Calculate the work done on the block by the spring during the motion of the bloc

Question

Calculate the work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its uncompressed length Express your answer using two significant figures Constants A block of ice of mass 3.70 kg is placed against a horizontal spring that has force constant k 190 N/m and is compressed a distance 2.20x10 m The spring is released and accelerates the block along a horizontal surface. You can ignore friction and the mass of the spring -2 Submit Answer PartB What is the speed of the block after it leaves the spring? Express your answer using two significant figures. m/s

Explanation / Answer

Given

mass of ice block is m = 3.70 kg ,

force constant k = 190 N/m

compression in the spring is x = 2.20*10^-2 m

Part A

the stored elastic potential energy will do work on the block

so W = 0.5*k*x^2

W = 0.5*190*(2.20*10^-2)^2 J

W = 0.04598 J

PArt B

the speed of the block when it leaves the spring is

W = 0.5*m*v^2

v^2 = 2*w/m

v = sqrt(2*w/m)

V = sqrt( 2*0.04598/3.7) m/s

V = 0.15765 m/s

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