IIT JEE , AIEEE Forum - Physics , Mechanics

frenied

An aeroplane moves in a circle in the vertical plane with a velocity varying with its ht. h from the lowermost level as v²=v₀²-2a₀h.If v₀/2 is its velocity at highest point then find its accn. at the point where its velocity becomes vertical.......2 salutes for the correct ans....solution by tomorrow.

shubham_sachdeva

can u attach a dia. qn. is sumwhat confusing....

frenied

sry pal no diag given

frenied

think i missed sumthng earlier....try this now.

shubham_sachdeva

vel. at highest point = Vo/2

so applying energy of conservetion at instance , when it was at highest point & when its velocity is vertical(i.e at R(radius) distance above the lowermost point)

1/2 m . Vo^2/4 + 2mgR = 1/2 m v^2 + mgR. ,where v is velocity at 2nd instance

from above we get

v^2 = Vo^2/4 + 2gR

now putting in eqn. we get

Vo^2/4 + 2gR = Vo^2 - 2aoR ao = Ao

from above we get

Vo^2/R = radial accn. = 8(g - ao)/3

frenied

sry thats incorrect....

khushi210

is it 10ao/3 ??

rabindra8

Horizontal component of velocity is constant in overall it's path and it is V₀/2.

due to height change vertical componet of velocity is change all time in it's path so the resultant velocity is change all time in it's path. velocity becomes vertical at two points and at that point ' a =

{g² + (5V₀²)/(8h) }^1/2

At one point acc is +ve and other point acc is -ve.

this is a good question.

karthik2007

Is the acceleration

=

100a_o²/9 + g²

spideyunlimited

Let max height = H

at max height if velocity is V

V² = v_o² - 2a_oH

H = ( v_o²- V²)/ 2a_o

H = 3 v_o²/ 8 a_o

Velocity will be vertical when h = H/2

v² = v_o² - 2a_o(H/2)

v² = v_o² - 2a_o . (v_o²/ 16 a_o)

v² = v_o² - (v_o²/ 8)

v² = 7 v_o²/ 8

Now use given equation again

v² = v_o² - 2a_oh

a_o = ( v_o² - v² ) / 2h

a_o = ( v_o² - (7 v_o²/ 8) ) / 2h

a_o = ( v_o²/ 8 ) / 2h

a_o = v_o²/ 16 h

karthik2007

Hmm... well I also got all the steps till the velocity, but do you think ao is being asked here? I was under the impression that ao is some crappy constant, though it dimensionally represents acceleration

spideyunlimited

maybe. maybe not. lets see couldnt figure out anything else cos shubham's answer he said was wrong

karthik2007

Hmm... okay lets wait for freined's reply

karthik2007

frenied
... reply please

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