle. It pays to read the question carefully - there is very little redundancy in maths A-level questions.
Original post by ghostwalker
Yes, you will need the radius, since you're told the particle will move in a horizontal circle. It pays to read the question carefully - there is very little redundancy in maths A-level questions.
Great, so how how do i find it?
Sorry if these are stupid sounding questions
Original post by marinacalder
Great, so how how do i find it?
Sorry if these are stupid sounding questions
Sorry if these are stupid sounding questions
Just express it in terms of values you know or are looking for.
Original post by marinacalder
Centrip F = mrw^2 => Tsin@ = 270r
Resolve Vert: Tcos@ = 30g
So: tan@ = 9r/g => r = (gtan@)/9
From the triangle @, r, 2:
sin@ = r/2 = gtan@/18
=> 1 = g/(18cos@)
=> cos@ = g/18
=> @ = 57°
For the 2nd bit: T = (10^4.x)/2 => x = 2T/10^4
Same eqs with T & @ apply => r = (gtan@)/9
(but these quantities will now be different)
Note: T = 30g/cos@.
From the triangle @, r, 2 + (2T/10^4):
sin@ = (g/9)tan@/[2 + 60g/(10^4.cos@)]
=> 2 + 60g/(10^4.cos@) = g/(9cos@)
=> 2 = (g/cos@)(1/9 - 60/10^4)
=> cos@ = (g/2)(1/9 - 60/10^4)
=> @ = 59°.
So a small ext means a slightly bigger angle (and radius) to allow circ motion at w = 3.
(edited 6 years ago)
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