Physics, asked by Aakrit6949, 9 months ago

A particle of mass m starts moving in a circular path of canstant radiur r , such that iss centripetal accelerationa_(c) is varying with time a=t as (a_(c)=k^(2)r//t) , where K is a contant. What is the power delivered to the particle by the force acting on it ?

Answers

Answered by RitaNarine
0

Given:

A particle of mass m.

Circular path of constant radius r

Centripetal acceleration, a(t) = k² r / t , where K is a contant

To Find:

The power delivered to the particle by the force acting on it.

Solution:

We know,

  • Centripetal acceleration = V²/r = k²r/t
  • V² = k²r²/t
  • V  = k r / √t

Tangential acceleration is given by dv/dt

Therefore from above V ,

  • dv/dt = -kr/2t^{3/2}

Power delivered = Force x Velocity

Therefore,

  • Power = ma x V
  • Power = m x dv/dt x V
  • Power = m x  -k r/2t^{3/2} x k r / √t
  • Power = \frac{-mk^{2}r^{2}}{2t^{2}}

The power delivered to the particle by the force acting on it is   P =  \frac{-mk^{2}r^{2}}{2t^{2}} W

Answered by mohnishkrishna05
0

Answer:

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