(a) Can a particle moving with instantaneous speed 7.00 m/s on a path with radiu

Question

(a) Can a particle moving with instantaneous speed 7.00 m/s on a path with radius of curvature 4.00 m have an acceleration of magnitude 24.00 m/s2?

24.00 m/s2? (a) Can a particle moving with instantaneous speed 7.00 m/s on a path with radius m ave an acceleration of magnitude of curvature 4.00 Yes No If the answer is yes, explain how it can happen; if the answer is no, explain why not. (b) Can it have an acceleration of magnitude 10.00 m/s2? Yes No If the answer is yes, explain how it can happen; if the answer is no, explain why not.

Explanation / Answer

Part a

Instantaneous speed of particle (v)=7.00 m/s

Radius of curvature (r)=4.00 m

Magnitude of acceleration (a)=24.00 m/s2

Radial acceleration (ar)=v2/r

            ar=v2/r=72/4 =49/4 m/s2

            ar= 49/4 m/s2

magnitude of total acceleration is

            a=( ar2 + at2)1/2        ……..(1)                       where at =tangential acceleration.

            24=( (49/4)2 + at2)1/2

            at=20.64 m/s2

so, particle can have acceleration of magnitude 24.00 m/s2 if it has tangential acceleration 20.64 m/s2.

Part b

Magnitude of acceleration (a)=10.00 m/s2

From ……..(1)

            a=( ar2 + at2)1/2        

            10= ((49/4)2 + at2)1/2

            at=(-50.0625)1/2   m/s2

which is imaginary number, so acceleration can’t have magnitude 10 m/s2

           

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