Potential energy of a spring
As shown above, a red ball with a mass of
kg is fixed on the right end of a spring with its left end fixed on the wall. The above right shows the potential energy
of the spring as a function of the extension, denoted
of the spring (the distance between Point
and Point
in the left bottom picture). Which of the following statements is correct?
a) The spring constant of the spring is N/m.
b) N of force is needed to extend the spring by cm.
c) If we extend the spring by cm and let it go, the speed of the red ball at Point is m/s.
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1 solution
Option c) is obviously true, since at point O the whole potential energy of 20 cm extension, that is given by the graph to be 16 J will be completely converted to kinetic energy 0.5*Mv^2. M is given, solve for v and it comes out to be 4 m/s. Using U=0.5kx^2, put x=o.1 m (for 10 cm= 0.1m) and put U=4, k comes out to be 800 N/m. Put thin in the formula F=kx and put x= 0.1 m, then F matches the value of 80 N. Thus option b) is also correct.