One end of a horizontal spring with force constant 130.0 N/m is attached to a ve

Question

One end of a horizontal spring with force constant 130.0 N/m is attached to a vertical wall. A 4.00-kg block sittingon the floor is placed against the spring. The coefficient of kinetic friction between the block and the floor is uk = 0.400. You apply a constant force F is directed toward the wall. F has magnitude of 82.0 N and is directed toward the wall. At the instant that the spring is compressed 80.0 cm, what are (a) the speed of the block, and (b) the magnitude and direction of the block’s acceleration?

Explanation / Answer

a) Use equation

KEf = EPEi - Wfrc

1/2mvf^2 = 1/2kx^2 - kmgd

1/2*4.0*vf^2 = 1/2*130*0.8^2 – 0.4*4.0*9.8*0.8   => vf= 3.8 m/s

b) vf^2 = vi^2 +2ad

3.8 =0^2 +2*a*0.8    => a= 2.8 m/s^2

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