physics question work power energy please help... please show the working?

Q1. a particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a is varying with time as a=(k^2)r(t^2) where k is constant. the power delivered to the particle by the forces acting on it is? (ans m(k^2)(r^2)t)

Q2. A body is moving along a straight line by a machine delivering constant power. the distance moved by the body in time t is proportional to ? (ans. t^3/2)

1 Answer

Relevance
  • 10 years ago
    Favorite Answer

    Q1

    a=(k^2)r(t^2)

    using F=ma

    F/m =(k^2)r(t^2)

    F=m(k^2)r(t^2)

    E= F x r (Energy=force x distance)

    F=E/r

    So E/r= m(k^2)r(t^2)

    E=m(k^2)(r^2)(t^2)

    Power =Energy/time =E/t

    Therefore P=m(k^2)(r^2)t

    Q2

    distance travelled,s = ut +1/2a(t^2) where u=initial velocity, a =acceleration, t=time

    Assuming u= 0

    s=1/2a(t^2)

    F=ma

    F = power/velocity

    P/v =ma , but P and m are constant so;

    1/v is proportional to a

    v =s/t

    1/v =t/s

    t/s proportional to a

    Substitute t/s for a in s=1/2a(t^2)

    s is proportional to (t/s) *(t^2)

    s is proportional to (t^3)/s

    so s^2 is proportional to t^3

    and s is proportional to t^3/2

    • Login to reply the answers
Still have questions? Get your answers by asking now.