spring problem?

Question

A 0.2 kg mass is attached to a spring k = 10 N/m) and hangs vertically near the earth's surface (g = 9.81 m/s2 ). The mass makes contact with a wall as it moves vertically and a constant frictional force of magnitude 5N acts on the mass as it moves.

a) Calculate the amount of work required to pull the spring down by 1 m.
b) Calculate the speed of the mass as it passes through the equilibrium position after being pulled down by 1 m.

Answer 1

assuming the spring starts in equilibrium
10*y0=0.2*9.81
y0=0.1962 m
the energy in the spring at that point is
.5*10*0.1962^2
0.1924722 J

a) The work will be the gain in energy of the spring + the work done by friction less the loss of potential energy
.5*10*1.1924722^2-0.1924722+
5*1-0.2*9.81*1
9.96 J

b) The KE of the mass .5*m*v^2 will be the recovered energy of the spring (all of it) less the gain in PE less the work done by friction

.5*10*1.1924722^2-0.1924722-5-1.*0.2*9.81

This is negative, it never makes it back, which makes sense because of the energy lost to friction.

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