The particle which moves along the curved path shown in Fig. 3 decelerates at a

Question

The particle which moves along the curved path shown in Fig. 3 decelerates at a rate proportional to the distance measured along the curve, from point O. It passes point O with a speed of 10 m/s and slows down to 8 m's at point A in a distance of 12 m, measured along the curve from O. The magnitude of the total acceleration of the particle is 5 m/s^2 as it passes point A. Determine a) The normal and tangential components of the acceleration at point A. b) The radius of curvature p of the path at A. c) The rectangular components of the acceleration at point A.

Explanation / Answer

a) tangential accleration=(v*v - u*u)/2S=(144-64)/(2*12)=3.33 m/s2

Radial =sqrt(25-3.33*3.33)=3.72 m/s2

b) radial accleration=v*v/r

At A, v=8

So r=17.17 m

c) rectangular component means in x and y direction

We got

Writing tangential accleration in this form

=3.33(0.6i-0.8j)=1.98i-2.64j

Writing radial in rectangular component

3.72(-0.8i-0.6j)=-2.976i-2.232j

Adding both we got

=-0.996i-4.872j

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