A massless spring of constant 79 N/m is fixed on the left end of a level track.

Question

A massless spring of constant 79 N/m is fixed on the left end of a level track. A block of mass 0.7 kg is pressed against he spring and compresses the spring a distance 'd', in METERS. The block, initially at rest, is released and travel towards a circular loop-the-loop of radius 1.6 m. The entire track is frictionless except the 2.5 m between points 'A' and 'B'. The coefficient of friction between 'A' and 'B' is 0.32. Determine the minimum compressed distance 'd' such that the block arrives at point 'C' such that it's on the verge of falling. Hint: Normal force at 'C' if the block is on the verge of falling.

Explanation / Answer

The minimum compressed distance 'd' which will be given as :

using work-energy theorem, we have

Einitial = Efinal + Wk

(K.E + P.Egravity + P.Espring) = (K.E + P.Egravity + P.Espring) + Wk

(0 J) + (0 J) + (1/2) k d2 = (0 J) + m g h + (0 J) + uk m g x

(0.5) (79 N/m) d2 = (0.7 kg) (9.8 m/s2) [(1.6 m) + (1.6 m)] + (0.32) (0.7 kg) (9.8 m/s2) (2.5 m)

(39.5 N/m) d2 = [(21.952 J) + (5.488 J)]

d = sqrt [(27.4 J) / (39.5 N/m)]

d = sqrt (0.6936)

d = 0.832 m

converting m into cm -

d = 83.2 cm

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