The system is released from rest with no slack in the cable and with the spring

Question

The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distanced s traveled by the 16-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 5.5 kg. Assume no mechanical interference.

The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distanced s traveled by the 16-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 5.5 kg. Assume no mechanical interference

Explanation / Answer

let the distance travelled be d.

then conserving the energy:

energy released by 16 kg when travelling down =energy gained by m in travelling up + enery stored in stretched spring

then 16*9.8*d*sin(30)=m*9.8*d+0.5*126*d^2

a)m=0

d=1.2444 m

b)if m=5.5kg

then d=0.3889 m

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