A block of mass m = 2.80 kg slides along a horizontal table with speed v0 = 3.00

Question

A block of mass m = 2.80 kg slides along a horizontal table with speed v0 = 3.00 m/s. At x = 0 it hits a spring with spring constant k = 20.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by ? = 0.100. How far did the spring compress when the block first momentarily comes to rest?

Explanation / Answer

from conservation of energy; total initial energy = total final energy + losses => K.E. = potential energy stored in spring + energy lost in friction => 0.5*m*v^2 = 0.5*k*x^2 + u*mg*x => 0.5*2.8*3^2 = 0.5*20*x^2 + 0.1*2.8*9.8*x => 10*x^2 + 2.744*x - 12.6 = 0 => x = 0.994 m

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