Challenging problem, can u solve it?

Question

The problem goes as follows:


A particle of mass 'm' moves along a circle of radius 'R' with a normal acceleration varying with time as a=k(t^2), where k is a constant. find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first 't' seconds of motion.


I've tried a lot but in vain. can anyone help me solve it? please explain how you solve this kind of problems. i'm a beginner to high school physics.

Answer 1

The normal (centripetal) acceleration of a particle moving along a circular path is always v^2/R where v is the instantaneous (tangential) speed:

a = v^2/R = kt^2

This gives you the value of v as a function of t, and therefore the kinetic energy:

T(t) = (1/2)mv^2 = (1/2)mkRt^2

The instantaneous power is the time derivative of energy:

P(t) = dT/dt = mkRt

The average power over the first t seconds is the energy at time t divided by the elapsed time t:

T(t)/t = (1/2)mkRt

Answer 2

Hi
1. Given data are
mass = M
Radius= r
Velocity = kt^2

Find
Acceleration = V/T
Force = M*A

Answer 3

Since Power= F vector dotted with V vector

and they are 2 orthogonal vectors. F towards center and V tangent at each point. !F!*!V!*Cos(90)=0 for Cosine of 90 degrees is zero.

PS: !F! and !V! stand for lengths of these vectors.

Power(t)=invariant of time= zero

Answer 4

i could try the grey section and refuse to pay the hire, enable them to take you to courtroom and spot what the Justice of the Peace has to assert. If the valuables develop into in that undesirable difficulty and the owner/agent knew this then they does no longer desire to proceed. ensure you have a good number of actual data nevertheless. If in certainty they resign the tenancy settlement they could would desire to provide the courtroom clarification why. i think of you have a good case and that i doubt very plenty in the event that they're going to proceed to litigation. you somewhat would desire to have appeared on the valuables earlier you took it on, yet i can work out you took it in good faith that it develop into and you additionally can state that if it got here to courtroom.