show work please A spring of constant 23 Ncm is compressed a

show work please

A spring of constant 23 N/cm is compressed a distance 7 cm by a(n) 0.4 kg mass, then released. It skids over a frictional surface of length 2.5 m with coefficient of friction 0.15, then compresses the second spring of constant 4 N/cm. The acceleration of gravity is 9.8 m/s^2. How far will the second spring compress in order to bring the mass to a stop?

Solution

Work energy theoram:

Ui = Uf + Wf

Wf = umgL = 0.15*0.4*9.81*2.5 = 1.471 J

Ui = 0.5*k1*x1^2 = 0.5*2300*0.07^2 = 5.635 J

Ui = 0.5*k*x2^2 + Wf

x2 = sqrt(2*(Ui -Wf)/k2) = sqrt(2*(5.635 - 1.471)/400)

x2 = 0.1442 m = 14.42 cm