IIT JEE , AIEEE Forum - Physics , Mechanics

twinkle_star

a particle is moving along a horizontal circle such that its total power varies with time as

p = k²rt² , r = radius of circle , find total acc. of particle as a function of time?

MUDIT

I REALLY DON'T KNOW IF THIS IS CORRECT BUT HAVE A LOOK AT IT
P=F x v WHERE P IS THE POWER, F IS THE FORCE AND v IS THE VELOCITY
BECAUSE THE PARTICLE IS MOVING IN A CIRCULAR PATH AT ANY TIME t F=mv^2/r
P=Fv=mv^3/r=(k^2)r(t^2)
NOW REARRANGE THE TERMS WRITING v IN TERMS OF THE k, r,t and m
NOW DEFFRENTIATE BOTH SIDES WITH RESPECT TO t
dv/dt=a=ans

twinkle_star

what is da final ans i want to confrm

shashankparewar

but mv^2/r is only the normal accn what about tangential accn

karthik2007

Isn't the mass of the body given? Anyway:

At t = 0, P = 0, note, hence we can write

Pt = 1/2mv² at any instant (WE theorem)

Or k²rt³ = 1/2mv²

or mv²/r = 2k²t³

Also, we have v =

2k²rt³/m

Find dv/dt.

Then use ma_resultant =

(mv²/r)² + (mdv/dt)²

thus find a

raulrag009

The answer should be

a=k

t[4/9k²t⁵ + 3/2r]

hsbhatt

Since the particle moves in the horizontal plane, the work W done by the external forces is completely converted to the K.E. (E) of the particle.

Hence P = dW/dt = dE/Dt

Thus dE/dt = k²rt² => E = k²rt³/3 (we'll ignore the constant)

Hence 1/2mv² = k²rt³/3.

Thus mv²/r = 2k²t³/3 ...... a₁ = centripetal acceleration

v =

2k²rt³/m and hence dv/dt = a₂. = tangential acceleration.

The resultant a =

a₁²+a₂²

chimanshu_007

karthik is right acc to me

in circular motion , we knw that

P = F_tangential . V

k²rt² = m dv/dt.V

integrate both sides

V comes out to be (2k²rt²/3m)^1/2

a_net = ( a_centrepital² + a_tangential²)^1/2

= [ (V²/r)² + (dv/dt)²]^1/2

so u can solve

anchitsaini

P=Ft * v         [Ft=tangential force]
k^2*rt^2=mvdv/dt
therefore v^2=2k^2*rt^3/3m

accn tangential =dv/dt=underroot(3k^2rt/2m)
accn centripetal=v^2/r=(2*k^2*t^3)/3m
a total=underroot[(3ksquare*r*t/2m)+ (4k^4*t^6/9m^2)]
         =underroot[ksquare*t/m * (3r/2 + 4ksquare*t^5/9m)]

i am almost sure the answer is wrong and hence would hope for some help!!

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