vidit g asked in Science & MathematicsPhysics · 10 years ago

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)

Relevance
• 10 years ago

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