Question Details: the horizontal surface on which the block slides is frictionle

Question

Question Details: the horizontal surface on which the block slides is frictionless.the speed of the block before it touches the spring is 6.5 m/s (a)how far will the spring compress to bring the block momentarialy torest (maximum compression)? (b) how muuch work does the spring doon the block to bring it to rest? (c) how fast is the block movingat the instant the spring has been compressed 4.0 cm?
Note: k=2.2 kN/m and m=2.0 kg Question Details: Question Details: the horizontal surface on which the block slides is frictionless.the speed of the block before it touches the spring is 6.5 m/s (a)how far will the spring compress to bring the block momentarialy torest (maximum compression)? (b) how muuch work does the spring doon the block to bring it to rest? (c) how fast is the block movingat the instant the spring has been compressed 4.0 cm?
Note: k=2.2 kN/m and m=2.0 kg

Explanation / Answer

kinetic energy just before the block touches thespring=(1/2)*m*v2=(1/2)*2*6.52=42.25 J let the spring is compressed by x m elastic potential energy when the spring is compressed by xm=(1/2)*k*x2=(1/2)*2.2*103*x2 according to conservation of energy (1/2)*2.2*103*x2=42.25 x=0.2 m work done by the spring to bring it to rest=change in kineticenergy of the block                                                               =42.25-0                                                               =42.25 J let the velocity of the block when the spring was compressed by0.04m =v kinetic energy of the block=(1/2)*2*v2=v2 elastic potentialenergy=(1/2)*2.2*103*0.042=1.76 v2=1.76 v=1.33 m/s

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