Question

a particle of mass m is moving in a circle of fixed radius r in such a way that its centripetal acceleration at time t is given by n2 r t2 where n is a constant. the power delivered to the particle by the force acting on it, is

Answer 1

Radial acceleration = v^2/r = n^2 r t^2

So,

v^2 = n^2 t^2 r^2

So

v = nrt

Tangential acceleration (a) = nr

Now,

Power = Force * velocity

= ma * v

= m(nr)(nrt)

= mn^2r^2 t

Hope this helps you !

Answer 2

The power delivered to the particle by the force acting on it is P = m.k^2 r^ 2 t.

Explanation:

Centripetal acceleration:

ac ​ = k^ 2  rt^2

where:

ac  =  v ^2/r

v^2 /r = k^ 2  rt^2

v = k.r.t

Tangential acceleration.

at  =  dt  / dv  = kr

Tangential force acting on the particle.

F = mat  = m.k.r

Power delivered

P =  F .  v = F.vcosθ

P = Fv = (mkr) × krt

θ = 0°

P = m.k^2 r^ 2 t

Thus the power delivered to the particle by the force acting on it is P = m.k^2 r^ 2 t.

Also learn more

A electric motor takes 5 ampere from a 220 volts line. determine the power of the motor and the energy consumed in 2 hour ?

https://brainly.in/question/3830583

 

​