wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as wn=at2, where a 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 after the beginning of motion.

Open in App
Solution

We have wn=ν2R=at2, or ν=aRt,
t is defined to start from the beginning of motion from rest
So, wt=dνdt=aR
Instantaneous power P=F.ν=m(wt^ut+wn^ut).(aRt^ut)
(where ^ut and ^ut are unit vectors along the direction of tangent (velocity) and normal respectively)
So, P=mwtaRt=maRt
Hence the sought average power
<P>=t0Pdtt0dt=t0maRtdtt
Hence <P>=maRt22t=maRt2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circular Permutations
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon