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I need some help with my spring physics questions?
A block of mass m is attached to the end of a spring (spring stiffness constant k), The mass is given an initial displacement x0 from equilibrium, and an initial speed v0.
Ignoring friction and the mass of the spring, use energy methods to find its maximum speed in terms of the given quantities.
Find its maximum stretch from equilibrium in terms of the given quantities.
Express your answer in terms of the variables m, v0, x0, and k.
1 Answer
- Andrew SmithLv 72 years agoFavorite Answer
Original energy = 1/2 k xo^2 + 1/2 m vo^2
At maximum stretch all this goes into potential
1/2 k x^2 = 1/2 k xo^2 + 1/2 m vo^2
At maximum speed all the energy is in kinetic
1/2 m v^2 =1/2 k xo^2 + 1/2 m vo^2
Just rewrite each of these in the form of an expression for the given quantities
v= sqrt( kx0^2/m + vo^2)
so the EXPRESSION for v is sqrt( kx0^2/m + vo^2)
in the same way the EXPRESSION for x is sqrt( xo^2 + m vo^2 / k )
