It consists of a block of mass attached to a spring of negligible mass and force

Question

It consists of a block of mass attached to a spring of negligible mass and force constant . The block is free to move on a frictionless horizontal surface, while the left end of the spring is held fixed. When the spring is neither compressed nor stretched, the block is in equilibrium. If the spring is stretched, the block is displaced to the right and when it is released, a force acts on it to pull it back toward equilibrium. By the time the block has returned to the equilibrium position, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, where it is again pulled back toward equilibrium. As a result, the block moves back and forth from one side of the equilibrium position to the other, undergoing oscillations. Since we are ignoring friction (a good approximation to many cases), the mechanical energy of the system is conserved and the oscillations repeat themselves over and over. The motion that we have just described is typical of most systems when they are displaced from equilibrium and experience a restoring force that tends to bring them back to their equilibrium position. The resulting oscillations take the name of periodic motion. An important example of periodic motion is simple harmonic motion (SHM) and we will use the mass-spring system described here to introduce some of its properties.

Explanation / Answer

Knowns: m = 2.00kg k = 400 N/m x = 0.220 m Energy of the compressed spring: E = .5*k*x^2 E = .5*400 N/m * (.220m)^2 E = 9.68 J Conservation of Energy, since surface is frictionless Horizontal surface (all spring energy is converted into kinetic energy) E = .5*m*v^2 v = sqrt(2E/m) v = sqrt(2*9.68J/2kg) v= 3.11 m/s Incline surface, all kinetic energy is converted to potential energy E = mgh h = E/(mg) h = 9.68 J/(2kg *9.8 m/s^2) h = 0.494m (vertical distance) along the incline is distance = h/sin(37) distance up the incline = 0.821 m

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