Saved Bookmarks
| 1. |
A particle of mass m moves along a circle of radius R. Find the modulus of the average vector of the force acting on the particle over the distance equal to a quarter of the circle, if the particle moves (a) uniformly with velocity v, (b) with constant tangential acceleration w_tau, the initial velocity being equal to zero. |
|
Answer» Solution :Let us sketch the diagram for the motion of the particle of mass m along the cirle of RADIUS R and indicate x and y axis, as shown in figure. (a) For the particle, CHANGE in momentum `Deltavecp=mv(-veci)-mv(vecj)` so, `|Deltavecp|=sqrt2mv` and time taken in describing quarter of the CIRCLE, `DELTAT=(piR)/(2v)` Hence, `lt vecF ge(|Deltavecp|)/(Deltat)=(sqrt2mv)/(piR//2v)=(2sqrt2mv^2)/(piR)` (b) In this case `vecp_i=0` and `vecp_f=mw_it(-veci)`, so `|Deltavecp|=mw_tt` Hence, `|lt vecF GT|=(|Deltavecp|)/(t)=mw_t` 
|
|