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 ?
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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/2
Power delivered = Force x Velocity
Therefore,
- Power = ma x V
- Power = m x dv/dt x V
- Power = m x -k r/2 x k r / √t
- Power =
The power delivered to the particle by the force acting on it is P = W
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