A 4.0 kg block at rest on a tabletopis attached to a horizontal spring having co

Question

A 4.0 kg block at rest on a tabletopis attached to a horizontal spring having constant 19.6 N/m as inFigure P13.12. The spring is initially unstretched. A constant 20 Nhorizontal force is applied to the object, causing the spring tostretch. (a) Determine the speed of the block after ithas moved 0.200 m from equilibrium ifthe surface between the block and tabletop is frictionless.


(b) Answer part (a) if the coefficient of kinetic friction betweenblock and tabletop is 0.200.
m/s (a) Determine the speed of the block after ithas moved 0.200 m from equilibrium ifthe surface between the block and tabletop is frictionless.


(b) Answer part (a) if the coefficient of kinetic friction betweenblock and tabletop is 0.200.
m/s

Explanation / Answer

total work done = final kinetic energy . work of applied force - work done byfriction - work done by spring = (1/2) mv2 .     20 *0.200      -           0                        - (1/2) *19.6 * 0.2002   = (1/2) *4.00 * v2 .            v =   1.343 m/s . Now for part b, the only thing different is work byfriction: .        20 *0.200    -     0.200*4.00*9.80*0.200     - (1/2) *19.6 * 0.2002   = (1/2) *4.00 * v2   .       v = 1.010   m/s .            v =   1.343 m/s . Now for part b, the only thing different is work byfriction: .        20 *0.200    -     0.200*4.00*9.80*0.200     - (1/2) *19.6 * 0.2002   = (1/2) *4.00 * v2   .       v = 1.010   m/s

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